FAILURE MAP
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FA-72276 / Error-correcting codes / Open access

Chase combining saturates after every addition · case 01

Retransmissions that disagree strongly are combined with the wrong sign or magnitude.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The running sum is clipped after each transmission, so a later opposite value is measured against the clipped total.

THE FAILURE

The running sum is clipped after each transmission, so a later opposite value is measured against the clipped total.

Unsuccessful approach: Removing saturation entirely overflows the decoder input range.

Case contract

Hybrid-ARQ chase combining. txs are equal-length LLR vectors from successive transmissions (None where a position was not received). Combined LLR = sum of received values, saturated once at the end to [-clip, clip]. Hard decision: positive -> 0, negative -> 1, zero -> None (undecided). Return [combined, hard]; empty or ragged input returns None.

Why this case matters

LTE/5G receivers soft-combine retransmissions before decoding; saturating too early discards information.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import functools
N = 1
observations = []
def solve(txs, clip):
    if not txs or any(len(t) != len(txs[0]) for t in txs):
        return None
    comb = []
    for k in range(len(txs[0])):
        s = functools.reduce(lambda a, v: max(-clip, min(clip, a + v)), [t[k] for t in txs if t[k] is not None], 0)
        comb.append(max(-clip, min(clip, s)))
    hard = [None if c == 0 else (1 if c < 0 else 0) for c in comb]
    return [comb, hard]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...', [[[None, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, None, -9, 5]], 7], [[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]], ['regression [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7]', [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7], [[1, -1, -6], [0, 1, 1]]], ['partial-repair [[[null, -1, -9, null, -3], [8, 8, -9, 8, -6]], 15]', [[[None, -1, -9, None, -3], [8, 8, -9, 8, -6]], 15], [[8, 7, -15, 8, -9], [0, 0, 1, 0, 1]]], ['control [[[2, null], [null, -3], [5, 8]], 10]', [[[2, None], [None, -3], [5, 8]], 10], [[7, 5], [0, 0]]], ['control [[[5, -9]], 15]', [[[5, -9]], 15], [[5, -9], [0, 1]]], ['control [[[-9, -3, 0, -6, 0], [11, 5, -3, 2, 5]], 10]', [[[-9, -3, 0, -6, 0], [11, 5, -3, 2, 5]], 10], [[2, 2, -3, -4, 5], [0, 0, 1, 1, 0]]], ['control [[[-3, -6], [-6, 5]], 15]', [[[-3, -6], [-6, 5]], 15], [[-9, -1], [1, 1]]], ['control [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15]', [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15], [[-9, -2, 5, -1], [1, 1, 0, 1]]]], [['regression [[[20], [20], [-30]], 16]', [[[20], [20], [-30]], 16], [[10], [0]]], ['regression [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...', [[[None, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, None, -9, 5]], 7], [[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]], ['partial-repair [[[8, -9], [2, null]], 7]', [[[8, -9], [2, None]], 7], [[7, -7], [0, 1]]], ['partial-repair [[[11, 8, null], [2, -6, -1], [8, null, -3]], 10]', [[[11, 8, None], [2, -6, -1], [8, None, -3]], 10], [[10, 2, -4], [0, 0, 1]]], ['control [[[5, null]], 7]', [[[5, None]], 7], [[5, 0], [0, None]]], ['control [[[0, -1, -3, -1], [2, null, 11, -3], [0, null, -6, 0]], 15]', [[[0, -1, -3, -1], [2, None, 11, -3], [0, None, -6, 0]], 15], [[2, -1, 2, -4], [0, 1, 0, 1]]], ['control [[[8, -6]], 10]', [[[8, -6]], 10], [[8, -6], [0, 1]]], ['control [[[5, -6, 0]], 10]', [[[5, -6, 0]], 10], [[5, -6, 0], [0, 1, None]]]], [['regression [[[12, -12], [-5, 5]], 10]', [[[12, -12], [-5, 5]], 10], [[7, -7], [0, 1]]], ['regression [[[20], [20], [-30]], 16]', [[[20], [20], [-30]], 16], [[10], [0]]], ['partial-repair [[[null, -1, -9, null, -3], [8, 8, -9, 8, -6]], 15]', [[[None, -1, -9, None, -3], [8, 8, -9, 8, -6]], 15], [[8, 7, -15, 8, -9], [0, 0, 1, 0, 1]]], ['partial-repair [[[-3, 11], [-3, 11], [-6, 5]], 10]', [[[-3, 11], [-3, 11], [-6, 5]], 10], [[-10, 10], [1, 0]]], ['control [[[11, -3, -1, null, -6, 8], [-3, -9, 11, null, -6, null], [null, 5...', [[[11, -3, -1, None, -6, 8], [-3, -9, 11, None, -6, None], [None, 5, -6, -6, 2, 5]], 15], [[8, -7, 4, -6, -10, 13], [0, 1, 0, 1, 1, 0]]], ['control [[[0, 2, -9, -3, -1], [11, -1, -6, null, 0]], 15]', [[[0, 2, -9, -3, -1], [11, -1, -6, None, 0]], 15], [[11, 1, -15, -3, -1], [0, 0, 1, 1, 1]]], ['control [[[-6, null, 8, 2, 8], [-9, 11, null, -3, -1]], 15]', [[[-6, None, 8, 2, 8], [-9, 11, None, -3, -1]], 15], [[-15, 11, 8, -1, 7], [1, 0, 0, 1, 0]]], ['control [[[-1, -6, null, -3], [null, 8, 2, 0]], 7]', [[[-1, -6, None, -3], [None, 8, 2, 0]], 7], [[-1, 2, 2, -3], [1, 0, 0, 1]]]], [['regression [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7]', [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7], [[1, -1, -6], [0, 1, 1]]], ['regression [[[12, -12], [-5, 5]], 10]', [[[12, -12], [-5, 5]], 10], [[7, -7], [0, 1]]], ['partial-repair [[[11, 8, null], [2, -6, -1], [8, null, -3]], 10]', [[[11, 8, None], [2, -6, -1], [8, None, -3]], 10], [[10, 2, -4], [0, 0, 1]]], ['partial-repair [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...', [[[None, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, None, -9, 5]], 7], [[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]], ['control [[], 5]', [[], 5], None], ['control [[[1, 2], [3]], 5]', [[[1, 2], [3]], 5], None], ['control [[[2, null], [null, -3], [5, 8]], 10]', [[[2, None], [None, -3], [5, 8]], 10], [[7, 5], [0, 0]]], ['control [[[5, -9]], 15]', [[[5, -9]], 15], [[5, -9], [0, 1]]]], [['regression [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...', [[[None, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, None, -9, 5]], 7], [[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]], ['regression [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7]', [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7], [[1, -1, -6], [0, 1, 1]]], ['partial-repair [[[-3, 11], [-3, 11], [-6, 5]], 10]', [[[-3, 11], [-3, 11], [-6, 5]], 10], [[-10, 10], [1, 0]]], ['partial-repair [[[8, -9], [2, null]], 7]', [[[8, -9], [2, None]], 7], [[7, -7], [0, 1]]], ['control [[[-3, -6], [-6, 5]], 15]', [[[-3, -6], [-6, 5]], 15], [[-9, -1], [1, 1]]], ['control [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15]', [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15], [[-9, -2, 5, -1], [1, 1, 0, 1]]], ['control [[[5, null]], 7]', [[[5, None]], 7], [[5, 0], [0, None]]], ['control [[[0, -1, -3, -1], [2, null, 11, -3], [0, null, -6, 0]], 15]', [[[0, -1, -3, -1], [2, None, 11, -3], [0, None, -6, 0]], 15], [[2, -1, 2, -4], [0, 1, 0, 1]]]]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...[[-4, 7, -3, 7, -7, 7], [1, 0, 1, 0, 1, 0]][[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]Failed
regression [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7][[4, -2, -6], [0, 1, 1]][[1, -1, -6], [0, 1, 1]]Failed
partial-repair [[[null, -1, -9, null, -3], [8, 8, -9, 8, -6]], 15][[8, 7, -15, 8, -9], [0, 0, 1, 0, 1]][[8, 7, -15, 8, -9], [0, 0, 1, 0, 1]]Passed
control [[[2, null], [null, -3], [5, 8]], 10][[7, 5], [0, 0]][[7, 5], [0, 0]]Passed
control [[[5, -9]], 15][[5, -9], [0, 1]][[5, -9], [0, 1]]Passed
control [[[-9, -3, 0, -6, 0], [11, 5, -3, 2, 5]], 10][[2, 2, -3, -4, 5], [0, 0, 1, 1, 0]][[2, 2, -3, -4, 5], [0, 0, 1, 1, 0]]Passed
control [[[-3, -6], [-6, 5]], 15][[-9, -1], [1, 1]][[-9, -1], [1, 1]]Passed
control [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15][[-9, -2, 5, -1], [1, 1, 0, 1]][[-9, -2, 5, -1], [1, 1, 0, 1]]Passed

SHA-256 / 4265ac4f840acffab5d578ab5358594386719a5a3e9b31ca8ff5534aa9b0982f

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import functools
N = 1
observations = []
def solve(txs, clip):
    if not txs or any(len(t) != len(txs[0]) for t in txs):
        return None
    comb = []
    for k in range(len(txs[0])):
        s = sum(t[k] for t in txs if t[k] is not None)
        comb.append(s)
    hard = [None if c == 0 else (1 if c < 0 else 0) for c in comb]
    return [comb, hard]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...', [[[None, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, None, -9, 5]], 7], [[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]], ['regression [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7]', [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7], [[1, -1, -6], [0, 1, 1]]], ['partial-repair [[[null, -1, -9, null, -3], [8, 8, -9, 8, -6]], 15]', [[[None, -1, -9, None, -3], [8, 8, -9, 8, -6]], 15], [[8, 7, -15, 8, -9], [0, 0, 1, 0, 1]]], ['control [[[2, null], [null, -3], [5, 8]], 10]', [[[2, None], [None, -3], [5, 8]], 10], [[7, 5], [0, 0]]], ['control [[[5, -9]], 15]', [[[5, -9]], 15], [[5, -9], [0, 1]]], ['control [[[-9, -3, 0, -6, 0], [11, 5, -3, 2, 5]], 10]', [[[-9, -3, 0, -6, 0], [11, 5, -3, 2, 5]], 10], [[2, 2, -3, -4, 5], [0, 0, 1, 1, 0]]], ['control [[[-3, -6], [-6, 5]], 15]', [[[-3, -6], [-6, 5]], 15], [[-9, -1], [1, 1]]], ['control [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15]', [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15], [[-9, -2, 5, -1], [1, 1, 0, 1]]]], [['regression [[[20], [20], [-30]], 16]', [[[20], [20], [-30]], 16], [[10], [0]]], ['regression [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...', [[[None, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, None, -9, 5]], 7], [[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]], ['partial-repair [[[8, -9], [2, null]], 7]', [[[8, -9], [2, None]], 7], [[7, -7], [0, 1]]], ['partial-repair [[[11, 8, null], [2, -6, -1], [8, null, -3]], 10]', [[[11, 8, None], [2, -6, -1], [8, None, -3]], 10], [[10, 2, -4], [0, 0, 1]]], ['control [[[5, null]], 7]', [[[5, None]], 7], [[5, 0], [0, None]]], ['control [[[0, -1, -3, -1], [2, null, 11, -3], [0, null, -6, 0]], 15]', [[[0, -1, -3, -1], [2, None, 11, -3], [0, None, -6, 0]], 15], [[2, -1, 2, -4], [0, 1, 0, 1]]], ['control [[[8, -6]], 10]', [[[8, -6]], 10], [[8, -6], [0, 1]]], ['control [[[5, -6, 0]], 10]', [[[5, -6, 0]], 10], [[5, -6, 0], [0, 1, None]]]], [['regression [[[12, -12], [-5, 5]], 10]', [[[12, -12], [-5, 5]], 10], [[7, -7], [0, 1]]], ['regression [[[20], [20], [-30]], 16]', [[[20], [20], [-30]], 16], [[10], [0]]], ['partial-repair [[[null, -1, -9, null, -3], [8, 8, -9, 8, -6]], 15]', [[[None, -1, -9, None, -3], [8, 8, -9, 8, -6]], 15], [[8, 7, -15, 8, -9], [0, 0, 1, 0, 1]]], ['partial-repair [[[-3, 11], [-3, 11], [-6, 5]], 10]', [[[-3, 11], [-3, 11], [-6, 5]], 10], [[-10, 10], [1, 0]]], ['control [[[11, -3, -1, null, -6, 8], [-3, -9, 11, null, -6, null], [null, 5...', [[[11, -3, -1, None, -6, 8], [-3, -9, 11, None, -6, None], [None, 5, -6, -6, 2, 5]], 15], [[8, -7, 4, -6, -10, 13], [0, 1, 0, 1, 1, 0]]], ['control [[[0, 2, -9, -3, -1], [11, -1, -6, null, 0]], 15]', [[[0, 2, -9, -3, -1], [11, -1, -6, None, 0]], 15], [[11, 1, -15, -3, -1], [0, 0, 1, 1, 1]]], ['control [[[-6, null, 8, 2, 8], [-9, 11, null, -3, -1]], 15]', [[[-6, None, 8, 2, 8], [-9, 11, None, -3, -1]], 15], [[-15, 11, 8, -1, 7], [1, 0, 0, 1, 0]]], ['control [[[-1, -6, null, -3], [null, 8, 2, 0]], 7]', [[[-1, -6, None, -3], [None, 8, 2, 0]], 7], [[-1, 2, 2, -3], [1, 0, 0, 1]]]], [['regression [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7]', [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7], [[1, -1, -6], [0, 1, 1]]], ['regression [[[12, -12], [-5, 5]], 10]', [[[12, -12], [-5, 5]], 10], [[7, -7], [0, 1]]], ['partial-repair [[[11, 8, null], [2, -6, -1], [8, null, -3]], 10]', [[[11, 8, None], [2, -6, -1], [8, None, -3]], 10], [[10, 2, -4], [0, 0, 1]]], ['partial-repair [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...', [[[None, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, None, -9, 5]], 7], [[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]], ['control [[], 5]', [[], 5], None], ['control [[[1, 2], [3]], 5]', [[[1, 2], [3]], 5], None], ['control [[[2, null], [null, -3], [5, 8]], 10]', [[[2, None], [None, -3], [5, 8]], 10], [[7, 5], [0, 0]]], ['control [[[5, -9]], 15]', [[[5, -9]], 15], [[5, -9], [0, 1]]]], [['regression [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...', [[[None, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, None, -9, 5]], 7], [[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]], ['regression [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7]', [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7], [[1, -1, -6], [0, 1, 1]]], ['partial-repair [[[-3, 11], [-3, 11], [-6, 5]], 10]', [[[-3, 11], [-3, 11], [-6, 5]], 10], [[-10, 10], [1, 0]]], ['partial-repair [[[8, -9], [2, null]], 7]', [[[8, -9], [2, None]], 7], [[7, -7], [0, 1]]], ['control [[[-3, -6], [-6, 5]], 15]', [[[-3, -6], [-6, 5]], 15], [[-9, -1], [1, 1]]], ['control [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15]', [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15], [[-9, -2, 5, -1], [1, 1, 0, 1]]], ['control [[[5, null]], 7]', [[[5, None]], 7], [[5, 0], [0, None]]], ['control [[[0, -1, -3, -1], [2, null, 11, -3], [0, null, -6, 0]], 15]', [[[0, -1, -3, -1], [2, None, 11, -3], [0, None, -6, 0]], 15], [[2, -1, 2, -4], [0, 1, 0, 1]]]]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression [[[null, 5, 8, 8, 0, 0], [-6, 2, -1, 2, 2, 11], [2, 0, -9, null, -9...[[-4, 7, -2, 10, -7, 16], [1, 0, 1, 0, 1, 0]][[-4, 7, -2, 7, -7, 7], [1, 0, 1, 0, 1, 0]]Failed
regression [[[-1, 0, 0], [-9, 8, 0], [11, -9, -6]], 7][[1, -1, -6], [0, 1, 1]][[1, -1, -6], [0, 1, 1]]Passed
partial-repair [[[null, -1, -9, null, -3], [8, 8, -9, 8, -6]], 15][[8, 7, -18, 8, -9], [0, 0, 1, 0, 1]][[8, 7, -15, 8, -9], [0, 0, 1, 0, 1]]Failed
control [[[2, null], [null, -3], [5, 8]], 10][[7, 5], [0, 0]][[7, 5], [0, 0]]Passed
control [[[5, -9]], 15][[5, -9], [0, 1]][[5, -9], [0, 1]]Passed
control [[[-9, -3, 0, -6, 0], [11, 5, -3, 2, 5]], 10][[2, 2, -3, -4, 5], [0, 0, 1, 1, 0]][[2, 2, -3, -4, 5], [0, 0, 1, 1, 0]]Passed
control [[[-3, -6], [-6, 5]], 15][[-9, -1], [1, 1]][[-9, -1], [1, 1]]Passed
control [[[0, -1, 0, 0], [-9, -1, 5, -1]], 15][[-9, -2, 5, -1], [1, 1, 0, 1]][[-9, -2, 5, -1], [1, 1, 0, 1]]Passed

SHA-256 / 640371ca1ab3c27c7e72ddfff1db4de37b70389b67bd443ef663abaebbba140d

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

A deterministic, bounded teaching model of the named code under the stated contract; not a production codec. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:48:37.149452+00:00.

Case digest / 64ee3379d47103c4cbbc5d322e416273eb249cba046d02e94e1ce83999b997ef