Two Applications of Coset Cardinality Spectrum of Distributed Arithmetic Coding

Distributed Arithmetic Coding (DAC) is a practical realization of Slepian-Wolf coding that partitions source space into cosets. Coset Cardinality Spectrum (CCS) is an important property of DAC that was defined in our previous work. In this paper, we give two applications of CCS. First, we find that...

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Veröffentlicht in:IEEE transactions on information theory Jg. 67; H. 12; S. 8335 - 8350
1. Verfasser: Fang, Yong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.12.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Arithmetic
Arithmetic coding
coset cardinality spectrum
Decoding
Digital to analog converters
distributed arithmetic coding
Distributed source coding
Encoding
Expected values
Infinity
max <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">a posteriori decoding
Measurement
Parity check codes
Random variables
Slepian-Wolf coding
Terminology
ISSN:0018-9448, 1557-9654
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Zusammenfassung:Distributed Arithmetic Coding (DAC) is a practical realization of Slepian-Wolf coding that partitions source space into cosets. Coset Cardinality Spectrum (CCS) is an important property of DAC that was defined in our previous work. In this paper, we give two applications of CCS. First, we find that DAC bitstream is not compact. The rate loss of DAC bitstream is caused by two factors: unequal coset partitioning and bit indivisibility . It is proved that as code length goes to infinity, the expected value of bit-indivisibility rate loss will tend to 0.5 for any irrational Rate Change Step (RCS), where the RCS refers to the rate change when one source bit is flipped. With the help of CCS, the bit-indivisibility rate loss can be compensated to some extend. Especially, for any irrational RCS, as code length goes to infinity, the expected value of the remaining bit-indivisibility rate loss after compensation will tend to about 0.47. The second application of CCS is DAC decoder design. We derive the formula of path metric and find that in the original paper on DAC, the intuitive formula of path metric is not correct. The backward-replacing algorithm is proposed to make full use of memory. Experimental results confirm the correctness of theoretical analyses.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2021.3116082