Speaker: Eldad Meller
M.Sc. student under the supervision of Prof. Simon Litsyn
Wednesday, August 9th 2017 at 15:30
Room 011, Kitot Bldg., Faculty of Engineering
High-Efficiency Codes and Decoding Methods Based on Polar Codes
Abstract
The first known codes that achieve the capacity over Binary Symmetric Channels (B-MC) with polynomial decoding time were introduced by Arikan in 1997. Arikan proposed a transformation over two channels with a capacity of I(W) that create two synthetic channels. The first channel has lower capacity then I(W) and the second have higher capacity than i(w), but the total capacity of the two original channels and the two synthetic channels are equal. By repeating this transformation, we get the phenomena of polarization of the synthetic channels. Some of the synthetic channels have a capacity approaching 1 and the others have a capacity approaching 0. Based on this phenomena Arikan named those codes as polar codes.
This thesis deals with two problems related to Polar Codes decoding. In the first part of this work, we show there is a bound that limits the maximum throughput a successive castellation polar decoder that implemented on a logic circus (such as FPGA) can achieve. This bound is caused by the difficulty to implement a parallel design of this decoder. We suggest a new method that based on product code that uses Reed-Solomon as column code and polar codes as rows code. We also suggest a decoding algorithm to this scheme that can improve significantly the parallelize of the decoder implementation. We show that the decoding throughput of this scheme can be up to 7 times faster than a regular polar decoder.
In the second part of this thesis, we deal with the problem of the high decoding complexity of polar codes over high alphabet size. Using high alphabet size can improve significantly the detecting performance of the polar codes. However, the decoding complexity increases exponentially with the alphabet size. We propose a new method, based on Hadamard transformation to decrease the decoding complexity of polar codes that based on high alphabet size. Our new method can reduce the computational complexity of those codes in up to 70%
