A Note on Comparison of Error Correction Codes

TL;DR

This paper explores methods to compare error correction codes by representing them as statistical experiments and applying matrix ordering techniques, providing a theoretical framework for evaluating code performance.

Contribution

It introduces a novel approach to compare error correction codes using Loewner matrix ordering and matrix majorization, linking coding theory with statistical experiment comparison.

Findings

Comparison of block error correction codes via Loewner matrix ordering.

Bit-error rate performance comparison using matrix majorization.

Provides a theoretical basis for code performance evaluation.

Abstract

Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different error correction codes. We present results on the comparison of block error correction codes using the representation of error correction code as a linear experiment. In this case the code comparison is based on the Loewner matrix ordering of respective code matrices. Next, we demonstrate the bit-error rate code performance comparison based on the representation of the codes as dichotomies, in which case the comparison is based on the matrix majorization ordering of their respective equivalent code matrices.