Construction of polar codes for channels with memory

Abstract

Polar codes for channels with memory are considered in this paper. ŗaşoğlu proved that Arikan's polarization applies to finite-state memory channels but practical decoding algorithms of polar codes for such channels have been unknown. This paper proposes a generalization of successive cancellation algorithm for channels with memory where the complexity is polynomial in the number of states. In addition, two polar coding scheme are proposed to generate codewords following non-i.i.d. process required to achieve the capacity. Whereas one is a simple application of the polar coding scheme for asymmetric memoryless channels, the other one combines a polar code with a fixed-to-variable length homophonic coding scheme, which can realize the input distribution exactly equal to the target process.