Joint Successive Cancellation List Decoding for the Double Polar Codes

Abstract

As a new joint source-channel coding scheme, the double polar (D-Polar) codes have been proposed recently. In this letter, a novel joint source-channel decoder, namely the joint successive cancellation list (J-SCL) decoder, is proposed to improve the decoding performance of the D-Polar codes. We merge the trellis of the source polar code and that of the channel polar code to construct a compound trellis. In this compound trellis, the variable nodes corresponding to the information bits of the channel polar code and the variable nodes representing the high-entropy bits are merged into the joint source-channel (JSC) nodes. Based on the compound trellis, the J-SCL decoder is designed to recover the source messages by combining the source SCL decoding and channel SCL decoding. The proposed J-SCL decoder doubles the number of the decoding paths for each JSC node and low-entropy node, and then discard all but the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> paths with the smallest joint path-metric (JPM). For the JSC node, the JPM is updated considering both the channel decision log-likelihood ratios (LLRs) and the source decision LLRs. Simulation results show that the J-SCL decoder outperforms the turbo-like BP (TL-BP) decoder with lower complexity.