Efficient Maximum-Likelihood Decoding for TBCC and CRC-TBCC Codes via Parallel List Viterbi

Maximum-likelihood (ML) decoding of tail-biting convolutional codes (TBCCs) with S=$2^{v}$ states traditionally requires a separate S-state trellis for each of the S possible starting/ending states, resulting in complexity proportional to $S^{2}$. Lower-complexity ML decoders for TBCCs have complexity proportional to S log S. This high complexity motivates the use of the wrap-around Viterbi algorithm, which sacrifices ML performance for complexity proportional to S.This paper presents an ML decoder for TBCCs that uses list decoding to achieve an average complexity proportional to S at operational signal-to-noise ratios where the expected list size is close to one. The new decoder uses parallel list Viterbi decoding with a progressively growing list size operating on a single S-state trellis. Decoding does not terminate until the most likely tailbiting codeword has been identified. This approach is extended to ML decoding of tail-biting convolutional codes concatenated with a cyclic redundancy check code as explored recently by Yang et al. and King et al. Constraining the maximum list size further reduces complexity but sacrifices guaranteed ML performance, increasing errors and introducing erasures.