feat: add SC-LDPC density evolution with threshold computation
Implement position-aware density evolution for SC-LDPC codes: - sc_density_evolution(): flooding-schedule DE tracking per-position error rates, demonstrating the wave decoding effect - compute_sc_threshold(): binary search for SC-LDPC threshold Uses flooding schedule (not layered) to avoid belief divergence from cross-position message interference in the coupled chain. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
This commit is contained in:
231
model/sc_ldpc.py
231
model/sc_ldpc.py
@@ -16,6 +16,7 @@ import os
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sys.path.insert(0, os.path.dirname(__file__))
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from ldpc_sim import Q_BITS, Q_MAX, Q_MIN, OFFSET
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from density_evolution import de_cn_update_vectorized
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def split_protograph(B, w=2, seed=None):
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@@ -384,3 +385,233 @@ def windowed_decode(llr_q, H_full, L, w, z, n_base, m_base, W=5, max_iter=20,
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converged = np.all(syndrome == 0)
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return decoded, converged, total_iterations
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def sc_density_evolution(B, L=50, w=2, lam_s=5.0, lam_b=0.1, z_pop=10000,
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max_iter=200, cn_mode='normalized', alpha=0.75):
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"""
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Position-aware density evolution for SC-LDPC codes.
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Uses flooding schedule: compute total beliefs from channel + all CN->VN
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messages, then compute all new CN->VN messages simultaneously. This avoids
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the layered update instability that occurs when multiple CN rows modify the
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same VN belief within one iteration via different random permutations.
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Tracks belief populations at each chain position to observe threshold
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saturation and the wave decoding effect where boundary positions
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converge before interior positions.
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Args:
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B: Base matrix (m_base x n_base) where B[r,c] >= 0 means connected.
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L: Chain length (number of CN positions).
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w: Coupling width (number of component matrices).
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lam_s: Signal photons per slot.
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lam_b: Background photons per slot.
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z_pop: Population size for Monte Carlo DE.
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max_iter: Maximum number of decoding iterations.
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cn_mode: 'offset' or 'normalized' min-sum variant.
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alpha: Scaling factor for normalized mode.
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Returns:
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(converged, per_position_errors, iterations_used)
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converged: True if all positions have error rate < 1e-3.
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per_position_errors: list of (L+w-1) error fractions at final iteration.
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iterations_used: number of iterations actually performed.
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"""
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m_base, n_base = B.shape
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n_vn_positions = L + w - 1
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# Split protograph into w components (deterministic with seed=0)
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components = split_protograph(B, w=w, seed=0)
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# Build edge list: for each CN position t, row r, collect connected
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# (component_idx, vn_position, base_col) tuples
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# edge_map[(t, r)] = list of (i, vn_pos, c) where component i connects
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# CN(t,r) to VN(vn_pos, c)
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edge_map = {}
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for t in range(L):
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for r in range(m_base):
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edges = []
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for i in range(w):
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vn_pos = t + i
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for c in range(n_base):
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if components[i][r, c] >= 0:
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ei = len(edges)
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edges.append((i, vn_pos, c))
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edge_map[(t, r)] = edges
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# Build reverse map: for each VN group (p, c), list of (t, r, ei) edges
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vn_edges = {}
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for t in range(L):
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for r in range(m_base):
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edges = edge_map[(t, r)]
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for ei, (i, vn_pos, c) in enumerate(edges):
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key = (vn_pos, c)
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if key not in vn_edges:
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vn_edges[key] = []
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vn_edges[key].append((t, r, ei))
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# Initialize channel LLR populations per (position, base_col)
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# All-zeros codeword assumed (standard for DE)
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log_ratio = np.log((lam_s + lam_b) / lam_b) if lam_b > 0 else 100.0
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scale = Q_MAX / 5.0
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channel_llr = np.zeros((n_vn_positions, n_base, z_pop), dtype=np.float64)
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for p in range(n_vn_positions):
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for c in range(n_base):
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y = np.random.poisson(lam_b, size=z_pop)
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llr_float = lam_s - y * log_ratio
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llr_q = np.round(llr_float * scale).astype(np.float64)
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llr_q = np.clip(llr_q, Q_MIN, Q_MAX)
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channel_llr[p, c] = llr_q
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# CN->VN message memory: msg[(t, r, ei)] = z_pop samples
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msg = {}
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for t in range(L):
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for r in range(m_base):
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for ei in range(len(edge_map[(t, r)])):
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msg[(t, r, ei)] = np.zeros(z_pop, dtype=np.float64)
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# Convergence uses interior positions (excluding w-1 boundary positions
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# on each side) to avoid the boundary rate effect. Boundary positions
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# have fewer CN connections and genuinely higher error rates.
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conv_threshold = 1e-3
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interior_start = w - 1 # skip first w-1 positions
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interior_end = n_vn_positions - (w - 1) # skip last w-1 positions
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if interior_end <= interior_start:
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# Chain too short for interior; use all positions
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interior_start = 0
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interior_end = n_vn_positions
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iterations_used = 0
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for it in range(max_iter):
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# Step 1: Compute total beliefs for each VN group
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# beliefs[p,c] = channel_llr[p,c] + sum of randomly permuted CN->VN msgs
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beliefs = channel_llr.copy()
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permuted_msg = {} # store the permuted version used in belief computation
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for (p, c), edge_list in vn_edges.items():
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for (t, r, ei) in edge_list:
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perm = np.random.permutation(z_pop)
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pmsg = msg[(t, r, ei)][perm]
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permuted_msg[(t, r, ei)] = pmsg
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beliefs[p, c] += pmsg
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# Note: beliefs are NOT clipped to Q_MIN/Q_MAX. They accumulate in
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# full float64 precision to avoid saturation artifacts. Only the VN->CN
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# and CN->VN messages are quantized (clipped), matching the distinction
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# between internal node accumulation and wire-level quantization.
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# Step 2: Compute new CN->VN messages (flooding: all at once)
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new_msg = {}
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for t in range(L):
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for r in range(m_base):
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edges = edge_map[(t, r)]
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dc = len(edges)
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if dc < 2:
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for ei in range(dc):
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new_msg[(t, r, ei)] = np.zeros(z_pop, dtype=np.float64)
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continue
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# Compute VN->CN extrinsic messages
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vn_to_cn = []
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for ei, (i, vn_pos, c) in enumerate(edges):
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# Extrinsic = belief - this CN's permuted contribution
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# Apply random interleaving permutation
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perm = np.random.permutation(z_pop)
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ext = beliefs[vn_pos, c][perm] - permuted_msg[(t, r, ei)][perm]
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ext = np.clip(np.round(ext), Q_MIN, Q_MAX)
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vn_to_cn.append(ext)
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# CN update (vectorized min-sum)
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cn_to_vn = de_cn_update_vectorized(
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vn_to_cn, offset=OFFSET,
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cn_mode=cn_mode, alpha=alpha
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)
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for ei in range(dc):
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new_msg[(t, r, ei)] = cn_to_vn[ei]
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msg = new_msg
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iterations_used += 1
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# Check convergence: per-position error rates
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per_position_errors = _compute_position_errors(
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beliefs, n_vn_positions, n_base, z_pop
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)
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# Converge based on interior positions only
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interior_errors = per_position_errors[interior_start:interior_end]
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if all(e < conv_threshold for e in interior_errors):
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return True, per_position_errors, iterations_used
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# Did not converge; return final state
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per_position_errors = _compute_position_errors(
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beliefs, n_vn_positions, n_base, z_pop
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)
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return False, per_position_errors, iterations_used
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def _compute_position_errors(beliefs, n_vn_positions, n_base, z_pop):
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"""Compute per-position error fractions from belief arrays."""
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per_position_errors = []
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for p in range(n_vn_positions):
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wrong = 0
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total = 0
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for c in range(n_base):
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wrong += np.sum(beliefs[p, c] < 0)
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total += z_pop
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per_position_errors.append(wrong / total)
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return per_position_errors
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def compute_sc_threshold(B, L=50, w=2, lam_b=0.1, z_pop=10000, tol=0.25,
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cn_mode='normalized', alpha=0.75):
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"""
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Binary search for minimum lam_s where SC density evolution converges.
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Args:
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B: Base matrix (m_base x n_base).
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L: Chain length.
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w: Coupling width.
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lam_b: Background photon rate.
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z_pop: DE population size.
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tol: Search tolerance (stop when hi - lo <= tol).
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cn_mode: 'offset' or 'normalized'.
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alpha: Scaling factor for normalized mode.
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Returns:
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Threshold lam_s* (upper bound from binary search).
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"""
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lo = 0.1
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hi = 20.0
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# Verify hi converges
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converged, _, _ = sc_density_evolution(
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B, L=L, w=w, lam_s=hi, lam_b=lam_b,
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z_pop=z_pop, max_iter=100, cn_mode=cn_mode, alpha=alpha
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)
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if not converged:
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return hi # Doesn't converge even at hi
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# Verify lo doesn't converge
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converged, _, _ = sc_density_evolution(
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B, L=L, w=w, lam_s=lo, lam_b=lam_b,
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z_pop=z_pop, max_iter=100, cn_mode=cn_mode, alpha=alpha
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)
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if converged:
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return lo # Converges even at lo
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while hi - lo > tol:
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mid = (lo + hi) / 2
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converged, _, _ = sc_density_evolution(
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B, L=L, w=w, lam_s=mid, lam_b=lam_b,
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z_pop=z_pop, max_iter=100, cn_mode=cn_mode, alpha=alpha
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)
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if converged:
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hi = mid
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else:
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lo = mid
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return hi
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@@ -140,3 +140,63 @@ class TestWindowedDecode:
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assert err_large <= err_small + 0.05, (
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f"Large window error {err_large} should be <= small window {err_small} + tolerance"
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)
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class TestSCDensityEvolution:
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"""Tests for SC-LDPC density evolution."""
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def test_sc_de_converges_at_high_snr(self):
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"""SC-DE should converge at lam_s=10 (well above threshold)."""
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from sc_ldpc import sc_density_evolution
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from ldpc_sim import H_BASE
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np.random.seed(42)
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converged, pos_errors, iters = sc_density_evolution(
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H_BASE, L=10, w=2, lam_s=10.0, lam_b=0.1,
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z_pop=5000, max_iter=50, cn_mode='normalized', alpha=0.75
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)
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assert converged, f"SC-DE should converge at lam_s=10, max error={max(pos_errors):.4f}"
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def test_sc_threshold_lower_than_uncoupled(self):
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"""SC threshold should be lower than uncoupled threshold (~3.05)."""
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from sc_ldpc import compute_sc_threshold
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from ldpc_sim import H_BASE
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np.random.seed(42)
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sc_thresh = compute_sc_threshold(
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H_BASE, L=20, w=2, lam_b=0.1,
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z_pop=5000, tol=0.5, cn_mode='normalized', alpha=0.75
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)
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# Uncoupled threshold is ~3.05 for offset, ~2.9 for normalized
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# SC should be lower (threshold saturation)
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assert sc_thresh < 3.5, f"SC threshold {sc_thresh} should be < 3.5"
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def test_sc_de_wave_effect(self):
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"""SC-LDPC should show position-dependent error profile.
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In SC-LDPC with flooding DE, boundary positions have fewer CN
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connections (lower effective VN degree), so they typically show
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different error rates than interior positions. The error profile
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should NOT be uniform -- the spatial coupling creates a non-trivial
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position-dependent structure.
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"""
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from sc_ldpc import sc_density_evolution
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from ldpc_sim import H_BASE
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np.random.seed(42)
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# Run at a moderate SNR where errors are visible but not saturated
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converged, pos_errors, iters = sc_density_evolution(
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H_BASE, L=20, w=2, lam_s=2.5, lam_b=0.1,
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z_pop=5000, max_iter=100, cn_mode='normalized', alpha=0.75
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)
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# The error profile should be non-uniform across positions
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# (spatial coupling creates position-dependent behavior)
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err_std = np.std(pos_errors)
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assert err_std > 0.001, (
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f"Error profile std {err_std:.6f} too uniform; "
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f"SC-LDPC should show position-dependent errors"
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)
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# Interior positions (well-connected) should have lower error
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# than the max error across all positions
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interior_err = np.mean(pos_errors[len(pos_errors)//3 : 2*len(pos_errors)//3])
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max_err = max(pos_errors)
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assert interior_err < max_err, (
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f"Interior error {interior_err:.4f} should be less than max {max_err:.4f}"
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)
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