High-Rate Convolutional Codes with CRC-Aided List Decoding for Short Blocklengths

TL;DR

This paper develops optimized CRCs for short convolutional codes with tail-biting and zero-termination, achieving near-optimal error performance with reduced decoding complexity at short blocklengths.

Contribution

It introduces a new CRC design tailored for short convolutional codes and employs a dual trellis to lower decoding complexity, closely approaching the RCU bound.

Findings

CRC-aided SLVD of TBCCs approaches RCU bound at blocklength 128

Optimized CRCs improve FER performance for short codes

Dual trellis reduces decoding complexity

Abstract

Recently, rate-$1/\omega$ zero-terminated and tail-biting convolutional codes (ZTCCs and TBCCs) 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 CRCs for rate-$(\omega-1)/\omega$ CCs with short blocklengths, considering both the ZT and TB cases. The CRC design seeks to optimize the frame error rate (FER) performance of the code resulting from the concatenation of the CRC and the CC. Utilization of the dual trellis proposed by Yamada \emph{et al.} lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD) of ZTCCs and TBCCs. CRC-aided SLVD of the TBCCs closely approaches the RCU bound at a blocklength of $128$.