feat: add degree distribution optimizer with exhaustive search

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

model/density_evolution.py

@@ -369,6 +369,149 @@ def compute_threshold_for_profile(vn_degrees, m_base=7, lam_b=0.1, z_pop=50000,
     return compute_threshold(profile, lam_b=lam_b, z_pop=z_pop, tol=tol)
 
 
+# =============================================================================
+# Degree Distribution Optimizer
+# =============================================================================
+
+def enumerate_vn_candidates(m_base=7):
+    """
+    Enumerate all VN degree distributions for parity columns.
+
+    Col 0 is always dv=m_base. Parity cols 1..m_base each have dv in {2, 3, 4}.
+    Returns list of degree vectors (length m_base+1).
+    """
+    from itertools import product
+    candidates = []
+    for combo in product([2, 3, 4], repeat=m_base):
+        degrees = [m_base] + list(combo)
+        candidates.append(degrees)
+    return candidates
+
+
+def filter_by_row_degree(candidates, m_base=7, dc_min=3, dc_max=6):
+    """
+    Filter candidates by row degree constraints.
+
+    For a valid distribution, the total edges must be distributable such that
+    each row has degree in [dc_min, dc_max].
+
+    For our structure: info col contributes 1 edge to each row (m_base total).
+    Parity edges must distribute to give each row dc in [dc_min, dc_max].
+    """
+    filtered = []
+    for degrees in candidates:
+        n_base = len(degrees)
+        # Total parity edges = sum of parity column degrees
+        parity_edges = sum(degrees[1:])
+        # Info col contributes 1 edge per row
+        # So total edges per row = 1 (from info) + parity edges assigned to that row
+        # Total parity edges must be distributable: each row gets (dc - 1) parity edges
+        # where dc_min <= dc <= dc_max
+        # So: m_base * (dc_min - 1) <= parity_edges <= m_base * (dc_max - 1)
+        min_parity = m_base * (dc_min - 1)
+        max_parity = m_base * (dc_max - 1)
+        if min_parity <= parity_edges <= max_parity:
+            filtered.append(degrees)
+    return filtered
+
+
+def coarse_screen(candidates, lam_s_test, lam_b, z_pop, max_iter, m_base=7):
+    """
+    Quick convergence test: run DE at a test point, keep candidates that converge.
+    """
+    survivors = []
+    for degrees in candidates:
+        profile = build_de_profile(degrees, m_base=m_base)
+        converged, error_frac = run_de(
+            profile, lam_s=lam_s_test, lam_b=lam_b,
+            z_pop=z_pop, max_iter=max_iter
+        )
+        if converged:
+            survivors.append(degrees)
+    return survivors
+
+
+def get_unique_distributions(candidates):
+    """
+    Group candidates by sorted parity degree sequence.
+
+    For DE, only the degree distribution matters, not which column has
+    which degree. Returns list of representative degree vectors (one per
+    unique distribution), with parity degrees sorted descending.
+    """
+    seen = set()
+    unique = []
+    for degrees in candidates:
+        # Sort parity degrees descending for canonical form
+        parity_sorted = tuple(sorted(degrees[1:], reverse=True))
+        if parity_sorted not in seen:
+            seen.add(parity_sorted)
+            # Use canonical form: info degree + sorted parity
+            unique.append([degrees[0]] + list(parity_sorted))
+    return unique
+
+
+def optimize_degree_distribution(m_base=7, lam_b=0.1, top_k=10,
+                                  z_pop_coarse=10000, z_pop_fine=50000,
+                                  tol=0.1):
+    """
+    Full optimization pipeline: enumerate, filter, coarse screen, fine threshold.
+
+    Key optimization: for DE, only the degree distribution matters (not column
+    ordering), so we group 2187 candidates into ~36 unique distributions.
+
+    Returns list of (vn_degrees, threshold) sorted by threshold ascending.
+    """
+    print("Step 1: Enumerating candidates...")
+    candidates = enumerate_vn_candidates(m_base=m_base)
+    print(f"  {len(candidates)} total candidates")
+
+    print("Step 2: Filtering by row degree constraints...")
+    filtered = filter_by_row_degree(candidates, m_base=m_base, dc_min=3, dc_max=6)
+    print(f"  {len(filtered)} candidates after filtering")
+
+    print("Step 3: Grouping by unique degree distribution...")
+    unique = get_unique_distributions(filtered)
+    print(f"  {len(unique)} unique distributions")
+
+    print("Step 4: Coarse screening at lam_s=2.0...")
+    survivors = coarse_screen(
+        unique, lam_s_test=2.0, lam_b=lam_b,
+        z_pop=z_pop_coarse, max_iter=50, m_base=m_base
+    )
+    print(f"  {len(survivors)} survivors after coarse screen")
+
+    if not survivors:
+        print("  No survivors at lam_s=2.0, trying lam_s=3.0...")
+        survivors = coarse_screen(
+            unique, lam_s_test=3.0, lam_b=lam_b,
+            z_pop=z_pop_coarse, max_iter=50, m_base=m_base
+        )
+        print(f"  {len(survivors)} survivors at lam_s=3.0")
+
+    if not survivors:
+        print("  No survivors found, returning empty list")
+        return []
+
+    print(f"Step 5: Fine threshold computation for {len(survivors)} survivors...")
+    results = []
+    for i, degrees in enumerate(survivors):
+        profile = build_de_profile(degrees, m_base=m_base)
+        threshold = compute_threshold(profile, lam_b=lam_b, z_pop=z_pop_fine, tol=tol)
+        results.append((degrees, threshold))
+        if (i + 1) % 5 == 0:
+            print(f"  {i+1}/{len(survivors)} done...")
+
+    # Sort by threshold ascending
+    results.sort(key=lambda x: x[1])
+
+    print(f"\nTop-{min(top_k, len(results))} degree distributions:")
+    for i, (degrees, threshold) in enumerate(results[:top_k]):
+        print(f"  #{i+1}: {degrees} -> threshold = {threshold:.2f} photons/slot")
+
+    return results[:top_k]
+
+
 # =============================================================================
 # CLI placeholder (will be extended in later tasks)
 # =============================================================================