FA-71953 / Error-correcting codes / Member archive

Viterbi scores a pair mismatch as one error · case 03

Pairs with both bits wrong are penalised like a single error, so wrong paths win.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Hard-decision Viterbi decoder for the terminated K=3 (7,5) code (outputs g=7 then g=5 per step, two zero tail bits). Branch metric is the Hamming distance between the received pair and the branch output. Survivors keep the first strictly better candidate (states in ascending order, input 0 before 1). Decoding ends in state 0 and the two tail bits are removed. Return [decoded bits, final path metric]; odd or too-short input returns None.

Why this case matters

Receivers recover convolutionally coded frames by maximum-likelihood trellis search.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression [[1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]	`[[1, 1, 0, 0, 0, 0], 1]`	`[[1, 1, 0, 0, 0, 0], 2]`	Failed

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