Analytical Bounds on Maximum-Likelihood Decoded Linear Codes with Applications to Turbo-Like Codes: An Overview
Abstract
Description
Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and their relation to a variety of other reported bounds. Within the class of lower bounds, we address de Caen's based bounds and their improvements, sphere-packing bounds, and information-theoretic bounds on the bit error probability of codes defined on graphs. A comprehensive overview is provided in a monograph by the authors which is currently in preparation.
6 pages, 3 figures. Accepted for presentation in Fourth International Symposium on Turbo Codes and Related Topics, Munich, Germany, 3--7 April, 2006
6 pages, 3 figures. Accepted for presentation in Fourth International Symposium on Turbo Codes and Related Topics, Munich, Germany, 3--7 April, 2006