One-bit error boundary aided successive cancellation list decoding of polar codes

Abstract

Polar codes have emerged as a remarkable code in that the codes have capacity-achieving error-correcting performance, and low complexity encoding and decoding structures. Accordingly, it has been studied by many researchers and the CRC aided Successive Cancellation List (SCL) decoding of polar codes was adopted for channel coding scheme of the 5G communication standard for its outstanding error-correcting performance. However, the SCL decoding suffers from long latency since it essentially has a sequential decoding process. There are two methods to reduce the decoding latency of SCL. First, there is a method to decrease the overall number of decoding procedures by pruning the Successive Cancellation (SC) decoding tree. The other method is to lessen the number of splits which occupies a large part of the SCL decoding latency. In this paper, we analyze error probability of multi-bit nodes in the SC decoding tree of polar codes and propose a method which can reduce decoding latency with efficient multi-bit decoding, attributed to the phenomenon that there are many non-leaf nodes consisting of multiple bits with low probability of having 2 or more errors. We also propose a process to construct a boundary with such nodes and we decode multi-bit nodes on the boundary with splitting candidates only once at the nodes, instead of going further down to child nodes. It is shown that compared to the conventional SCL decoding when the list sizes are 2, 4, and 8, the proposed method reduces the overall decoding cycles by 69%, 70%, and 71% respectively, with almost no degradation of error-correcting performance. In addition, we can expect a further decoding cycles reduction by 11%, 12%, and 11% with small degradation of less than 0.3dB at target FER when list sizes are 2, 4, and 8, respectively.