Polarization-adjusted convolutional (PAC) codes have better error-correcting performance than polar codes mostly because of the improved weight distribution brought by the convolutional pre-transformation. In this paper, we propose the parity check PAC (PC-PAC) codes to further improve error-correcting performance of PAC codes. The design principle is to establish parity check functions between bits with distinct row weights, such that information bits of lower reliability are re-protected by the PC relation. Moreover, an algorithm to select which bits to be involved in parity-check functions is also proposed to make sure that the constructed codes have fewer minimum-weight codewords. Simulation results show that the proposed PC-PAC codes can achieve nearly 0.2dB gain over PAC codes at frame error rate (FER) about 10-3 codes.

In this letter, a deep neural network (DNN) aided joint source-channel (JSCC) decoding scheme is proposed for polar codes. In the proposed scheme, an integrated factor graph with an unfolded structure is first designed. Then a DNN aided flooding belief propagation decoding (FBP) algorithm is proposed based on the integrated factor, in which both source and channel scaling parameters in the BP decoding are optimized for better performance. Experimental results show that, with the proposed DNN aided FBP decoder, the polar coded JSCC scheme can have about 2-2.5 dB gain over different source statistics p with source message length NSC = 128 and 0.2-1 dB gain over different source statistics p with source message length NSC = 512 over the polar coded JSCC system with existing BP decoder.