Codebook Cardinality Spectrum of Distributed Arithmetic Coding for Independent and Identically-Distributed Binary Sources

It was demonstrated that, as a nonlinear implementation of Slepian-Wolf Coding, Distributed Arithmetic Coding (DAC) outperforms traditional Low-Density Parity-Check (LPDC) codes for short code length and biased sources. This fact triggers research efforts into theoretical analysis of DAC. In our pre...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 66; no. 10; pp. 6580 - 6596
Main Authors: Fang, Yong, Stankovic, Vladimir
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Arithmetic coding
biased sources
Channel coding
codebook cardinality spectrum
Codes
Complexity theory
Correlation
Decoding
distributed arithmetic coding
Distributed source coding
Estimation
Numerical analysis
Parity check codes
Slepian-Wolf coding
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:It was demonstrated that, as a nonlinear implementation of Slepian-Wolf Coding, Distributed Arithmetic Coding (DAC) outperforms traditional Low-Density Parity-Check (LPDC) codes for short code length and biased sources. This fact triggers research efforts into theoretical analysis of DAC. In our previous work, we proposed two analytical tools, Codebook Cardinality Spectrum (CCS) and Hamming Distance Spectrum, to analyze DAC for independent and identically-distributed (i.i.d.) binary sources with uniform distribution. This article extends our work on CCS from uniform i.i.d. binary sources to biased i.i.d. binary sources. We begin with the final CCS and then deduce each level of CCS backwards by recursion. The main finding of this article is that the final CCS of biased i.i.d. binary sources is not uniformly distributed over [0, 1). This article derives the final CCS of biased i.i.d. binary sources and proposes a numerical algorithm for calculating CCS effectively in practice. All theoretical analyses are well verified by experimental results.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2020.3014965