Non-Binary Polar Codes using Reed-Solomon Codes and Algebraic Geometry Codes

Details Non-Binary Polar Codes using Reed-Solomon Codes and Algebraic Geometry Codes Non-Binary Polar Codes using Reed-Solomon Codes and Algebraic Geometry Codes

2010-07-21

arxiv.org/abs/1007.3661v1

Computer Science

Information Theory

5 pages, 3 figures, to appear in ITW 2010 Dublin

Scientific paper

Polar codes, introduced by Arikan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error probability of non-binary polar codes constructed on the basis of Reed-Solomon matrices by numerical simulations. It is confirmed that 4-ary polar codes have significantly better performance than binary polar codes on binary-input AWGN channel. We also discuss an interpretation of polar codes in terms of algebraic geometry codes, and further show that polar codes using Hermitian codes have asymptotically good performance.

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