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Exploiting Applications and Improving Performance of Polar Codes in Information Theory

Khatami, Mehrdad | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41885 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Marvasti, Farrokh
  7. Abstract:
  8. The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find practical schemes that approach these limits.Polar codes, recently invented by Arıkan, are the first practical codes that are known to achieve the capacity for a large class of channels. Their code construction is based on a phenomenon called “channel polarization”.
    Since the performance of polar code degrades when the block length is small, several kinds of Reed – Solomon concatenation is considered in order to improve the performance.
    Polar codes are suitable not only for channel coding but also achieve optimal performance for several other important problems in information theory. The first problem is lossy source compression. Polar codes asymptotically approach Shannon’s rate-distortion bound for a large class of sources. Polar codes can also achieve the optimal performance for the Slepian-Wolf, Wyner-Ziv and the Gelfand-Pinsker problems. We further show that polar codes achieve the capacity of asymmetric channels, multi-terminal scenarios like multiple access channels, and degraded broadcast channels.
    The encoding as well as the decoding operation of polar codes can be implemented with O(N logN) complexity, where N is the blocklength of the code
  9. Keywords:
  10. Coding ; Reed-Solomon Code ; Channel Coding ; Information Theory ; Polar Code ; Channel Polarization ; Source Coding

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