Coding for Parallel Channels: Gallager Bounds and Applications to Repeat-Accumulate Codes

摘要

This paper is focused on the performance analysis of binary linear blockcodes (or ensembles) whose transmission takes place over independent andmemoryless parallel channels. New upper bounds on the maximum-likelihood (ML)decoding error probability are derived. The framework of the second version ofthe Duman and Salehi (DS2) bounds is generalized to the case of parallelchannels, along with the derivation of optimized tilting measures. Theconnection between the generalized DS2 and the 1961 Gallager bounds, knownpreviously for a single channel, is revisited for the case of parallelchannels. The new bounds are used to obtain improved inner bounds on theattainable channel regions under ML decoding. These improved bounds are appliedto ensembles of turbo-like codes, focusing on repeat-accumulate codes and theirrecent variations.