48 research outputs found
An Enhanced Covering Lemma for Multiterminal Source Coding
An enhanced covering lemma for a Markov chain is proved in this paper, and
then the distributed source coding problem of correlated general sources with
one average distortion criterion under fixed-length coding is investigated.
Based on the enhanced lemma, a sufficient and necessary condition for
determining the achievability of rate-distortion triples is given.Comment: To appear in Proc. 2006 IEEE Information Theory Workshop, October
22-26, 2006, Chengdu, China. (5 pages
On the Performance of Lossless Joint Source-Channel Coding Based on Linear Codes
A general lossless joint source-channel coding scheme based on linear codes
is proposed and then analyzed in this paper. It is shown that a linear code
with good joint spectrum can be used to establish limit-approaching joint
source-channel coding schemes for arbitrary sources and channels, where the
joint spectrum of the code is a generalization of the input-output weight
distribution.Comment: To appear in Proc. 2006 IEEE Information Theory Workshop, October
22-26, 2006, Chengdu, China. (5 pages, 2 figures
Linear-Codes-Based Lossless Joint Source-Channel Coding for Multiple-Access Channels
A general lossless joint source-channel coding (JSCC) scheme based on linear
codes and random interleavers for multiple-access channels (MACs) is presented
and then analyzed in this paper. By the information-spectrum approach and the
code-spectrum approach, it is shown that a linear code with a good joint
spectrum can be used to establish limit-approaching lossless JSCC schemes for
correlated general sources and general MACs, where the joint spectrum is a
generalization of the input-output weight distribution. Some properties of
linear codes with good joint spectra are investigated. A formula on the
"distance" property of linear codes with good joint spectra is derived, based
on which, it is further proved that, the rate of any systematic codes with good
joint spectra cannot be larger than the reciprocal of the corresponding
alphabet cardinality, and any sparse generator matrices cannot yield linear
codes with good joint spectra. The problem of designing arbitrary rate coding
schemes is also discussed. A novel idea called "generalized puncturing" is
proposed, which makes it possible that one good low-rate linear code is enough
for the design of coding schemes with multiple rates. Finally, various coding
problems of MACs are reviewed in a unified framework established by the
code-spectrum approach, under which, criteria and candidates of good linear
codes in terms of spectrum requirements for such problems are clearly
presented.Comment: 18 pages, 3 figure
Weight Distributions of Regular Low-Density Parity-Check Codes over Finite Fields
The average weight distribution of a regular low-density parity-check (LDPC)
code ensemble over a finite field is thoroughly analyzed. In particular, a
precise asymptotic approximation of the average weight distribution is derived
for the small-weight case, and a series of fundamental qualitative properties
of the asymptotic growth rate of the average weight distribution are proved.
Based on this analysis, a general result, including all previous results as
special cases, is established for the minimum distance of individual codes in a
regular LDPC code ensemble.Comment: 15 pages, 5 figures, accepted for publication in IEEE Transactions on
Information Theory, July 201
Constructing Linear Encoders with Good Spectra
Linear encoders with good joint spectra are suitable candidates for optimal
lossless joint source-channel coding (JSCC), where the joint spectrum is a
variant of the input-output complete weight distribution and is considered good
if it is close to the average joint spectrum of all linear encoders (of the
same coding rate). In spite of their existence, little is known on how to
construct such encoders in practice. This paper is devoted to their
construction. In particular, two families of linear encoders are presented and
proved to have good joint spectra. The first family is derived from Gabidulin
codes, a class of maximum-rank-distance codes. The second family is constructed
using a serial concatenation of an encoder of a low-density parity-check code
(as outer encoder) with a low-density generator matrix encoder (as inner
encoder). In addition, criteria for good linear encoders are defined for three
coding applications: lossless source coding, channel coding, and lossless JSCC.
In the framework of the code-spectrum approach, these three scenarios
correspond to the problems of constructing linear encoders with good kernel
spectra, good image spectra, and good joint spectra, respectively. Good joint
spectra imply both good kernel spectra and good image spectra, and for every
linear encoder having a good kernel (resp., image) spectrum, it is proved that
there exists a linear encoder not only with the same kernel (resp., image) but
also with a good joint spectrum. Thus a good joint spectrum is the most
important feature of a linear encoder.Comment: v5.5.5, no. 201408271350, 40 pages, 3 figures, extended version of
the paper to be published in IEEE Transactions on Information Theor