Channel Coding and Lossy Source Coding Using a Generator of Constrained Random Numbers

Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code are finite. Random numbers, which satisfy a condition specif...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 60; no. 5; pp. 2667 - 2686
Main Author Muramatsu, Jun
Format Journal Article
LanguageEnglish
Published New York IEEE 01.05.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Alphabets
Channel capacity
Channel coding
Channels
Coders
Coding
Electrical engineering
Encoders
Hash based algorithms
Manganese
Manganese compounds
Probability distribution
Random numbers
Random variables
Rate-distortion
Sparse matrices
Sparsity
information spectrum methods
channel coding
Shannon theory
LDPC codes
lossy source coding
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Summary:Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code are finite. Random numbers, which satisfy a condition specified by a function and its value, are used to construct stochastic encoders. The proof of the theorems is based on the hash property of an ensemble of functions, where the results are extended to general channels/sources and alternative formulas are introduced for channel capacity and the rate-distortion region. Since an ensemble of sparse matrices has a hash property, we can construct a code by using sparse matrices.
Bibliography:ObjectType-Article-1
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content type line 23
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2309140