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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| Vydáno v: | IEEE transactions on information theory Ročník 67; číslo 12; s. 8335 - 8350 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
IEEE
01.12.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Fang, Yong |
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| SubjectTerms | 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 |
| Title | Two Applications of Coset Cardinality Spectrum of Distributed Arithmetic Coding |
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