LDPC codes and convolutional codes with equal structural delay: a comparison
IEEE Transactions on Communications
IEEE Transactions on Signal Processing
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
Lower bounds on the graphical complexity of finite-length LDPC codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Performance bounds for nonbinary linear block codes over memoryless symmetric channels
IEEE Transactions on Information Theory
Improving the sphere-packing bound for binary codes over memoryless symmetric channels
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Channel coding rate in the finite blocklength regime
IEEE Transactions on Information Theory
Performance bounds for erasure, list and decision feedback schemes with linear block codes
IEEE Transactions on Information Theory
| Hi-index | 755.08 |
This paper derives an improved sphere-packing (ISP) bound for finite-length error-correcting codes whose transmission takes place over symmetric memoryless channels, and the codes are decoded with an arbitrary list decoder. We first review classical results, i.e., the 1959 sphere-packing (SP59) bound of Shannon for the Gaussian channel, and the 1967 sphere-packing (SP67) bound of Shannon et al. for discrete memoryless channels. An improvement on the SP67 bound, as suggested by Valembois and Fossorier, is also discussed. These concepts are used for the derivation of a new lower bound on the error probability of list decoding (referred to as the ISP bound) which is uniformly tighter than the SP67 bound and its improved version. The ISP bound is applicable to symmetric memoryless channels, and some of its applications are presented. Its tightness under maximum-likelihood (ML) decoding is studied by comparing the ISP bound to previously reported upper and lower bounds on the ML decoding error probability, and also to computer simulations of iteratively decoded turbo-like codes. This paper also presents a technique which performs the entire calculation of the SP59 bound in the logarithmic domain, thus facilitating the exact calculation of this bound for moderate to large block lengths without the need for the asymptotic approximations provided by Shannon.