# Frame Sync & Code Analysis Implementation Plan

> **For Claude:** REQUIRED SUB-SKILL: Use superpowers:executing-plans to implement this plan task-by-task.

**Goal:** Build a frame synchronization prototype and four quantitative code analyses to validate design decisions for the LDPC optical decoder (target: 1-2 photons/slot).

**Architecture:** Two new scripts (`frame_sync.py`, `ldpc_analysis.py`) import encoder/decoder/channel from existing `ldpc_sim.py`. Frame sync simulates a continuous stream with unknown offset. Analyses compare rates, matrices, quantization, and Shannon limits. All output summary tables to stdout and save results to `data/`.

**Tech Stack:** Python 3, numpy, scipy (for Poisson PMF and optimization in Shannon gap). pytest for validation tests.

**Key reference files:**
- `model/ldpc_sim.py` — encoder, decoder, channel, syndrome check (DO NOT MODIFY)
- `docs/plans/2026-02-23-frame-sync-and-code-analysis-design.md` — design document

---

### Task 1: Test Harness — Validate Existing Model

**Files:**
- Create: `model/test_ldpc.py`

**Step 1: Write validation tests for existing ldpc_sim.py**

These tests establish a known-good baseline before we build on top.

```python
"""Tests for ldpc_sim.py — validates encoder, decoder, channel, syndrome."""
import numpy as np
import pytest
from ldpc_sim import (
    build_full_h_matrix, ldpc_encode, poisson_channel, quantize_llr,
    decode_layered_min_sum, compute_syndrome_weight, cyclic_shift,
    sat_add_q, sat_sub_q, min_sum_cn_update,
    N, K, M, Z, N_BASE, M_BASE, H_BASE, Q_MAX, Q_MIN,
)


class TestCodeParameters:
    def test_dimensions(self):
        assert N == 256
        assert K == 32
        assert M == 224
        assert Z == 32
        assert N_BASE == 8
        assert M_BASE == 7

    def test_h_base_shape(self):
        assert H_BASE.shape == (M_BASE, N_BASE)

    def test_h_base_info_column_fully_connected(self):
        """Column 0 (info) should connect to all 7 rows."""
        for r in range(M_BASE):
            assert H_BASE[r, 0] >= 0

    def test_h_base_staircase_structure(self):
        """Parity columns should form lower-triangular staircase."""
        for r in range(M_BASE):
            # Diagonal parity column (r+1) should be connected
            assert H_BASE[r, r + 1] >= 0
            # Above diagonal should be -1 (not connected)
            for c in range(r + 2, N_BASE):
                assert H_BASE[r, c] == -1


class TestHMatrix:
    def test_full_h_dimensions(self):
        H = build_full_h_matrix()
        assert H.shape == (M, N)

    def test_full_h_binary(self):
        H = build_full_h_matrix()
        assert set(np.unique(H)).issubset({0, 1})

    def test_full_h_row_weights(self):
        """Each row in a Z-block should have the same weight (QC property)."""
        H = build_full_h_matrix()
        for r in range(M_BASE):
            weights = [H[r * Z + z].sum() for z in range(Z)]
            assert len(set(weights)) == 1, f"Row block {r} has inconsistent weights"

    def test_full_h_rank(self):
        """H should have rank M (full rank) for the code to work."""
        H = build_full_h_matrix()
        rank = np.linalg.matrix_rank(H.astype(float))
        assert rank == M


class TestEncoder:
    def test_encode_all_zeros(self):
        H = build_full_h_matrix()
        info = np.zeros(K, dtype=np.int8)
        codeword = ldpc_encode(info, H)
        assert len(codeword) == N
        assert np.all(codeword == 0)  # all-zero is always a codeword

    def test_encode_satisfies_parity(self):
        H = build_full_h_matrix()
        np.random.seed(123)
        info = np.random.randint(0, 2, K).astype(np.int8)
        codeword = ldpc_encode(info, H)
        syndrome = H @ codeword % 2
        assert np.all(syndrome == 0)

    def test_encode_preserves_info_bits(self):
        H = build_full_h_matrix()
        np.random.seed(456)
        info = np.random.randint(0, 2, K).astype(np.int8)
        codeword = ldpc_encode(info, H)
        assert np.array_equal(codeword[:K], info)

    def test_encode_multiple_random(self):
        """Encode 20 random messages, all must satisfy parity."""
        H = build_full_h_matrix()
        for seed in range(20):
            np.random.seed(seed)
            info = np.random.randint(0, 2, K).astype(np.int8)
            codeword = ldpc_encode(info, H)
            syndrome = H @ codeword % 2
            assert np.all(syndrome == 0), f"Failed for seed {seed}"


class TestSaturatingArithmetic:
    def test_sat_add_normal(self):
        assert sat_add_q(10, 5) == 15

    def test_sat_add_positive_overflow(self):
        assert sat_add_q(Q_MAX, 1) == Q_MAX

    def test_sat_add_negative_overflow(self):
        assert sat_add_q(Q_MIN, -1) == Q_MIN

    def test_sat_sub(self):
        assert sat_sub_q(10, 3) == 7
        assert sat_sub_q(Q_MIN, 1) == Q_MIN


class TestMinSumCN:
    def test_all_positive(self):
        """All positive inputs: output signs should all be positive."""
        msgs = [5, 10, 15]
        out = min_sum_cn_update(msgs, offset=1)
        assert all(o >= 0 for o in out)

    def test_one_negative(self):
        """One negative: that output positive, others negative."""
        msgs = [-5, 10, 15]
        out = min_sum_cn_update(msgs, offset=1)
        assert out[0] >= 0  # extrinsic sign excludes own sign
        assert out[1] <= 0
        assert out[2] <= 0

    def test_magnitude_is_min_of_others(self):
        """Output magnitude = min of OTHER magnitudes - offset."""
        msgs = [3, 10, 20]
        out = min_sum_cn_update(msgs, offset=1)
        # out[0]: min of {10,20} - 1 = 9
        assert abs(out[0]) == 9
        # out[1]: min of {3,20} - 1 = 2
        assert abs(out[1]) == 2
        # out[2]: min of {3,10} - 1 = 2
        assert abs(out[2]) == 2


class TestDecoder:
    def test_decode_noiseless(self):
        """Noiseless channel (huge lambda_s) should decode perfectly."""
        H = build_full_h_matrix()
        np.random.seed(789)
        info = np.random.randint(0, 2, K).astype(np.int8)
        codeword = ldpc_encode(info, H)
        # Noiseless: LLR is just +/- large value
        llr = np.where(codeword == 0, 20.0, -20.0)
        llr_q = quantize_llr(llr)
        decoded, converged, iters, syn_wt = decode_layered_min_sum(llr_q, max_iter=5)
        assert converged
        assert np.array_equal(decoded, info)
        assert iters == 1  # should converge in 1 iteration with perfect input

    def test_decode_high_snr(self):
        """High SNR (lambda_s=10) should decode reliably."""
        H = build_full_h_matrix()
        np.random.seed(101)
        info = np.random.randint(0, 2, K).astype(np.int8)
        codeword = ldpc_encode(info, H)
        llr, _ = poisson_channel(codeword, lam_s=10.0, lam_b=0.1)
        llr_q = quantize_llr(llr)
        decoded, converged, _, _ = decode_layered_min_sum(llr_q)
        assert converged
        assert np.array_equal(decoded, info)


class TestSyndrome:
    def test_valid_codeword_syndrome_zero(self):
        H = build_full_h_matrix()
        np.random.seed(202)
        info = np.random.randint(0, 2, K).astype(np.int8)
        codeword = ldpc_encode(info, H)
        assert compute_syndrome_weight(codeword.tolist()) == 0

    def test_flipped_bit_nonzero_syndrome(self):
        H = build_full_h_matrix()
        info = np.zeros(K, dtype=np.int8)
        codeword = ldpc_encode(info, H)
        corrupted = codeword.copy()
        corrupted[0] ^= 1  # flip one bit
        assert compute_syndrome_weight(corrupted.tolist()) > 0
```

**Step 2: Run tests to verify they pass**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 -m pytest model/test_ldpc.py -v`
Expected: All tests PASS (these test existing working code)

**Step 3: Commit**

```bash
git add model/test_ldpc.py
git commit -m "test: add validation tests for existing LDPC model"
```

---

### Task 2: Frame Sync — Streaming Infrastructure

**Files:**
- Create: `model/frame_sync.py`
- Create: `model/test_frame_sync.py`

**Step 1: Write the test for stream generation and syndrome screening**

```python
"""Tests for frame synchronization."""
import numpy as np
import pytest
from ldpc_sim import (
    build_full_h_matrix, ldpc_encode, poisson_channel, quantize_llr,
    compute_syndrome_weight, N, K, Z,
)
from frame_sync import generate_stream, syndrome_screen


class TestStreamGeneration:
    def test_stream_length(self):
        """Stream should be n_frames * N + offset samples long."""
        H = build_full_h_matrix()
        np.random.seed(42)
        stream_llr, true_offset, info_list = generate_stream(
            H, n_frames=5, lam_s=5.0, lam_b=0.1, offset=10
        )
        assert len(stream_llr) == 5 * N + 10
        assert true_offset == 10
        assert len(info_list) == 5

    def test_stream_zero_offset(self):
        H = build_full_h_matrix()
        np.random.seed(42)
        stream_llr, true_offset, _ = generate_stream(
            H, n_frames=3, lam_s=5.0, lam_b=0.1, offset=0
        )
        assert true_offset == 0
        assert len(stream_llr) == 3 * N

    def test_stream_random_offset(self):
        H = build_full_h_matrix()
        np.random.seed(42)
        stream_llr, true_offset, _ = generate_stream(
            H, n_frames=5, lam_s=5.0, lam_b=0.1, offset=None
        )
        assert 0 <= true_offset < N
        assert len(stream_llr) == 5 * N + true_offset


class TestSyndromeScreen:
    def test_correct_offset_low_syndrome(self):
        """At high SNR, correct offset should have very low syndrome weight."""
        H = build_full_h_matrix()
        np.random.seed(42)
        stream_llr, true_offset, _ = generate_stream(
            H, n_frames=5, lam_s=10.0, lam_b=0.1, offset=37
        )
        scores = syndrome_screen(stream_llr, n_offsets=N)
        # Correct offset should have the lowest (or near-lowest) syndrome
        best_offset = min(scores, key=scores.get)
        assert best_offset == 37

    def test_wrong_offsets_high_syndrome(self):
        """Wrong offsets should have syndrome weight near M/2 ~ 112."""
        H = build_full_h_matrix()
        np.random.seed(42)
        stream_llr, true_offset, _ = generate_stream(
            H, n_frames=5, lam_s=10.0, lam_b=0.1, offset=0
        )
        scores = syndrome_screen(stream_llr, n_offsets=N)
        wrong_scores = [v for k, v in scores.items() if k != 0]
        avg_wrong = np.mean(wrong_scores)
        assert avg_wrong > 80  # should be near 112 for random
```

**Step 2: Run tests to verify they fail**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 -m pytest model/test_frame_sync.py -v`
Expected: FAIL — `frame_sync` module doesn't exist yet

**Step 3: Implement generate_stream and syndrome_screen**

```python
#!/usr/bin/env python3
"""
Frame Synchronization Prototype for LDPC Optical Decoder.

Simulates a continuous photon-counting stream with unknown frame alignment.
Tests acquisition (finding codeword boundaries) and re-sync after loss.

Usage:
    python3 frame_sync.py                  # Quick demo at a few lambda_s
    python3 frame_sync.py --sweep          # Acquisition success vs lambda_s
    python3 frame_sync.py --resync-test    # Re-sync after offset slip
"""
import numpy as np
import argparse
import json
import os
from ldpc_sim import (
    build_full_h_matrix, ldpc_encode, poisson_channel, quantize_llr,
    decode_layered_min_sum, compute_syndrome_weight,
    N, K, M, Z, N_BASE, M_BASE, H_BASE,
)

SCREENING_THRESHOLD = 50  # syndrome weight below this triggers full decode


def generate_stream(H, n_frames=10, lam_s=2.0, lam_b=0.1, offset=None):
    """
    Generate a continuous stream of channel LLRs with unknown frame offset.

    Args:
        H: full parity check matrix
        n_frames: number of codewords to concatenate
        lam_s: signal photons/slot
        lam_b: background photons/slot
        offset: bit offset to insert (None = random 0..N-1)

    Returns:
        stream_llr: continuous LLR stream (float, not quantized)
        true_offset: the actual offset used
        info_list: list of info bit arrays for each frame (ground truth)
    """
    if offset is None:
        offset = np.random.randint(0, N)

    # Generate random prefix LLRs for the offset (noise-only, no codeword)
    # These represent receiving channel output before the first codeword starts
    prefix_llr = np.random.normal(0, 1, offset)  # just noise

    # Generate codewords and their channel outputs
    info_list = []
    codeword_llrs = []
    for _ in range(n_frames):
        info = np.random.randint(0, 2, K).astype(np.int8)
        codeword = ldpc_encode(info, H)
        llr, _ = poisson_channel(codeword, lam_s, lam_b)
        info_list.append(info)
        codeword_llrs.append(llr)

    stream_llr = np.concatenate([prefix_llr] + codeword_llrs)
    return stream_llr, offset, info_list


def syndrome_screen(stream_llr, n_offsets=None):
    """
    Screen all candidate offsets using hard-decision syndrome weight.

    Args:
        stream_llr: continuous LLR stream
        n_offsets: number of offsets to try (default N=256)

    Returns:
        scores: dict mapping offset -> syndrome weight
    """
    if n_offsets is None:
        n_offsets = N

    scores = {}
    for off in range(n_offsets):
        if off + N > len(stream_llr):
            break
        window = stream_llr[off:off + N]
        hard = [0 if v > 0 else 1 for v in window]
        syn_wt = compute_syndrome_weight(hard)
        scores[off] = syn_wt
    return scores


def acquire_sync(stream_llr, max_confirm=2, max_iter=30, verbose=False):
    """
    Acquire frame synchronization from a continuous stream.

    Algorithm:
        1. Syndrome-screen all 256 offsets
        2. For offsets below threshold, run full iterative decode
        3. Confirm by decoding next max_confirm consecutive frames

    Args:
        stream_llr: continuous LLR stream
        max_confirm: number of consecutive frames to confirm sync
        max_iter: decoder max iterations
        verbose: print screening details

    Returns:
        dict with keys:
            locked: bool
            offset: detected offset (or -1)
            offsets_screened: number of offsets tried
            full_decodes: number of full iterative decodes run
            screening_cost: equivalent decode cycles for syndrome screening
    """
    scores = syndrome_screen(stream_llr)
    # Sort by syndrome weight (best candidates first)
    ranked = sorted(scores.items(), key=lambda x: x[1])

    full_decodes = 0
    for off, syn_wt in ranked:
        if syn_wt >= SCREENING_THRESHOLD:
            break  # all remaining offsets are worse

        # Full iterative decode at this offset
        window = stream_llr[off:off + N]
        llr_q = quantize_llr(window)
        decoded, converged, iters, _ = decode_layered_min_sum(llr_q, max_iter)
        full_decodes += 1

        if not converged:
            continue

        # Confirm with consecutive frames
        confirmed = True
        for f in range(1, max_confirm + 1):
            start = off + f * N
            if start + N > len(stream_llr):
                confirmed = False
                break
            win_f = stream_llr[start:start + N]
            llr_q_f = quantize_llr(win_f)
            _, conv_f, _, _ = decode_layered_min_sum(llr_q_f, max_iter)
            full_decodes += 1
            if not conv_f:
                confirmed = False
                break

        if confirmed:
            # Cost model: syndrome screening ~ 1/30 of a full decode each
            screening_cost = len(scores) / 30.0
            return {
                'locked': True,
                'offset': off,
                'offsets_screened': len(scores),
                'full_decodes': full_decodes,
                'screening_cost': screening_cost,
                'total_equiv_decodes': screening_cost + full_decodes,
            }

    return {
        'locked': False,
        'offset': -1,
        'offsets_screened': len(scores),
        'full_decodes': full_decodes,
        'screening_cost': len(scores) / 30.0,
        'total_equiv_decodes': len(scores) / 30.0 + full_decodes,
    }


def resync_test(stream_llr, true_offset, slip_amount, search_radius=16,
                max_iter=30):
    """
    Test re-synchronization after an offset slip.

    Simulates the receiver losing sync by `slip_amount` bits,
    then searching nearby offsets to re-acquire.

    Returns:
        dict with locked, detected offset, cost
    """
    slipped_offset = (true_offset + slip_amount) % N

    # First try nearby offsets (fast re-sync)
    for delta in range(-search_radius, search_radius + 1):
        off = (slipped_offset + delta) % N
        if off + N > len(stream_llr):
            continue
        window = stream_llr[off:off + N]
        hard = [0 if v > 0 else 1 for v in window]
        syn_wt = compute_syndrome_weight(hard)
        if syn_wt < SCREENING_THRESHOLD:
            llr_q = quantize_llr(window)
            _, converged, _, _ = decode_layered_min_sum(llr_q, max_iter)
            if converged:
                return {
                    'locked': True,
                    'offset': off,
                    'slip': slip_amount,
                    'search_radius_used': search_radius,
                    'needed_full_search': False,
                }

    # Fall back to full search
    result = acquire_sync(stream_llr)
    result['slip'] = slip_amount
    result['search_radius_used'] = search_radius
    result['needed_full_search'] = True
    return result


def run_acquisition_sweep(lam_s_values, lam_b=0.1, n_trials=50, n_frames=10):
    """Sweep lambda_s and measure acquisition success rate."""
    H = build_full_h_matrix()
    print(f"{'lam_s':>8s} {'success%':>10s} {'avg_decodes':>12s} "
          f"{'avg_cost':>10s} {'false_lock':>10s}")
    print("-" * 55)

    results = []
    for lam_s in lam_s_values:
        successes = 0
        false_locks = 0
        total_decodes = 0
        total_cost = 0

        for trial in range(n_trials):
            np.random.seed(trial * 1000 + int(lam_s * 100))
            stream, true_off, _ = generate_stream(
                H, n_frames=n_frames, lam_s=lam_s, lam_b=lam_b, offset=None
            )
            result = acquire_sync(stream)

            if result['locked']:
                if result['offset'] == true_off:
                    successes += 1
                else:
                    false_locks += 1
            total_decodes += result['full_decodes']
            total_cost += result['total_equiv_decodes']

        pct = 100 * successes / n_trials
        avg_dec = total_decodes / n_trials
        avg_cost = total_cost / n_trials
        fl_pct = 100 * false_locks / n_trials

        print(f"{lam_s:8.1f} {pct:9.1f}% {avg_dec:12.1f} "
              f"{avg_cost:10.1f} {fl_pct:9.1f}%")
        results.append({
            'lam_s': lam_s, 'success_pct': pct,
            'avg_full_decodes': avg_dec, 'avg_equiv_cost': avg_cost,
            'false_lock_pct': fl_pct,
        })
    return results


def run_resync_sweep(lam_s=5.0, lam_b=0.1, n_trials=20, n_frames=10):
    """Test re-sync at various slip amounts."""
    H = build_full_h_matrix()
    print(f"\nRe-sync test at lam_s={lam_s}")
    print(f"{'slip':>6s} {'success%':>10s} {'full_search%':>12s}")
    print("-" * 32)

    for slip in [1, 2, 4, 8, 16, 32, 64, 128]:
        successes = 0
        full_searches = 0
        for trial in range(n_trials):
            np.random.seed(trial * 100 + slip)
            stream, true_off, _ = generate_stream(
                H, n_frames=n_frames, lam_s=lam_s, lam_b=lam_b, offset=None
            )
            result = resync_test(stream, true_off, slip)
            if result['locked']:
                successes += 1
            if result.get('needed_full_search'):
                full_searches += 1

        print(f"{slip:6d} {100*successes/n_trials:9.1f}% "
              f"{100*full_searches/n_trials:11.1f}%")


def main():
    parser = argparse.ArgumentParser(description='LDPC Frame Sync Prototype')
    parser.add_argument('--sweep', action='store_true',
                        help='Acquisition success rate vs lambda_s')
    parser.add_argument('--resync-test', action='store_true',
                        help='Re-sync after offset slip')
    parser.add_argument('--lam-s', type=float, default=5.0,
                        help='Signal photons/slot (default: 5.0)')
    parser.add_argument('--lam-b', type=float, default=0.1,
                        help='Background photons/slot (default: 0.1)')
    parser.add_argument('--n-trials', type=int, default=50,
                        help='Trials per data point (default: 50)')
    parser.add_argument('--seed', type=int, default=42)
    args = parser.parse_args()

    if args.sweep:
        print("=== Frame Sync Acquisition Sweep ===")
        lam_s_values = [0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0, 7.0, 10.0]
        results = run_acquisition_sweep(lam_s_values, args.lam_b, args.n_trials)
        out_path = os.path.join(os.path.dirname(__file__), '..', 'data',
                                'sync_acquisition_results.json')
        os.makedirs(os.path.dirname(out_path), exist_ok=True)
        with open(out_path, 'w') as f:
            json.dump(results, f, indent=2)
        print(f"\nResults saved to {out_path}")

    elif args.resync_test:
        run_resync_sweep(args.lam_s, args.lam_b, args.n_trials)

    else:
        # Quick demo
        print("=== Frame Sync Demo ===")
        H = build_full_h_matrix()
        np.random.seed(args.seed)
        stream, true_off, infos = generate_stream(
            H, n_frames=10, lam_s=args.lam_s, lam_b=args.lam_b, offset=None
        )
        print(f"Stream: {len(stream)} samples, true offset: {true_off}")
        print(f"Signal: lam_s={args.lam_s}, lam_b={args.lam_b}")

        result = acquire_sync(stream, verbose=True)
        if result['locked']:
            match = "CORRECT" if result['offset'] == true_off else "WRONG"
            print(f"Locked at offset {result['offset']} ({match})")
            print(f"  Screened {result['offsets_screened']} offsets")
            print(f"  Full decodes: {result['full_decodes']}")
            print(f"  Total cost: {result['total_equiv_decodes']:.1f} "
                  f"equiv decodes")
        else:
            print("FAILED to acquire sync")


if __name__ == '__main__':
    main()
```

**Step 4: Run tests to verify they pass**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 -m pytest model/test_frame_sync.py -v`
Expected: All PASS

**Step 5: Run the demo to verify it works end-to-end**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 model/frame_sync.py --lam-s 5.0`
Expected: Should lock at the correct offset

**Step 6: Commit**

```bash
git add model/frame_sync.py model/test_frame_sync.py
git commit -m "feat: add frame synchronization prototype with tests"
```

---

### Task 3: Code Analysis — Rate Comparison

**Files:**
- Create: `model/ldpc_analysis.py`
- Create: `model/test_ldpc_analysis.py`

**Step 1: Write the test for rate sweep**

```python
"""Tests for ldpc_analysis.py."""
import numpy as np
import pytest
from ldpc_analysis import build_ira_staircase, rate_sweep_single


class TestIRAStaircase:
    def test_rate_1_2(self):
        """Rate 1/2: 1x2 base matrix, n=64, k=32."""
        H_base, H_full = build_ira_staircase(m_base=1, z=32)
        assert H_base.shape == (1, 2)
        assert H_full.shape == (32, 64)
        assert np.linalg.matrix_rank(H_full.astype(float)) == 32

    def test_rate_1_4(self):
        """Rate 1/4: 3x4 base matrix, n=128, k=32."""
        H_base, H_full = build_ira_staircase(m_base=3, z=32)
        assert H_base.shape == (3, 4)
        assert H_full.shape == (96, 128)
        assert np.linalg.matrix_rank(H_full.astype(float)) == 96

    def test_rate_1_8_matches_existing(self):
        """Rate 1/8 staircase should produce a valid code."""
        H_base, H_full = build_ira_staircase(m_base=7, z=32)
        assert H_base.shape == (7, 8)
        assert H_full.shape == (224, 256)

    def test_encode_decode_roundtrip(self):
        """Any generated staircase code should encode/decode at high SNR."""
        for m_base in [1, 2, 3, 5]:
            H_base, H_full = build_ira_staircase(m_base=m_base, z=32)
            n_base = m_base + 1
            k = 32
            n = n_base * 32
            np.random.seed(42)
            info = np.random.randint(0, 2, k).astype(np.int8)
            # Use generic IRA encoder
            from ldpc_analysis import ira_encode
            codeword = ira_encode(info, H_base, H_full, z=32)
            syndrome = H_full @ codeword % 2
            assert np.all(syndrome == 0), f"Failed for m_base={m_base}"


class TestRateSweep:
    def test_high_snr_all_rates_decode(self):
        """At very high SNR, all rates should achieve FER=0."""
        for m_base in [1, 3, 7]:
            result = rate_sweep_single(m_base=m_base, z=32, lam_s=20.0,
                                       lam_b=0.1, n_frames=10)
            assert result['fer'] == 0.0, f"m_base={m_base} failed at lam_s=20"
```

**Step 2: Run tests to verify they fail**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 -m pytest model/test_ldpc_analysis.py::TestIRAStaircase -v`
Expected: FAIL — module doesn't exist

**Step 3: Implement build_ira_staircase, ira_encode, and rate_sweep_single**

The key functions:
- `build_ira_staircase(m_base, z)`: Generate an IRA staircase base matrix and expand to full H. Info column connected to all rows, lower-triangular parity with spread shift values.
- `ira_encode(info, H_base, H_full, z)`: Generic IRA encoder that works for any staircase code (sequential parity solve, same algorithm as ldpc_sim.py).
- `rate_sweep_single(m_base, z, lam_s, lam_b, n_frames)`: Run n_frames through encode/channel/decode, return BER/FER.
- `run_rate_sweep(...)`: Full sweep over rates and lambda_s values, print summary table.

```python
#!/usr/bin/env python3
"""
LDPC Code Analysis Tool — Quantitative design validation.

Four analyses:
  --rate-sweep:     Compare code rates (1/2 through 1/8) vs lambda_s
  --matrix-compare: Compare base matrix designs at rate 1/8
  --quant-sweep:    Quantization bits (4-32) impact on FER
  --shannon-gap:    Distance from Poisson channel capacity

Usage:
    python3 ldpc_analysis.py --rate-sweep
    python3 ldpc_analysis.py --matrix-compare
    python3 ldpc_analysis.py --quant-sweep
    python3 ldpc_analysis.py --shannon-gap
    python3 ldpc_analysis.py --all
"""
import numpy as np
import argparse
import json
import os
from ldpc_sim import (
    poisson_channel, quantize_llr, decode_layered_min_sum,
    compute_syndrome_weight, sat_add_q, sat_sub_q, min_sum_cn_update,
    Q_BITS, Q_MAX, Q_MIN, OFFSET,
)


# ============================================================================
# Generic IRA staircase code construction
# ============================================================================

def build_ira_staircase(m_base, z=32):
    """
    Build an IRA (Irregular Repeat-Accumulate) staircase QC-LDPC code.

    Structure:
      - Column 0: info bits, connected to ALL m_base rows (high protection)
      - Columns 1..m_base: parity bits, lower-triangular staircase
      - Each row has 2-3 nonzero entries (sparse)
      - Shift values spread across [0, z-1] to maximize girth

    Args:
        m_base: number of base matrix rows (rate = 1 / (m_base + 1))
        z: lifting factor

    Returns:
        H_base: (m_base, m_base+1) array of shift values (-1 = not connected)
        H_full: (m_base*z, (m_base+1)*z) full binary parity check matrix
    """
    n_base = m_base + 1
    H_base = np.full((m_base, n_base), -1, dtype=np.int16)

    # Info column (col 0): connect to all rows with spread shifts
    for r in range(m_base):
        H_base[r, 0] = (r * z // m_base) % z

    # Staircase parity: row r connects to col r+1 (diagonal)
    # Row 0: col 1 only (besides info)
    # Row r>0: col r and col r+1
    H_base[0, 1] = (5 * z // m_base) % z if m_base > 1 else 0

    for r in range(1, m_base):
        # Sub-diagonal: connect to previous parity column
        H_base[r, r] = (r * 7) % z
        # Diagonal: connect to own parity column
        H_base[r, r + 1] = 0

    # Expand to full binary matrix
    n = n_base * z
    m = m_base * z
    H_full = np.zeros((m, n), dtype=np.int8)
    for r in range(m_base):
        for c in range(n_base):
            shift = int(H_base[r, c])
            if shift < 0:
                continue
            for zz in range(z):
                col_idx = c * z + (zz + shift) % z
                H_full[r * z + zz, col_idx] = 1

    return H_base, H_full


def ira_encode(info, H_base, H_full, z=32):
    """
    Encode using IRA staircase structure (generic, any rate).

    Same algorithm as ldpc_sim.ldpc_encode but works for any staircase.
    """
    m_base = H_base.shape[0]
    n_base = H_base.shape[1]
    k = z

    assert len(info) == k

    def apply_p(x, s):
        return np.roll(x, -int(s))

    def inv_p(y, s):
        return np.roll(y, int(s))

    p = [np.zeros(z, dtype=np.int8) for _ in range(n_base)]

    # Row 0: solve for p[1]
    accum = apply_p(info, H_base[0, 0])
    p[1] = inv_p(accum, H_base[0, 1])

    # Rows 1..m_base-1: solve for p[2]..p[m_base]
    for r in range(1, m_base):
        accum = apply_p(info, H_base[r, 0])
        accum = (accum + apply_p(p[r], H_base[r, r])) % 2
        p[r + 1] = inv_p(accum, H_base[r, r + 1])

    codeword = np.concatenate([info] + [p[c] for c in range(1, n_base)])

    # Verify
    check = H_full @ codeword % 2
    assert np.all(check == 0), f"Encoding failed: syndrome weight = {check.sum()}"

    return codeword


def generic_decode(llr_q, H_base, z=32, max_iter=30, early_term=True,
                   q_bits=Q_BITS):
    """
    Generic layered min-sum decoder for any IRA staircase code.

    Same algorithm as ldpc_sim.decode_layered_min_sum but parameterized.
    """
    m_base = H_base.shape[0]
    n_base = H_base.shape[1]
    n = n_base * z
    k = z
    q_max = 2**(q_bits-1) - 1
    q_min = -(2**(q_bits-1))

    def sat_add(a, b):
        s = int(a) + int(b)
        return max(q_min, min(q_max, s))

    def sat_sub(a, b):
        return sat_add(a, -b)

    beliefs = [int(x) for x in llr_q]
    msg = [[[0]*z for _ in range(n_base)] for _ in range(m_base)]

    for iteration in range(max_iter):
        for row in range(m_base):
            connected = [c for c in range(n_base) if H_base[row, c] >= 0]
            dc = len(connected)

            vn_to_cn = [[0]*z for _ in range(dc)]
            for ci, col in enumerate(connected):
                shift = int(H_base[row, col])
                for zz in range(z):
                    sz = (zz + shift) % z
                    bi = col * z + sz
                    vn_to_cn[ci][zz] = sat_sub(beliefs[bi], msg[row][col][zz])

            cn_to_vn = [[0]*z for _ in range(dc)]
            for zz in range(z):
                cn_in = [vn_to_cn[ci][zz] for ci in range(dc)]
                cn_out = min_sum_cn_update(cn_in)
                for ci in range(dc):
                    cn_to_vn[ci][zz] = cn_out[ci]

            for ci, col in enumerate(connected):
                shift = int(H_base[row, col])
                for zz in range(z):
                    sz = (zz + shift) % z
                    bi = col * z + sz
                    beliefs[bi] = sat_add(vn_to_cn[ci][zz], cn_to_vn[ci][zz])
                    msg[row][col][zz] = cn_to_vn[ci][zz]

        # Syndrome check
        hard = [1 if b < 0 else 0 for b in beliefs]
        syn_wt = 0
        for r in range(m_base):
            for zz in range(z):
                parity = 0
                for c in range(n_base):
                    shift = int(H_base[r, c])
                    if shift < 0:
                        continue
                    sz = (zz + shift) % z
                    bi = c * z + sz
                    parity ^= hard[bi]
                if parity:
                    syn_wt += 1

        if early_term and syn_wt == 0:
            return np.array(hard[:k]), True, iteration + 1, 0

    hard = [1 if b < 0 else 0 for b in beliefs]
    return np.array(hard[:k]), syn_wt == 0, max_iter, syn_wt


def rate_sweep_single(m_base, z=32, lam_s=2.0, lam_b=0.1, n_frames=100,
                      max_iter=30, q_bits=Q_BITS):
    """
    Run FER simulation for a single code rate and lambda_s.

    Returns dict with ber, fer, avg_iter.
    """
    H_base, H_full = build_ira_staircase(m_base, z)
    k = z
    bit_errors = 0
    frame_errors = 0
    total_bits = 0
    total_iter = 0

    for _ in range(n_frames):
        info = np.random.randint(0, 2, k).astype(np.int8)
        codeword = ira_encode(info, H_base, H_full, z)
        llr, _ = poisson_channel(codeword, lam_s, lam_b)

        # Quantize with configurable bits
        q_max = 2**(q_bits-1) - 1
        q_min = -(2**(q_bits-1))
        scale = q_max / 5.0
        llr_q = np.clip(np.round(llr * scale), q_min, q_max).astype(int)

        decoded, converged, iters, _ = generic_decode(
            llr_q, H_base, z, max_iter, q_bits=q_bits
        )
        total_iter += iters
        errs = np.sum(decoded != info)
        bit_errors += errs
        total_bits += k
        if errs > 0:
            frame_errors += 1

    return {
        'rate': f"1/{m_base+1}",
        'rate_val': 1.0 / (m_base + 1),
        'm_base': m_base,
        'lam_s': lam_s,
        'ber': bit_errors / total_bits if total_bits > 0 else 0,
        'fer': frame_errors / n_frames,
        'avg_iter': total_iter / n_frames,
    }


# ============================================================================
# Analysis 1: Rate Comparison
# ============================================================================

def run_rate_sweep(lam_b=0.1, n_frames=500, max_iter=30):
    """Compare code rates across lambda_s range."""
    rates = [
        (1, "1/2"),
        (2, "1/3"),
        (3, "1/4"),
        (5, "1/6"),
        (7, "1/8"),
    ]
    lam_s_values = [0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0, 7.0, 10.0]

    print("=== Rate Comparison: FER vs lambda_s ===")
    print(f"Frames per point: {n_frames}, lam_b={lam_b}, max_iter={max_iter}")
    print()

    # Header
    header = f"{'lam_s':>8s}"
    for _, name in rates:
        header += f" {name:>8s}"
    print(header)
    print("-" * (8 + 9 * len(rates)))

    all_results = []
    for lam_s in lam_s_values:
        row = f"{lam_s:8.1f}"
        for m_base, name in rates:
            np.random.seed(42)
            r = rate_sweep_single(m_base, lam_s=lam_s, lam_b=lam_b,
                                  n_frames=n_frames, max_iter=max_iter)
            row += f" {r['fer']:8.3f}"
            all_results.append(r)
        print(row)

    # Summary: threshold lambda_s for each rate (FER < 10%)
    print("\n--- Threshold lambda_s (FER < 10%) ---")
    for m_base, name in rates:
        rate_results = [r for r in all_results if r['m_base'] == m_base]
        threshold = None
        for r in sorted(rate_results, key=lambda x: x['lam_s']):
            if r['fer'] < 0.10:
                threshold = r['lam_s']
                break
        t_str = f"{threshold:.1f}" if threshold else ">10"
        print(f"  Rate {name}: threshold lam_s = {t_str} photons/slot")

    return all_results


# ============================================================================
# Analysis 2: Base Matrix Comparison
# ============================================================================

def compute_girth(H_base, z):
    """
    Compute girth (shortest cycle) of the Tanner graph.

    Uses BFS from each VN to find shortest cycle.
    """
    m_base = H_base.shape[0]
    n_base = H_base.shape[1]
    n = n_base * z
    m = m_base * z

    # Build adjacency: VN -> list of CN neighbors, CN -> list of VN neighbors
    vn_to_cn = [[] for _ in range(n)]
    cn_to_vn = [[] for _ in range(m)]
    for r in range(m_base):
        for c in range(n_base):
            shift = int(H_base[r, c])
            if shift < 0:
                continue
            for zz in range(z):
                vn = c * z + (zz + shift) % z
                cn = r * z + zz
                vn_to_cn[vn].append(cn)
                cn_to_vn[cn].append(vn)

    min_cycle = float('inf')

    # BFS from a subset of VNs (all VNs for small codes)
    sample_vns = range(min(n, 64))  # sample for speed
    for start_vn in sample_vns:
        # BFS: track (node_type, node_id) with distances
        # node_type: 0=VN, 1=CN
        dist = {}
        parent = {}
        queue = [(0, start_vn, -1, -1)]  # (distance, node, parent_type, parent_id)
        dist[(0, start_vn)] = 0
        parent[(0, start_vn)] = None

        qi = 0
        while qi < len(queue):
            d, node, pt, pid = queue[qi]
            qi += 1
            node_type = 0 if (0, node) in dist and dist[(0, node)] == d else 1

            # Determine actual type
            if qi == 1:
                node_type = 0  # start is VN

            # Get neighbors
            if (0, node) in dist and dist[(0, node)] == d:
                # This is a VN, go to CN neighbors
                for cn in vn_to_cn[node]:
                    if (1, cn) == (pt, pid):
                        continue  # don't go back
                    if (1, cn) in dist:
                        cycle_len = d + 1 + dist[(1, cn)]
                        min_cycle = min(min_cycle, cycle_len)
                    else:
                        dist[(1, cn)] = d + 1
                        queue.append((d + 1, cn, 0, node))
            elif (1, node) in dist and dist[(1, node)] == d:
                # This is a CN, go to VN neighbors
                for vn in cn_to_vn[node]:
                    if (0, vn) == (pt, pid):
                        continue
                    if (0, vn) in dist:
                        cycle_len = d + 1 + dist[(0, vn)]
                        min_cycle = min(min_cycle, cycle_len)
                    else:
                        dist[(0, vn)] = d + 1
                        queue.append((d + 1, vn, 1, node))

            if d > min_cycle:
                break

    return min_cycle if min_cycle < float('inf') else -1


def build_improved_staircase(z=32):
    """
    Improved IRA staircase with better degree distribution.

    Adds extra connections to low-degree columns while keeping
    lower-triangular parity structure for easy encoding.
    Key improvement: col 7 gets extra connection (dv=1 -> dv=2).
    """
    m_base = 7
    n_base = 8
    H_base = np.full((m_base, n_base), -1, dtype=np.int16)

    # Info column (col 0): connect to all rows (same as original)
    H_base[0, 0] =  0
    H_base[1, 0] = 11
    H_base[2, 0] = 17
    H_base[3, 0] = 23
    H_base[4, 0] = 29
    H_base[5, 0] =  3
    H_base[6, 0] =  9

    # Staircase parity (same diagonal structure)
    H_base[0, 1] =  5
    H_base[1, 1] =  3;  H_base[1, 2] =  0
    H_base[2, 2] =  7;  H_base[2, 3] =  0
    H_base[3, 3] = 13;  H_base[3, 4] =  0
    H_base[4, 4] = 19;  H_base[4, 5] =  0
    H_base[5, 5] = 25;  H_base[5, 6] =  0
    H_base[6, 6] = 31;  H_base[6, 7] =  0

    # Improvements: add connections to boost weak columns
    # Col 7 (dv=1 -> dv=2): connect to row 0
    H_base[0, 7] = 15
    # Col 1 currently dv=2, boost to dv=3: connect to row 3
    H_base[3, 1] = 21

    # Expand
    n = n_base * z
    m = m_base * z
    H_full = np.zeros((m, n), dtype=np.int8)
    for r in range(m_base):
        for c in range(n_base):
            shift = int(H_base[r, c])
            if shift < 0:
                continue
            for zz in range(z):
                col_idx = c * z + (zz + shift) % z
                H_full[r * z + zz, col_idx] = 1

    return H_base, H_full


def build_peg_matrix(z=32):
    """
    PEG-constructed base matrix for rate 1/8.

    Progressive Edge Growth: greedily add edges to maximize local girth.
    Target degree distribution: VN degrees [3,2,2,2,2,2,2,2] average ~2.1.
    More uniform than staircase.

    Note: this loses the trivial staircase encoding property.
    Encoding requires solving H*c=0 via back-substitution on the
    parity submatrix, which must still be full-rank.
    """
    m_base = 7
    n_base = 8
    H_base = np.full((m_base, n_base), -1, dtype=np.int16)

    # PEG-like construction: spread edges to maximize girth
    # Col 0 (info): connect to all 7 rows (dv=7, high protection)
    H_base[0, 0] =  0
    H_base[1, 0] = 11
    H_base[2, 0] = 17
    H_base[3, 0] = 23
    H_base[4, 0] = 29
    H_base[5, 0] =  3
    H_base[6, 0] =  9

    # Parity columns: each connected to exactly 2 rows (dv=2)
    # with shifts chosen for maximum girth spread
    # Ensure parity sub-matrix is invertible for encoding
    H_base[0, 1] =  5;  H_base[1, 1] =  3
    H_base[1, 2] =  0;  H_base[2, 2] =  7
    H_base[2, 3] =  0;  H_base[3, 3] = 13
    H_base[3, 4] =  0;  H_base[4, 4] = 19
    H_base[4, 5] =  0;  H_base[5, 5] = 25
    H_base[5, 6] =  0;  H_base[6, 6] = 31
    H_base[6, 7] =  0;  H_base[0, 7] = 15

    # This is actually a ring structure (not strictly lower-triangular)
    # Encoding: need to solve via the ring structure

    # Expand
    n = n_base * z
    m = m_base * z
    H_full = np.zeros((m, n), dtype=np.int8)
    for r in range(m_base):
        for c in range(n_base):
            shift = int(H_base[r, c])
            if shift < 0:
                continue
            for zz in range(z):
                col_idx = c * z + (zz + shift) % z
                H_full[r * z + zz, col_idx] = 1

    return H_base, H_full


def peg_encode(info, H_base, H_full, z=32):
    """
    Encode for PEG matrix using Gaussian elimination on parity submatrix.

    For non-staircase matrices, we solve H_parity * p = H_info * info (mod 2)
    using the full H matrix.
    """
    m_base = H_base.shape[0]
    n_base = H_base.shape[1]
    k = z
    m = m_base * z
    n = n_base * z

    # H = [H_info | H_parity], solve H_parity * p = H_info * info mod 2
    H_info = H_full[:, :k]
    H_parity = H_full[:, k:]

    rhs = H_info @ info % 2

    # Solve via GF(2) Gaussian elimination
    # Augmented matrix [H_parity | rhs]
    aug = np.hstack([H_parity.copy(), rhs.reshape(-1, 1)]).astype(np.int8)
    rows, cols_p = H_parity.shape

    pivot_row = 0
    pivot_cols = []
    for col in range(cols_p):
        # Find pivot
        found = -1
        for r in range(pivot_row, rows):
            if aug[r, col] == 1:
                found = r
                break
        if found == -1:
            continue
        # Swap
        aug[[pivot_row, found]] = aug[[found, pivot_row]]
        pivot_cols.append(col)
        # Eliminate
        for r in range(rows):
            if r != pivot_row and aug[r, col] == 1:
                aug[r] = (aug[r] + aug[pivot_row]) % 2
        pivot_row += 1

    # Back-substitute
    parity = np.zeros(cols_p, dtype=np.int8)
    for i, col in enumerate(pivot_cols):
        parity[col] = aug[i, -1]

    codeword = np.concatenate([info, parity])
    check = H_full @ codeword % 2
    assert np.all(check == 0), f"PEG encoding failed: syn={check.sum()}"
    return codeword


def run_matrix_comparison(lam_b=0.1, n_frames=500, max_iter=30):
    """Compare base matrix designs at rate 1/8."""
    from ldpc_sim import H_BASE as ORIG_H_BASE, build_full_h_matrix, ldpc_encode

    matrices = {
        'Original staircase': (ORIG_H_BASE, build_full_h_matrix(), ldpc_encode),
    }

    # Improved staircase
    imp_base, imp_full = build_improved_staircase()
    # Need a custom encoder since it's not pure staircase anymore
    # Actually it IS still lower-triangular in parity, but with extra
    # connections — we can use the PEG encoder (GF2 solve) for safety
    matrices['Improved staircase'] = (imp_base, imp_full, None)

    # PEG
    peg_base, peg_full = build_peg_matrix()
    matrices['PEG ring'] = (peg_base, peg_full, None)

    z = 32
    lam_s_values = [0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0, 7.0, 10.0]

    print("=== Base Matrix Comparison (Rate 1/8) ===")
    print(f"Frames per point: {n_frames}, lam_b={lam_b}")
    print()

    # Degree distributions and girth
    for name, (H_base, H_full, _) in matrices.items():
        m_base_m = H_base.shape[0]
        n_base_m = H_base.shape[1]
        vn_degrees = []
        for c in range(n_base_m):
            dv = sum(1 for r in range(m_base_m) if H_base[r, c] >= 0)
            vn_degrees.append(dv)
        cn_degrees = []
        for r in range(m_base_m):
            dc = sum(1 for c in range(n_base_m) if H_base[r, c] >= 0)
            cn_degrees.append(dc)
        girth = compute_girth(H_base, z)
        print(f"{name}:")
        print(f"  VN degrees: {vn_degrees}")
        print(f"  CN degrees: {cn_degrees}")
        print(f"  Girth: {girth}")
        rank = np.linalg.matrix_rank(H_full.astype(float))
        print(f"  H rank: {rank} / {H_base.shape[0]*z}")
    print()

    # FER sweep
    header = f"{'lam_s':>8s}"
    for name in matrices:
        short = name[:12]
        header += f" {short:>14s}"
    print(header)
    print("-" * (8 + 15 * len(matrices)))

    all_results = []
    for lam_s in lam_s_values:
        row = f"{lam_s:8.1f}"
        for name, (H_base, H_full, enc_fn) in matrices.items():
            np.random.seed(42)
            k = z
            n = H_base.shape[1] * z
            frame_errors = 0

            for _ in range(n_frames):
                info = np.random.randint(0, 2, k).astype(np.int8)
                if enc_fn is not None:
                    codeword = enc_fn(info, H_full)
                else:
                    codeword = peg_encode(info, H_base, H_full, z)
                llr, _ = poisson_channel(codeword, lam_s, lam_b)
                llr_q = quantize_llr(llr)
                decoded, converged, _, _ = generic_decode(
                    llr_q, H_base, z, max_iter
                )
                if np.any(decoded != info):
                    frame_errors += 1

            fer = frame_errors / n_frames
            row += f" {fer:14.3f}"
            all_results.append({
                'matrix': name, 'lam_s': lam_s, 'fer': fer
            })
        print(row)

    return all_results


# ============================================================================
# Analysis 3: Quantization Sweep
# ============================================================================

def run_quant_sweep(lam_s=None, lam_b=0.1, n_frames=500, max_iter=30):
    """Sweep quantization bits and measure FER impact."""
    from ldpc_sim import H_BASE, build_full_h_matrix, ldpc_encode

    H_base = H_BASE
    H_full = build_full_h_matrix()
    z = 32

    quant_bits = [4, 5, 6, 8, 10, 16]

    # If no lambda_s given, test at a few points
    if lam_s is None:
        lam_s_values = [2.0, 3.0, 5.0]
    else:
        lam_s_values = [lam_s]

    print("=== Quantization Sweep ===")
    print(f"Frames per point: {n_frames}, lam_b={lam_b}")
    print()

    header = f"{'lam_s':>8s}"
    for q in quant_bits:
        header += f" {q:>6d}-bit"
    header += f" {'float':>10s}"
    print(header)
    print("-" * (8 + 10 * (len(quant_bits) + 1)))

    all_results = []
    for ls in lam_s_values:
        row = f"{ls:8.1f}"

        # Fixed quantization levels
        for q in quant_bits:
            np.random.seed(42)
            frame_errors = 0
            for _ in range(n_frames):
                info = np.random.randint(0, 2, z).astype(np.int8)
                codeword = ldpc_encode(info, H_full)
                llr, _ = poisson_channel(codeword, ls, lam_b)

                q_max = 2**(q-1) - 1
                q_min = -(2**(q-1))
                scale = q_max / 5.0
                llr_q = np.clip(np.round(llr * scale), q_min, q_max).astype(int)

                decoded, _, _, _ = generic_decode(
                    llr_q, H_base, z, max_iter, q_bits=q
                )
                if np.any(decoded != info):
                    frame_errors += 1

            fer = frame_errors / n_frames
            row += f" {fer:9.3f}"
            all_results.append({
                'lam_s': ls, 'q_bits': q, 'fer': fer
            })

        # Float (no quantization — use very wide integers to approximate)
        np.random.seed(42)
        frame_errors = 0
        for _ in range(n_frames):
            info = np.random.randint(0, 2, z).astype(np.int8)
            codeword = ldpc_encode(info, H_full)
            llr, _ = poisson_channel(codeword, ls, lam_b)

            # Use 16-bit with high scale for "float-like" precision
            scale = 1000.0
            llr_q = np.clip(np.round(llr * scale), -32768, 32767).astype(int)
            decoded, _, _, _ = generic_decode(
                llr_q, H_base, z, max_iter, q_bits=16
            )
            if np.any(decoded != info):
                frame_errors += 1

        fer = frame_errors / n_frames
        row += f" {fer:9.3f}"
        all_results.append({
            'lam_s': ls, 'q_bits': 'float', 'fer': fer
        })
        print(row)

    return all_results


# ============================================================================
# Analysis 4: Shannon Gap
# ============================================================================

def poisson_channel_capacity(lam_s, lam_b, max_y=50):
    """
    Compute binary-input Poisson channel capacity.

    C = max_p I(X;Y) where X in {0,1}, Y ~ Poisson(x*lam_s + lam_b)

    For OOK with equal priors (p=0.5):
      I(X;Y) = H(Y) - 0.5*H(Y|X=0) - 0.5*H(Y|X=1)
    """
    from scipy.stats import poisson

    def entropy_poisson(lam, max_y):
        """Entropy of Poisson(lam) truncated to [0, max_y]."""
        if lam < 1e-10:
            return 0.0
        pmf = [poisson.pmf(y, lam) for y in range(max_y + 1)]
        total = sum(pmf)
        h = 0.0
        for p in pmf:
            if p > 0:
                h -= p * np.log2(p / total)
        return h

    # H(Y|X=0) and H(Y|X=1)
    h_y_x0 = entropy_poisson(lam_b, max_y)
    h_y_x1 = entropy_poisson(lam_s + lam_b, max_y)

    # Optimize over input probability p
    best_c = 0.0
    for p1_pct in range(0, 101):
        p1 = p1_pct / 100.0
        p0 = 1.0 - p1

        # H(Y) where Y has mixture distribution
        pmf_mix = []
        for y in range(max_y + 1):
            pmf_mix.append(p0 * poisson.pmf(y, lam_b) +
                           p1 * poisson.pmf(y, lam_s + lam_b))
        h_y = 0.0
        for p in pmf_mix:
            if p > 0:
                h_y -= p * np.log2(p)

        c = h_y - p0 * h_y_x0 - p1 * h_y_x1
        best_c = max(best_c, c)

    return best_c


def run_shannon_gap(lam_b=0.1):
    """Compute Shannon limits and compare to decoder thresholds."""
    print("=== Shannon Gap Analysis ===")
    print(f"Binary-input Poisson channel, lam_b={lam_b}")
    print()

    rates = [
        (1, "1/2", 0.5),
        (2, "1/3", 1/3),
        (3, "1/4", 0.25),
        (5, "1/6", 1/6),
        (7, "1/8", 0.125),
    ]

    print(f"{'Rate':>8s} {'Shannon':>10s} {'Capacity':>10s}")
    print(f"{'':>8s} {'lam_s':>10s} {'at limit':>10s}")
    print("-" * 32)

    results = []
    for m_base, name, rate_val in rates:
        # Binary search for minimum lam_s where C >= rate
        lo, hi = 0.01, 50.0
        for _ in range(50):  # bisection
            mid = (lo + hi) / 2.0
            c = poisson_channel_capacity(mid, lam_b)
            if c >= rate_val:
                hi = mid
            else:
                lo = mid
        shannon_lam_s = (lo + hi) / 2.0
        cap_at_limit = poisson_channel_capacity(shannon_lam_s, lam_b)

        print(f"{name:>8s} {shannon_lam_s:10.3f} {cap_at_limit:10.4f}")
        results.append({
            'rate': name, 'rate_val': rate_val,
            'shannon_lam_s': shannon_lam_s,
            'capacity_at_limit': cap_at_limit,
        })

    print()
    print("Shannon limit = minimum lam_s (photons/slot) where")
    print("channel capacity >= code rate. Decoder must operate above this.")
    print()
    print("Compare decoder thresholds (from --rate-sweep) to these limits")
    print("to compute the gap in dB: gap = 10*log10(decoder_threshold / shannon_limit)")

    return results


# ============================================================================
# Main
# ============================================================================

def main():
    parser = argparse.ArgumentParser(description='LDPC Code Analysis')
    parser.add_argument('--rate-sweep', action='store_true',
                        help='Compare code rates vs lambda_s')
    parser.add_argument('--matrix-compare', action='store_true',
                        help='Compare base matrix designs')
    parser.add_argument('--quant-sweep', action='store_true',
                        help='Quantization bits impact')
    parser.add_argument('--shannon-gap', action='store_true',
                        help='Distance from channel capacity')
    parser.add_argument('--all', action='store_true',
                        help='Run all analyses')
    parser.add_argument('--n-frames', type=int, default=500,
                        help='Frames per data point (default: 500)')
    parser.add_argument('--lam-b', type=float, default=0.1,
                        help='Background photons/slot (default: 0.1)')
    parser.add_argument('--seed', type=int, default=42)
    args = parser.parse_args()

    np.random.seed(args.seed)

    results = {}

    if args.rate_sweep or args.all:
        results['rate_sweep'] = run_rate_sweep(args.lam_b, args.n_frames)
        print()

    if args.matrix_compare or args.all:
        results['matrix_compare'] = run_matrix_comparison(
            args.lam_b, args.n_frames
        )
        print()

    if args.quant_sweep or args.all:
        results['quant_sweep'] = run_quant_sweep(
            lam_b=args.lam_b, n_frames=args.n_frames
        )
        print()

    if args.shannon_gap or args.all:
        results['shannon_gap'] = run_shannon_gap(args.lam_b)
        print()

    if results:
        out_path = os.path.join(os.path.dirname(__file__) or '.', '..',
                                'data', 'analysis_results.json')
        os.makedirs(os.path.dirname(out_path), exist_ok=True)
        with open(out_path, 'w') as f:
            json.dump(results, f, indent=2, default=str)
        print(f"Results saved to {out_path}")
    else:
        parser.print_help()


if __name__ == '__main__':
    main()
```

**Step 4: Run tests**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 -m pytest model/test_ldpc_analysis.py -v`
Expected: All PASS

**Step 5: Commit**

```bash
git add model/ldpc_analysis.py model/test_ldpc_analysis.py
git commit -m "feat: add code analysis tool with rate sweep and matrix comparison"
```

---

### Task 4: Run All Analyses and Capture Results

**Step 1: Run rate sweep**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 model/ldpc_analysis.py --rate-sweep --n-frames 200`
Expected: Table showing FER vs lambda_s for each rate. Rate 1/8 should have the lowest threshold.

**Step 2: Run matrix comparison**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 model/ldpc_analysis.py --matrix-compare --n-frames 200`
Expected: Table comparing original vs improved vs PEG matrices.

**Step 3: Run quantization sweep**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 model/ldpc_analysis.py --quant-sweep --n-frames 200`
Expected: FER vs quantization bits table.

**Step 4: Run Shannon gap**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 model/ldpc_analysis.py --shannon-gap`
Expected: Shannon limit lambda_s for each rate.

**Step 5: Run frame sync sweep**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 model/frame_sync.py --sweep --n-trials 20`
Expected: Acquisition success rate vs lambda_s.

**Step 6: Run frame sync re-sync test**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 model/frame_sync.py --resync-test --lam-s 5.0 --n-trials 20`
Expected: Re-sync success at various slip amounts.

**Step 7: Review results, fix any bugs, commit data**

```bash
git add data/
git commit -m "data: add analysis and frame sync simulation results"
```

---

### Task 5: Run Full Test Suite

**Step 1: Run all tests**

Run: `cd /home/cah/r2d2/code/fpga/claude_project/ldpc_optical && python3 -m pytest model/ -v`
Expected: All tests PASS

**Step 2: Final commit**

```bash
git add -A
git commit -m "test: all model tests passing for frame sync and code analysis"
```
