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.
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This content will become publicly available on July 7, 2025
Linearity-Enhanced Serial List Decoding of Linearly Expurgated Tail-Biting Convolutional Codes
With a sufficiently large list size, the serial list Viterbi algorithm (S-LVA) provides maximum likelihood (ML) decoding of a concatenated convolutional code (CC) and an expurgating linear function (ELF), which is similar in function to a cyclic redundancy check (CRC), but doesn't enforce that the code be cyclic. However, S-LVA with a large list size requires considerable complexity. This paper exploits linearity to reduce decoding complexity for tail-biting CCs (TBCCs) concatenated with ELFs.
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- Award ID(s):
- 2008918
- NSF-PAR ID:
- 10540377
- Publisher / Repository:
- IEEE
- Date Published:
- ISSN:
- 2157-8117
- ISBN:
- 979-8-3503-8284-6
- Page Range / eLocation ID:
- 1770 to 1775
- Subject(s) / Keyword(s):
- Convolutional Codes List Decoding Tail-biting Convolutional Codes Cyclic Redundancy Check Expurgating Linear Function Linearity
- Format(s):
- Medium: X
- Location:
- Athens, Greece
- Sponsoring Org:
- National Science Foundation
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Maximum-likelihood (ML) decoding of tail-biting convolutional codes (TBCCs) with S=2v states traditionally requires a separate S-state trellis for each of the S possible starting/ending states, resulting in complexity proportional to S2. 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.more » « less
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