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arXiv · 1206.6584

An Approximate Coding-Rate Versus Minimum Distance Formula for Binary Codes

Yosef Akhtman·Robert G. Maunder·Lajos Hanzo
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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.

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Yosef Akhtman, Robert G. Maunder, Lajos Hanzo. 2012-06-28. An Approximate Coding-Rate Versus Minimum Distance Formula for Binary Codes. https://arxiv.org/abs/1206.6584

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