feat: add SC-LDPC chain construction

Implement spatially-coupled LDPC code construction with:
- split_protograph(): split base matrix edges into w components
- build_sc_chain(): build full SC-LDPC H matrix with L positions
- sc_encode(): GF(2) Gaussian elimination encoder for SC chain

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

model/test_sc_ldpc.py

@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Tests for SC-LDPC construction."""
+
+import numpy as np
+import pytest
+import sys
+import os
+
+sys.path.insert(0, os.path.dirname(__file__))
+
+
+class TestSCLDPCConstruction:
+    """Tests for SC-LDPC chain construction."""
+
+    def test_split_preserves_edges(self):
+        """Split B into components, verify sum(B_i >= 0) == (B >= 0) for each position."""
+        from sc_ldpc import split_protograph
+        from ldpc_sim import H_BASE
+        components = split_protograph(H_BASE, w=2, seed=42)
+        assert len(components) == 2
+        # Each edge in B should appear in exactly one component
+        for r in range(H_BASE.shape[0]):
+            for c in range(H_BASE.shape[1]):
+                if H_BASE[r, c] >= 0:
+                    count = sum(1 for comp in components if comp[r, c] >= 0)
+                    assert count == 1, f"Edge ({r},{c}) in {count} components, expected 1"
+                else:
+                    for comp in components:
+                        assert comp[r, c] < 0, f"Edge ({r},{c}) should be absent"
+
+    def test_chain_dimensions(self):
+        """Build chain with L=5, w=2, Z=32. Verify H dimensions."""
+        from sc_ldpc import build_sc_chain
+        from ldpc_sim import H_BASE
+        m_base, n_base = H_BASE.shape
+        L, w, z = 5, 2, 32
+        H_full, components, meta = build_sc_chain(H_BASE, L=L, w=w, z=z, seed=42)
+        expected_rows = L * m_base * z  # 5*7*32 = 1120
+        expected_cols = (L + w - 1) * n_base * z  # 6*8*32 = 1536
+        assert H_full.shape == (expected_rows, expected_cols), (
+            f"Expected ({expected_rows}, {expected_cols}), got {H_full.shape}"
+        )
+
+    def test_chain_has_coupled_structure(self):
+        """Verify non-zero blocks only appear at positions t and t+1 for w=2."""
+        from sc_ldpc import build_sc_chain
+        from ldpc_sim import H_BASE
+        m_base, n_base = H_BASE.shape
+        L, w, z = 5, 2, 32
+        H_full, components, meta = build_sc_chain(H_BASE, L=L, w=w, z=z, seed=42)
+        # For each CN position t, check which VN positions have connections
+        for t in range(L):
+            cn_rows = slice(t * m_base * z, (t + 1) * m_base * z)
+            for v in range(L + w - 1):
+                vn_cols = slice(v * n_base * z, (v + 1) * n_base * z)
+                block = H_full[cn_rows, vn_cols]
+                has_connections = np.any(block != 0)
+                if t <= v <= t + w - 1:
+                    # Should have connections (t connects to t..t+w-1)
+                    assert has_connections, f"CN pos {t} should connect to VN pos {v}"
+                else:
+                    # Should NOT have connections
+                    assert not has_connections, f"CN pos {t} should NOT connect to VN pos {v}"