On the Weight Enumerator and the Maximum Likelihood Performance of Linear Product Codes
Abstract
Product codes are widely used in data-storage, optical and wireless applications. Their analytical performance evaluation usually relies on the truncated union bound, which provides a low error rate approximation based on the minimum distance term only. In fact, the complete weight enumerator of most product codes remains unknown. In this paper, concatenated representations are introduced and applied to compute the complete average enumerators of arbitrary product codes over a field Fq. The split weight enumerators of some important constituent codes (Hamming, Reed-Solomon) are studied and used in the analysis. The average binary weight enumerators of Reed Solomon product codes are also derived. Numerical results showing the enumerator behavior are presented. By using the complete enumerators, Poltyrev bounds on the maximum likelihood performance, holding at both high and low error rates, are finally shown and compared against truncated union bounds and simulation results.
Keywords
Cite
@article{arxiv.cs/0601095,
title = {On the Weight Enumerator and the Maximum Likelihood Performance of Linear Product Codes},
author = {Mostafa El-Khamy and Roberto Garello},
journal= {arXiv preprint arXiv:cs/0601095},
year = {2007}
}
Comments
26 pages, 10 figures, submitted to IEEE transactions in December 2005