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Polar codes, introduced by Arikan, achieve symmetric capacity of any discretememoryless channels under low encoding and decoding complexity. Recently,non-binary polar codes have been investigated. In this paper, we calculateerror probability of non-binary polar codes constructed on the basis ofReed-Solomon matrices by numerical simulations. It is confirmed that 4-arypolar codes have significantly better performance than binary polar codes onbinary-input AWGN channel. We also discuss an interpretation of polar codes interms of algebraic geometry codes, and further show that polar codes usingHermitian codes have asymptotically good performance.

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