An Approximate Coding-Rate Versus Minimum Distance Formula for Binary Codes
Abstract
We devise an analytically simple as well as invertible approximate expression, which describes the relation between the minimum distance of a binary code and the corresponding maximum attainable code-rate. For example, for a rate-(1/4), length-256 binary code the best known bounds limit the attainable minimum distance to 65<d(n=256,k=64)<90, while our solution yields d(n=256,k=64)=74.4. The proposed formula attains the approximation accuracy within the rounding error for ~97% of (n,k) scenarios, where the exact value of the minimum distance is known. The results provided may be utilized for the analysis and design of efficient communication systems.
Cite
@article{arxiv.1206.6584,
title = {An Approximate Coding-Rate Versus Minimum Distance Formula for Binary Codes},
author = {Yosef Akhtman and Robert G. Maunder and Lajos Hanzo},
journal= {arXiv preprint arXiv:1206.6584},
year = {2012}
}
Comments
4 pages, 4 figures. Earlier version was presented at IEEE VTC'09 Fall, Anchorage, Alaska, USA