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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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This content will become publicly available on August 18, 2026
Bounded-Metric List Decoding of Linearly Expurgated Tail-Biting Convolutional Codes
In the short blocklength regime, serial list decoding of tail-biting (TB) convolutional codes concatenated with an expurgating linear function (ELF) can approach the random coding union bound on frame error rate (FER) performance. Decoding complexity for a particular received word depends on how deep in the list the decoder must search to find a valid TB-ELF codeword. The average list size is close to one at low-FER operating points such as 10^−6, and serial list decoding provides a favorable average complexity compared to other decoders with similar performance for these cases. However, the average list size can be on the order of a hundred or a thousand at higher, but still practically important, FER operating points such as 10−3. It is useful to study the tradeoff between how deep the decoder is willing to search and the proximity to the frame error rate (FER) achieved by an ML decoder. Often, this tradeoff is framed in terms of a maximum list depth. However, this paper frames the tradeoff in terms of a maximum allowable metric between the received word and the trellis paths on the list. We consider metrics of Euclidean distance and angle. This new approach draws on the wealth of existing literature on bounded-metric decoding to provide characterizations of how the choice of maximum allowable metric controls the tradeoffs between FER performance and both decoding complexity and undetected error rate. These characterizations lead to an example of an ELF-TB convolutional code that outperforms recent results for polar codes in terms of the lowest SNR that simultaneously achieves both a total error rate less than T = 10^−3 and an undetected error rate below U = 10^−5.
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- Award ID(s):
- 2008918
- PAR ID:
- 10638481
- 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 bounded-distance decoding bounded-metric decoding undetected error rate tail-biting convolutional codes expurgation expurgating linear function
- Format(s):
- Medium: X
- Location:
- Los Angeles, California
- Sponsoring Org:
- National Science Foundation
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