Abstract
Belief propagation (BP) decoding of polar codes, which can be executed in parallel, is suitable for low-latency applications. In this paper, we first give a sparse parity-check matrix representation for polar codes, based on which several strategies for performance improvement are proposed. We then devise a scheme of which the performance can approach the maximum-likelihood lower bound and that of successive cancellation list (SCL) decoding. For cyclic redundancy check (CRC)-concatenated polar codes, a parity-check matrix representation is also presented so that joint decoding between the CRC code and polar code is possible. An improved CRC-aided BP decoder is hence proposed with performance close to that of the state-of-the-art CRC-aided SCL decoder.