Bit-interleaved coded modulation with iterative decoding (BICM-ID) is a key technology enabling communication systems to realize high-throughput and high-reliability. In contrast to previous studies focused exclusively on uniformly distributed sources, this work investigates irregular mapping (IM)-based BICM-ID systems for sources with non-uniform distributions. First, a density evolution (DE) algorithm based on Gaussian weighted mixture approximation (GWMA) is put forward to estimate the convergence performance of the IM-BICM-ID systems with non-uniform sources, where the probability density function of the log-likelihood ratio messages output from the bit-level channels in this system is neither Gaussian nor symmetric. Then, by employing the GWMA-DE algorithm and the achievable system rates analysis, a design strategy for optimal IM labelings is established, which utilizes the inherent redundancy in non-uniform sources to achieve shaping gains. Furthermore, channel codes tailored to the proposed IM labelings are designed to further improve the bit error rate performance. Both analytical results and simulations indicate that the proposed labelings and codes outperform existing counterparts in IM-BICM-ID systems with non-uniform sources.

Due to the duality between source coding and channel coding, high-performance channel codes are often adopted for addressing source coding problems. In this paper, we investigate the design and analysis of protograph low-density parity-check (P-LDPC) codes in lossy source coding systems. First, we propose a novel lossy source coding architecture based on P-LDPC codes, and empirically verify that although high-performance channel codes perform exceptionally well in their intended domain, they are not inherently optimal for lossy compression. To facilitate analysis, we introduce the lossy compression protograph extrinsic information transfer (LC-PEXIT) algorithm, which aids in evaluating the rate-distortion (RD) performance of P-LDPC codes. Additionally, the LC-PEXIT algorithm allows for the prediction of key parameters, such as the prior coefficientPand the reinforcement rateR, both of which critically influence system performance. We further propose a design algorithm for lossy P-LDPC codes and provide two sets of design examples. Experimental results show strong alignment between the predicted and actual values ofPandRf, with the designed P-LDPC codes exhibiting superior RD performance compared to classical P-LDPC and state-of-the-art ultra-sparse LDPC (US-LDPC) codes. In particular, the designed P-LDPC codes over benchmark codes increases the system coding efficiency of up to approximate 70% and achieves a performance gain of 1.69 ~ 3.26 dB, making it highly effective for lossy compression applications.

This letter proposes a high-order probabilistic shaped (PS) system for joint source-channel coding (JSCC) using polar codes, which are employed for both source compression and channel coding. The modulation is based on a selection rule derived from the proposed bit classification distribution matching (BCDM) algorithm. An external binary random sequence is used to select and redundantly insert the codeword sequence, which makes the modulation symbol probability approach the Gaussian distribution, instead of being uniformly distributed as in the conventional constellation mapping. At the receiver, a joint belief propagation (JBP) decoder, which consists of a source and a channel BP decoder, is applied. Simulation results demonstrate that the proposed PS joint source-channel polar-coded modulation (PS-JSCPCM) system yields a significant enhancement to the bit error rate (BER) performance compared with the traditional unshaped joint source-channel code-modulation (JSCCM) system.

This paper investigates the possibilities of optimizing existing protograph low-density parity-check (PLDPC) codes and designing optimal PLDPC codes on both AWGN and Rayleigh channels under binary modulation with unequal power allocation (UPA) for nonuniform sources. While the binary UPA modulation achieves a power gain, it also results in unequal error protection on the coded bits in systematic codewords during transmission. For irregular codes, it is possible to best protect the information bits by optimizing the classification of variable nodes (VNs). Those VNs represent the coded bits in protograph that allows exploiting jointly the degree irregularity and the power differentiation. An algorithm for UPA-based protograph extrinsic information transfer (UPA-PEXIT) analysis on the Rayleigh channel is proposed with the concept of surrogate channel which circumvents the channel asymmetry problem with UPA. With the RJA code as example, it is shown that classification optimization does improve the decoding threshold when the source entropy is small. To design optimal codes, a UPA-based differential evolution (UPA-DE) algorithm is proposed in conjunction with the UPA-PEXIT analysis. A family of optimized codes are illustrated for three typical nonuniform source distributions and compared with the RJA and NND codes by simulations in error rate performance.

Probabilistic amplitude shaping (PAS) has proved to be a promising way to achieve the shaping gain for an additive white Gaussian noise channel with a distribution matcher (DM). However, the DM schemes may suffer a rate loss and increase both complexity and latency, when they are not suited for the input bit stream with redundancy. In this paper, a novel PAS strategy is proposed for a joint source and channel coded modulation system, where the residual source redundancy after source coding can be exploited to obtain both shaping and coding gains. It is shown that the residual source redundancy can be controlled by choosing the row weight distribution for source code, thus making the probability distribution of the modulated symbols be optimized under an appropriate interleaver design. To guarantee the error-floor performance, the source code is constrained by predicting the probability distribution of source bits within target finite-length frames. By jointly designing source and channel codes, the residual source redundancy can also be exploited to achieve the coding gain. Compared with the state-of-the-art code pairs, the proposed code pairs have better error-floor performance, and achieve higher coding and shaping gains without suffering from the rate-loss and the latency caused by DM.

Double protograph low-density parity-check code has been shown to be a good solution for joint source-channel coding. Moreover, the source code and channel code (as one code pair) can be jointly optimized to achieve a good bit error rate (BER) performance. In this paper, first, an optimal design criterion of this code pair based on an extended curve-fitting algorithm is proposed. Second, a joint optimization procedure which searches for both the optimal decoding threshold and the optimal code pair is presented. In addition, for short-to-moderate-length codewords, the finite-length effect cannot be ignored and the procedure has to be modified with a new notion named length-N decoding threshold. The protograph extrinsic information transfer analysis and the BER simulation have shown that our optimized code pairs acquire lower decoding thresholds than conventional code pairs. Moreover, the optimized code pairs with short-to-moderate-length codewords can mitigate the finite-length effect and obtain low length-N decoding thresholds.