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Article: 5 Sphere-packing bounds on the decoding error probability: classical and recent results.(Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial)(Report)
- Article from:
- Foundations and Trends in Communications and Information Theory
- Article date:
- August 1, 2006
- Author:
CopyrightCOPYRIGHT 2006 Now Publishers, Inc. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Overview: This section reviews the concepts used in the derivation of sphere-packing lower bounds on the block error probability. We review both the 1959 sphere-packing bound derived by Shannon for the Gaussian channel and the 1967 sphere-packing bound derived by Shannon, Gallager and Berlekamp for discrete memoryless channels. These ideas serve for presenting recent improvements on the tightness of the 1967 sphere-packing bound, as suggested by Valembois and Fossorier. These modifications provide an improved version of the classical 1967 sphere-packing bound whose tightness is enhanced especially for block codes of short to moderate block lengths. These modifications also ...