Generalized Partially Information Coupled Polar Codes With Arbitrary Coupling Depth and Their Decoding Algorithms

Abstract

We propose generalized partially information coupled (PIC) polar codes and their construction method. In the proposed codes, each code block (CB) shares systematic information bits partially with $J$ adjacent CBs on each side, where $J$ is referred to as the coupling depth. The conventional PIC polar code is a special case of the generalized PIC polar codes for $J=1$ . We modify the polar CB decoding and propose various inter-CB decoding schemes which apply to the code of arbitrary coupling depth $J$ . We also propose a low complexity evaluation method for the error rate of the generalized PIC polar codes, without channel generation and decoding operation. Numerical results show that this approximate evaluation is very accurate. It is verified by simulation that more coding gain can be attained for $J\ge 2$ . Finally, we compare the decoding complexities of the conventional inter-CB decoding algorithms and the proposed algorithms with which a lower decoding complexity is achieved without performance degradation.