Non-binary polar codes using Reed-Solomon codes and algebraic geometry codes
Non-binary polar codes using Reed-Solomon codes and algebraic geometry codes
复制标题
DOI：
10.1109/cig.2010.5592755
复制
发表时间：
2010-07
期刊：
影响因子：
--
通讯作者：
R. Mori;Toshiyuki TANAKA
中科院分区：
文献类型：
--
作者：
R. Mori;Toshiyuki TANAKA
Arıkan提出的Polar码在低编解码复杂度下实现了任意离散无记忆信道的对称容量。最近，人们对非二进制极性码进行了研究。本文通过数值模拟计算了基于Reed-Solomon矩阵构造的非二进制极性码的错误概率。经证实，在二进制输入 AWGN 信道上，4 进制极性码比二进制极性码具有明显更好的性能。我们还讨论了代数几何码对极坐标码的解释，并进一步表明使用埃尔米特码的极坐标码具有渐近良好的性能。
Polar codes, introduced by Arıkan, 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.