Performance of Parallel Concatenated Coding Schemes

In this paper, ensembles of parallel concatenated codes are studied and rigorous results on their asymptotic performance, under the assumption of maximum-likelihood (ML) decoding, are presented. In particular, it is proven that in any parallel concatenation scheme with
k
branches where all
k
encoders are recursive and the Bhattacharyya parameter of the channel is sufficiently small, the bit-error rate (BER) and the word-error rate go to 0 exactly like
N

^1-

k
and
N

^2-

k
, respectively. Different types of ensembles by changing the subgroup of permutations used to interconnect the various encoders, are considered.