FA-72113 / Error-correcting codes / Member archive

Bit flipping flips only the first most-suspect bit · case 03

Decoding needs more iterations or fails where parallel flipping succeeds.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Parallel Gallager bit-flipping decoder. H lists the variable indices of each parity check. In each iteration: if every check is satisfied stop with success; otherwise count, per bit, the unsatisfied checks it joins and flip all bits that reach the maximum count. At most max_iter flipping iterations are performed and the syndrome is checked after the last one. Return [bits, iterations performed, success].

Why this case matters

Hard-decision LDPC decoders in flash controllers use bit flipping as a low-power first pass.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression [[[0, 2, 4, 6], [1, 2, 5, 6], [3, 4, 5, 6]], [0, 0, 0, 0, 0, 1, 0], 3]	`[[0, 0, 0, 0, 0, 0, 0], 1, true]`	`[[0, 0, 0, 0, 0, 0, 0], 2, true]`	Failed

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