Paper Info
Title
Sphere-packing bounds revisited for moderate block lengths
Abstract
The main reference of this paper is the sphere-packing bound of 1967 (SP67) derived by Shannon, Gallager, and Berlekamp. It offers a lower bound on the decoding error probability over a very large variety of channels. If it has failed so far to provide any usable material in practical implementation of telecommunication systems, it is due to an original focus on asymptotic results (making it inapplicable for moderate code lengths) and to the difficulty of the involved methods (which makes the derivation of SP67 quite hermetic and uninspiring for further research). The purpose of this paper is two-fold: 1) to stir up some renewed interest in the topic on which Shannon concluded his career in information theory thanks to a qualitative (rather than technical) review of the derivation of SP67, introduced by a review of the simpler sphere-packing bound derived by Shannon in 1959; 2) to prove the practical interest of SP67 by extending its field of application to continuous output channels and particularly the additive white Gaussian noise (AWGN) channel used with any particular modulation scheme, and by improving its lower bound for the moderate code length case so that it becomes the best lower bound for most iteratively decodable codes (turbo codes, low-density parity-check (LDPC) codes, repeat-accumulate (RA) codes, etc.) of usual lengths.
Year
DOI
Venue
2004
10.1109/TIT.2004.838090
IEEE Transactions on Information Theory
Keywords
Field
DocType
renewed interest,moderate code length,moderate code length case,moderate block length,practical implementation,iteratively decodable code,simpler sphere-packing,practical interest,additive white gaussian noise,turbo code,asymptotic result,error probability,ldpc code,low density parity check,block codes,awgn,lower bound,information theory,sphere packing,channel coding
Information theory,Discrete mathematics,Combinatorics,Low-density parity-check code,Sphere packing,Upper and lower bounds,Turbo code,Block code,Decoding methods,Additive white Gaussian noise,Mathematics
Journal
Volume
Issue
ISSN
50
12
0018-9448
Citations 
PageRank 
References 
36
3.63
17
Authors
2
Name
Order
Citations
PageRank
A. Valembois1866.72
M. P.C. Fossorier292073.03