CRC-Aided High-Rate Convolutional Codes With Short Blocklengths for List Decoding
Wenhui Sui, Brendan Towell, Ava Asmani, Hengjie Yang, Holden Grissett,, Richard D. Wesel

TL;DR
This paper designs CRC polynomials for short blocklength convolutional codes, optimizing their minimum distance and decoding complexity, and demonstrates that CRC-aided list decoding approaches the theoretical performance limits.
Contribution
It introduces optimized CRC polynomial design for short convolutional codes and analyzes decoding complexity-performance trade-offs, achieving near-bound performance.
Findings
CRC-aided list decoding approaches the RCU bound at blocklength 128.
Optimized CRC polynomials improve minimum distance and decoding efficiency.
Different decoding strategies offer trade-offs between complexity and performance.
Abstract
Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutional codes (CCs) with cyclic redundancy check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths. This paper designs CRC polynomials for rate- (n-1)/n ZT and TB CCs with short blocklengths. This paper considers both standard rate-(n-1)/n CC polynomials and rate- (n-1)/n designs resulting from puncturing a rate-1/2 code. The CRC polynomials are chosen to maximize the minimum distance d_min and minimize the number of nearest neighbors A_(d_min) . For the standard rate-(n-1)/n codes, utilization of the dual trellis proposed by Yamada et al. lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD). CRC-aided SLVD of the TBCCs closely approaches the RCU bound at a blocklength of 128. This paper compares the FER performance (gap to the RCU…
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · Error Correcting Code Techniques
