248 research outputs found
Coding for Parallel Channels: Gallager Bounds for Binary Linear Codes with Applications to Repeat-Accumulate Codes and Variations
This paper 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 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. The framework of
the second version of the Duman and Salehi (DS2) bounds is generalized to the
case of parallel channels, along with the derivation of their optimized tilting
measures. The connection between the generalized DS2 and the 1961 Gallager
bounds, addressed by Divsalar and by Sason and Shamai 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 re-derive
specific bounds which were originally derived by Liu et al. as special cases of
the Gallager bound. 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.Comment: Submitted to IEEE Trans. on Information Theory, June 2006 (57 pages,
9 figures
Strong Secrecy on a Class of Degraded Broadcast Channels Using Polar Codes
Different polar coding schemes are proposed for the memoryless degraded
broadcast channel under different reliability and secrecy requirements: layered
decoding and/or layered secrecy. In this setting, the transmitter wishes to
send multiple messages to a set of legitimate receivers keeping them masked
from a set of eavesdroppers. The layered decoding structure requires receivers
with better channel quality to reliably decode more messages, while the layered
secrecy structure requires eavesdroppers with worse channel quality to be kept
ignorant of more messages. The implementation of the proposed polar coding
schemes is discussed and their performance is evaluated by simulations for the
symmetric degraded broadcast channel.Comment: 35 pages. Published in "MDPI Entropy". A short version of this paper
had been accepted to the 3rd Workshop on Physical-Layer Methods for Wireless
Security, IEEE CNS 201
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