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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 March 10, 2026
Parallel Decoding of Trellis Stages for Low Latency Decoding of Tail-Biting Convolutional Codes
Convolutional codes are widely used in many applications. The encoders can be implemented with a simple circuit. Decoding is often accomplished by the Viterbi algorithm or the maximum a-posteriori decoder of Bahl et al. These algorithms are sequential in nature, requiring a decoding time proportional to the message length. For low latency applications this this latency might be problematic. This paper introduces a low-latency decoder for tail-biting convolutional codes TBCCs that processes multiple trellis stages in parallel. The new decoder is designed for hardware with parallel processing capabilities. The overall decoding latency is proportional to the log of the message length. The new decoding architecture is modified into a list decoder, and the list decoding performance can be enhanced by exploiting linearity to expand the search space. Certain modifications to standard TBCCs are supported by the new architecture and improve frame error rate performance.
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- Award ID(s):
- 2008918
- PAR ID:
- 10587930
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 979-8-3315-2289-6
- Page Range / eLocation ID:
- 1 to 6
- Subject(s) / Keyword(s):
- Convolutional codes Maximum a posteriori estimation Viterbi algorithm Parallel processing Turbo codes Hardware Parallel architectures Low latency communication Standards Maximum likelihood decoding
- Format(s):
- Medium: X
- Location:
- Karlsruhe, Germany
- Sponsoring Org:
- National Science Foundation
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