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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 44858 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Behroozi, Hamid
- Abstract:
- Polar codes were introduced by Arikan in 2009. These codes are the first family of codes that with low encoding complexity and successive cancellation decoder, can achieve the channel capacity. Polar codes, at first were implemented for channel coding, but in 2010 performance of these codes in binary and q-ary alphabet source was studied. It is shown that these codes can perform efficiently in channel coding and source coding. On the other hand, one of the most important continuous sources are Gaussian sources. Due to the importance of Gaussian sources and good performance of polar codes, we try to evaluate the performance of these codes in Gaussian sources. Note that, these codes have discrete nature but here we extend their application for compression of continues sources. We study Polar codes for compression of Gaussian sources through two distributions on discrete alphabet: quantize approach as well as central limit theorem approach. Polar codes achieve the rate-distortion bound for Gaussian sources when the alphabet size tends to infinity.Then lossy compression of Gausian sources, with side information at decoder is investigated. This problem is known as the Gaussian Wyner-Ziv problem. First, the application of polar codes for binary Wyner-Ziv problem is extended to qary alphabet sources. It is shown that q-ary polar codes are optimal. Then we present two polar coding schemes for the Gaussian Wyner-Ziv problem. In the first scheme, we achieve a rate above the Wyner-Ziv rate-distortion function with a gap of 0.5 bits compared with the optimal rate. This scheme utilizes a successive cancellation decoder and is optimal in weak side-information cases when the decoder side-information noise variance is extremely higher than the source variance, referred to as low signal-to-noise ratios (SNRs). In the second scheme, we achieve the optimal rate in strong side-information cases, i.e., at high SNRs. The decoder utilizes an estimator to achieve the optimal distortion. Thus, with both schemes, we can achieve the optimal rate depending on the quality of side information at the decoder
- Keywords:
- Polar Code ; Source Coding ; Gaussian Sources ; Wyner/Ziv Coding ; Continuous Source
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