An Improved Sphere-Packing Bound Targeting Codes of Short to Moderate Block Lengths and Applications
Abstract
This paper derives an improved sphere-packing (ISP) bound targeting codes of short to moderate block lengths. We first review the 1967 sphere-packing (SP67) bound for discrete memoryless channels, and a recent improvement by Valembois and Fossorier. These concepts are used for the derivation of a new lower bound on the decoding error probability (referred to as the ISP bound) which is uniformly tighter than the SP67 bound and its recent improved version. Under a mild condition, the ISP bound is applicable to general memoryless channels, and some of its applications are exemplified. Its tightness is studied by comparing it with bounds on the ML decoding error probability. It is exemplified that the ISP bound suggests an interesting alternative to the 1959 sphere-packing (SP59) bound of Shannon for the Gaussian channel, especially for digital modulations of high spectral efficiency.
Keywords
Cite
@article{arxiv.cs/0609094,
title = {An Improved Sphere-Packing Bound Targeting Codes of Short to Moderate Block Lengths and Applications},
author = {Gil Wiechman and Igal Sason},
journal= {arXiv preprint arXiv:cs/0609094},
year = {2007}
}
Comments
To be presented in the 44th Allerton conference, 27-29 September 2006. The full paper version was submitted to the IEEE Trans. on Information Theory, August 2006 (see http://www.ee.technion.ac.il/people/sason/ISP.pdf)