Polar codes for distributed source coding
저자
발행사항
Seoul : Sungkyunkwan University, 2012
학위논문사항
Thesis(M.A)-- Sungkyunkwan University : Department of Electrical and Computer Engineering 2012.8
발행연도
2012
작성언어
한국어
주제어
DDC
621.3 판사항(22)
발행국(도시)
서울
형태사항
v, ii, 44 p. : ill., chart ; 30 cm
일반주기명
Adviser: Sang-Hyo Kim
Includes bibliographical references(p. 42)
DOI식별코드
소장기관
Since the inception, information theory has been applied to many areas, including statistical inference, natural language processing, cryptography, networks especially communication networks. In the seminal work, Claude E. Shannon developed information theory to find fundamental limits on compressing data, reliably storing and communicating data. Till now, the two most important sub-fields of information theory, which are channel coding and source coding, have been developed to find the practical schemes that approach those limits.
In the main ideas of information theory, Shannon mentioned about the information entropy and redundancy of a source, and its relevance through the source coding theorem; and the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem. Furthermore, with the debut of distributed source coding theory, the relation between channel coding and source coding was proved.
Polar codes, invented by Arikan, are the first provable codes that achieve the capacity for a large class of channels with low complexity in both encoding and decoding. Polar codes has been studied by many researchers and has shown that suitable not only for channel coding but also for several other important problems in information theory such as multi-terminals problems. In the earliest schemes, polar coding comes with successive cancellation decoding and the approximate recursive construction. However, in practice, this scheme does not show a good performance and much worse than other codes such as LDPC or turbo codes. In this thesis, we study first about the basics of polar coding, including the structure of polar encoding and decoding, the ideas of constructing polar codes based on ?channel polarization?. The practical implementation in both encoding and decoding is examined. Two constructions of polar codes applied for binary symmetric channel are considered. One construction adopts the approximate recursion equations from Arikan and the other exploits density evolution for tracking the quality of the sub-channels.
The optimality of polar codes for multi-terminals problem is also shown, such as Slepian-Wolf, and Wyner-Ziv problems. For the Slepian Wold Coding and lossless compression, the optimality is proved by using the fact that the entropy of the source gathers only in a set of indices and the complementary brings no information. In Wynner Ziv problem, using "nested" codes and polar codes are naturally suited to approach and verify the optimality.
The main problem we consider is an application of polar coding for source compression, especially Slepian Wolf coding (SWC). We construct polar codes that asymptotically approach Slepian Wolf bound for rate adaptive scheme. The encoder transmits the syndrome set which includes high entropy bits to the decoder to achieve the optimal compression. It means that the encoder must know the correlation between two sources and the syndrome set varies according to this correlation. This makes the complexity of the encoder increase since the structure of the code should vary according to the conditional entropy of two sources. However, the proposed construction which is designed combining optimal sequences can overcome that problem. For the specific purpose of rate adaptive SWC, the optimal sequence is designed at fixed rates for Target Error Rate 10^ -1. This is because the region which has critically affects the rate compression performance of rate adaptive scheme. We empirically show that by applying this construction, the optimal compression rate is obtained regardless the statistic dependency of two sources.
Furthermore, we propose the practical scheme by combining polar codes with list decoding method. It is shown that polar source coding with list decoding method performs close to Slepian Wolf bound and comparably with other Shannon limit approaching codes such as low density parity check accumulate (LDPCA) codes. However, since polar coding performs much better than LDPC codes in the region which has probability of error less than 10^ -1, it is shown that polar codes outperforms LDPCA codes in rate adaptive scheme. With the aids of CRC codes, the polar source coding system for SWC is completed.
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