Information-bit error rate and false positives in an MDS code

TL;DR

This paper refines the weight distribution of MDS codes to improve theoretical estimates of error rates and false positives in block transmission over discrete memoryless channels, offering a new performance analysis.

Contribution

It provides a refined weight distribution for MDS codes and computes false positives, enhancing the accuracy of error rate predictions.

Findings

Improved approximation of information-bit error rate.

Explicit computation of false positives.

Enhanced performance analysis of MDS codes.

Abstract

In this paper, a refinement of the weight distribution in an MDS code is computed. Concretely, the number of codewords with a fixed amount of nonzero bits in both information and redundancy parts is obtained. This refinement improves the theoretical approximation of the information-bit and -symbol error rate, in terms of the channel bit-error rate, in a block transmission through a discrete memoryless channel. Since a bounded distance reproducing encoder is assumed, the computation of the here-called false positive (a decoding failure with no information-symbol error) is provided. As a consequence, a new performance analysis of an MDS code is proposed.