Some communication scenarios can be modeled as
standard coded transmission over a set of parallel communication channels. These
include transmission over block fading channels, rate-compatible puncturing of
turbo-like codes, multi-carrier signaling and others. This thesis is focused on
the performance analysis of binary linear block codes (or ensembles) whose
transmission takes place over independent and memoryless parallel channels. New
upper bounds on the maximum-likelihood (ML) decoding error probability are derived.
These bounds include the generalization of the second version of the Duman and
Salehi (DS2) bound to the case of parallel channels and a generalization of the
classic 1961 Gallager bound to parallel channels. Optimized tilting measures
for the new bound are derived. The connection between the generalized DS2 and
the 1961 Gallager bounds, which was previously addressed for a single channel,
is explored in the case of an arbitrary number of independent parallel
channels. The generalization of the DS2 bound for parallel channels enables to
rederive specific bounds which were previously derived as special cases of the
Gallager bound. The new bounds are applied to various ensembles of turbo-like
codes, focusing especially on repeat-accumulate codes and their recent
variations which possess low encoding and decoding complexity and exhibit
remarkable performance under iterative decoding. In the asymptotic case where
we let the block length tend to infinity, the new bounds are used to obtain
improved inner bounds on the attainable channel regions under ML decoding. The
tightness of the new bounds for independent parallel channels is exemplified
for structured ensembles of turbo-like codes. The improved bounds with their
optimized tilting measures show, irrespectively of the block length of the
codes, an improvement over the union bound and other previously reported bounds
for independent parallel channels; this improvement is especially pronounced
for moderate to large block lengths.
