feat: add windowed SC-LDPC decoder

Implement windowed_decode() for SC-LDPC codes using flooding
min-sum with sliding window of W positions. Supports both
normalized and offset min-sum modes.

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

model/sc_ldpc.py

@@ -15,6 +15,8 @@ import os
 
 sys.path.insert(0, os.path.dirname(__file__))
 
+from ldpc_sim import Q_BITS, Q_MAX, Q_MIN, OFFSET
+
 
 def split_protograph(B, w=2, seed=None):
     """
@@ -210,3 +212,175 @@ def sc_encode(info_bits, H_full, k_total):
         )
 
     return codeword
+
+
+def windowed_decode(llr_q, H_full, L, w, z, n_base, m_base, W=5, max_iter=20,
+                    cn_mode='normalized', alpha=0.75):
+    """
+    Windowed decoding for SC-LDPC codes.
+
+    Decode a sliding window of W positions at a time, fixing decoded positions
+    as the window advances. Uses flooding schedule within each window iteration
+    to avoid message staleness on the expanded binary H matrix.
+
+    Args:
+        llr_q: quantized channel LLRs for entire SC codeword
+        H_full: full SC-LDPC parity check matrix (binary)
+        L: chain length (number of CN positions)
+        w: coupling width
+        z: lifting factor
+        n_base: base matrix columns
+        m_base: base matrix rows
+        W: window size in positions (default 5)
+        max_iter: iterations per window position
+        cn_mode: 'offset' or 'normalized'
+        alpha: scaling factor for normalized mode
+
+    Returns:
+        (decoded_bits, converged, total_iterations)
+    """
+    total_rows, total_cols = H_full.shape
+    n_vn_positions = L + w - 1
+
+    def sat_clip(v):
+        return max(Q_MIN, min(Q_MAX, int(v)))
+
+    def cn_update_row(msgs_in):
+        """Min-sum CN update for a list of incoming VN->CN messages."""
+        dc = len(msgs_in)
+        if dc == 0:
+            return []
+        signs = [1 if m < 0 else 0 for m in msgs_in]
+        mags = [abs(m) for m in msgs_in]
+        sign_xor = sum(signs) % 2
+
+        min1 = Q_MAX
+        min2 = Q_MAX
+        min1_idx = 0
+        for i in range(dc):
+            if mags[i] < min1:
+                min2 = min1
+                min1 = mags[i]
+                min1_idx = i
+            elif mags[i] < min2:
+                min2 = mags[i]
+
+        msgs_out = []
+        for j in range(dc):
+            mag = min2 if j == min1_idx else min1
+            if cn_mode == 'normalized':
+                mag = int(mag * alpha)
+            else:
+                mag = max(0, mag - OFFSET)
+            sgn = sign_xor ^ signs[j]
+            val = -mag if sgn else mag
+            msgs_out.append(val)
+        return msgs_out
+
+    # Precompute CN->VN adjacency: for each row, list of connected column indices
+    cn_neighbors = []
+    for row in range(total_rows):
+        cn_neighbors.append(np.where(H_full[row] == 1)[0].tolist())
+
+    # Precompute VN->CN adjacency: for each column, list of connected row indices
+    vn_neighbors = []
+    for col in range(total_cols):
+        vn_neighbors.append(np.where(H_full[:, col] == 1)[0].tolist())
+
+    # Channel LLRs (fixed, never modified)
+    channel_llr = np.array([int(x) for x in llr_q], dtype=np.int32)
+
+    # CN->VN message memory: msg_mem[(row, col)] = last CN->VN message
+    msg_mem = {}
+    for row in range(total_rows):
+        for col in cn_neighbors[row]:
+            msg_mem[(row, col)] = 0
+
+    # Output array for hard decisions
+    decoded = np.zeros(total_cols, dtype=np.int8)
+    total_iterations = 0
+
+    # Process each target VN position
+    for p in range(n_vn_positions):
+        # Define window CN positions: max(0, p-W+1) to min(p, L-1)
+        cn_pos_start = max(0, p - W + 1)
+        cn_pos_end = min(p, L - 1)
+
+        # Collect all CN rows in the window
+        window_cn_rows = []
+        for cn_pos in range(cn_pos_start, cn_pos_end + 1):
+            row_start = cn_pos * m_base * z
+            row_end = (cn_pos + 1) * m_base * z
+            for r in range(row_start, row_end):
+                window_cn_rows.append(r)
+
+        if len(window_cn_rows) == 0:
+            # No CN rows cover this position; just make hard decisions from channel LLR
+            # plus accumulated CN messages
+            vn_col_start = p * n_base * z
+            vn_col_end = min((p + 1) * n_base * z, total_cols)
+            for c in range(vn_col_start, vn_col_end):
+                belief = int(channel_llr[c])
+                for row in vn_neighbors[c]:
+                    belief += msg_mem[(row, c)]
+                decoded[c] = 1 if belief < 0 else 0
+            continue
+
+        # Collect all VN columns that are touched by the window CN rows
+        window_vn_cols_set = set()
+        for row in window_cn_rows:
+            for col in cn_neighbors[row]:
+                window_vn_cols_set.add(col)
+        window_vn_cols = sorted(window_vn_cols_set)
+
+        # Run max_iter flooding iterations on the window CN rows
+        for it in range(max_iter):
+            # Step 1: Compute beliefs for all VN columns in window
+            # belief[col] = channel_llr[col] + sum of all CN->VN messages to col
+            beliefs = {}
+            for col in window_vn_cols:
+                b = int(channel_llr[col])
+                for row in vn_neighbors[col]:
+                    b += msg_mem[(row, col)]
+                beliefs[col] = sat_clip(b)
+
+            # Step 2: For each CN row in the window, compute VN->CN and CN->VN
+            new_msgs = {}
+            for row in window_cn_rows:
+                cols = cn_neighbors[row]
+                dc = len(cols)
+                if dc == 0:
+                    continue
+
+                # VN->CN messages: belief - old CN->VN message from this row
+                vn_to_cn = []
+                for col in cols:
+                    vn_to_cn.append(sat_clip(beliefs[col] - msg_mem[(row, col)]))
+
+                # CN update
+                cn_to_vn = cn_update_row(vn_to_cn)
+
+                # Store new messages (apply after all rows computed)
+                for ci, col in enumerate(cols):
+                    new_msgs[(row, col)] = cn_to_vn[ci]
+
+            # Step 3: Update message memory
+            for (row, col), val in new_msgs.items():
+                msg_mem[(row, col)] = val
+
+            total_iterations += 1
+
+        # Make hard decisions for VN position p's bits
+        vn_col_start = p * n_base * z
+        vn_col_end = min((p + 1) * n_base * z, total_cols)
+        for c in range(vn_col_start, vn_col_end):
+            belief = int(channel_llr[c])
+            for row in vn_neighbors[c]:
+                belief += msg_mem[(row, c)]
+            decoded[c] = 1 if belief < 0 else 0
+
+    # Check if all decoded bits form a valid codeword
+    syndrome = (H_full @ decoded) % 2
+    converged = np.all(syndrome == 0)
+
+    return decoded, converged, total_iterations