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.

Kudekar et al. proved an interesting result in low-density parity-check (LDPC) convolutional codes: The belief-propagation (BP) threshold is boosted to the maximum-a-posteriori (MAP) threshold by spatial coupling. Furthermore, the authors showed that the BP threshold for code-division multiple-access (CDMA) systems is improved up to the optimal one via spatial coupling. In this letter, a phenomenological model for elucidating the essence of these phenomenon, called threshold improvement, is proposed. The main result implies that threshold improvement occurs for spatially-coupled general graphical models.

In this letter, we propose a new modification to the belief propagation (BP) decoding algorithm for Finite-Geometry low-density parity-check (LDPC) codes. The modification is based on introducing feedback into the iterative process, which can break the oscillations of bit log-likelihood ratio (LLR) values. Simulations show that, with a given maximum iteration, the "feedback BP" (FBP) algorithm can achieve better performance than the conventional belief propagation algorithm.

Recently, low-density parity-check (LDPC) codes have attracted much attention. LDPC codes can achieve the near Shannon limit performance like turbo codes. For the LDPC codes, the reduced complexity decoding algorithms referred to as uniformly most powerful (UMP) BP- and normalized BP-based algorithms were proposed for BPSK on an additive white Gaussian noise (AWGN) channel. The conventional BP and BP-based algorithms can be applied to BPSK modulation. For high bit-rate transmission, multilevel modulation is preferred. Thus, the BP algorithm for multilevel modulations is proposed in . In this paper, we propose the BP algorithm with reduced complexity for multilevel modulations, where the first likelihood of the proposed BP algorithm is modified to adjust multilevel modulations. We compare the error rate performance of the proposed algorithm with that of the conventional algorithm on AWGN and flat Rayleigh fading channels. We also propose the UMP BP- and normalized BP-based algorithms for multilevel modulations on AWGN and flat Rayleigh fading channels. We show that the error rate performance of the proposed BP algorithm is almost identical to that of the algorithm in, where the decoding complexity of the proposed BP algorithm is less than that of the algorithm in. We also show that the proposed BP-based algorithms can achieve the good trade-off between the complexity and the error rate performance.