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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.
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This content will become publicly available on August 18, 2026
Syndrome Sphere Decoding of Linearly Expurgated Tail-Biting Convolutional Codes
This paper proposes a syndrome sphere decoding (SSD) algorithm. SSD achieves the frame error rate (FER) of maximum likelihood (ML) decoding for a tail-biting convolutional code (TBCC) concatenated with an expurgating linear function (ELF) with significantly lower average and maximum decoding complexity than serial list Viterbi decoding (SLVD). SSD begins by using a Viterbi decoder to find the closest trellis path, which may not be tail-biting and may not satisfy the ELF. This trellis path has a syndrome comprised of the difference between the received ELF and the ELF computed from the received message and the difference between the beginning and ending state of the trellis path. This syndrome is used to find all valid tail-biting codewords that satisfy the ELF constraint and lie within a specified distance from the closest trellis path. The proposed algorithm avoids the complexity of SLVD at the cost of a large table containing all the offsets needed for each syndrome. A hybrid decoder combines SSD and SLVD with a fixed maximum list size, balancing the maximum list size for SLVD against the size of the SSD offset table.
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- Award ID(s):
- 2008918
- PAR ID:
- 10638480
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 979-8-3315-8983-7
- Page Range / eLocation ID:
- 1 to 5
- Subject(s) / Keyword(s):
- convolutional codes list decoding expurgation expurgating linear function sphere decoding syndrome decoding Viterbi decoding
- Format(s):
- Medium: X
- Location:
- Los Angeles, California
- Sponsoring Org:
- National Science Foundation
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