Performance Comparison of Short-Length Error-Correcting Codes

Abstract

We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based Maximum-Likelihood decoder on the erasure channel and probabilistic Ordered Statistics Decoder on the Gaussian channel. As such we compare codes and not decoders. The word error rate versus the channel parameter is found for LDPC, Reed-Muller, Polar, and BCH codes at length 256 bits. BCH codes outperform other codes in absence of cyclic redundancy check. Under joint decoding, the concatenation of a cyclic redundancy check makes all codes perform very close to optimal lower bounds.

6 pages, 5 figures, paper submitted to the IEEE SCVT 2016 conference

References in corpus (3)

• Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels
• A Comparative Study of Polar Code Constructions for the AWGN Channel
• Reed-Muller Codes Achieve Capacity on Erasure Channels

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• A Revisit to Ordered Statistics Decoding: Distance Distribution and Decoding Rules
• RNN Decoding of Linear Block Codes
• Segmentation-Discarding Ordered-Statistic Decoding for Linear Block Codes
• Perturbed Adaptive Belief Propagation Decoding for High-Density Parity-Check Codes