This paper is concerned with sparse code multiple access (SCMA) with protograph-based low-density parity-check (P-LDPC) codes over Rayleigh fading channels. To be specific, we first propose a two-step design method consisting of both low-density factor graph (LDFG) and energy-based constellation superposition (ECS) principles to construct a new type of non-uniform codebooks (CBs), which have superior robustness against inter-user interference. We also develop a new segment-wise interleaved transmission (SWIT) scheme, which features a systematic optimization among repetition coding, resource mapping, and cross-slot data coupling, to further improve the performance of P-LDPC-coded SCMA. Additionally, we conceive a decoding-threshold-guided multi-objective optimization (DT-MOO) method to construct protograph-based enhanced multi-user codes (EMUCs), which exhibit excellent error-rate performance under both turbo and non-turbo decoding compared to traditional single-user and existing multi-user codes. Theoretical and simulated results validate the superiorities of proposed non-uniform SCMA scheme with SWIT and EMUCs compared to state-of-the-art benchmarks. Owing to the above advantages, the proposed designs are competent to provide massive connectivity and energy-efficient transmission for simultaneous wireless information and power transfer (SWIPT) applications in 6G networks.

The study of anytime codes over non-ergodic block-fading (BF) channels remains largely unexplored. To address this gap, we propose a novel root-protograph-based anytime (RP-anytime) coding framework and develop modified density evolution (DE) equations. Leveraging these equations, we introduce two performance metrics to evaluate the asymptotic behavior of RP-anytime codes under the assumption of infinite frame length: the average asymptotic bit error rate (BER), which characterizes anytime reliability, and the anytime outage region, which reflects the code’s ability to achieve full diversity. Using these metrics, we analyze the performance of the proposed RP-anytime codes and compare them with both root-protograph LDPC codes and conventional anytime codes. The results demonstrate the superiority of the RP-anytime structure in terms of reliability and diversity over non-ergodic BF channels. Furthermore, we employ a multi-objective differential evolution (MODE) algorithm to design optimized RP-anytime codes. Simulation results confirm that the newly designed codes achieve excellent anytime reliability, full diversity, and near-outage-limit error performance—significantly outperforming prior-art root-protograph LDPC codes and anytime codes.

To enhance the adaptability and performance of multi-stream transmissions over non-ergodic block fading (BF) channels, this paper studies a multilevel-priority incremental-redundancy hybrid ARQ (MP-IR-HARQ) system with nested root-protograph-based low-density parity-check (NRP-LDPC) codes. Specifically, we analyze the performance of traditional RP-LDPC codes and reveal that they are unable to achieve full diversity in the IR-HARQ system over non-ergodic BF channels. To address this limitation, we propose a design methodology to construct a family of NRP-LDPC codes having the full-diversity property, throughput-limit-approaching property, outage-limit-approaching performance, and rate compatibility tailored for the IR-HARQ system. Additionally, we incorporate a multilevel-priority design composed of the adaptive modulation, adaptive detection, and successive decoding into the traditional IR-HARQ framework. The designed MP-IR-HARQ system can support the transmission of multiple data streams while providing unequal error protection (UEP) across them. The outage-boundary analyses, throughput analyses, and word-error-rate (WER) simulations demonstrate that the proposed NRP-LDPC-coded MP-IR-HARQ system can not only significantly outperform prior-art counterparts over non-ergodic BF channels, but also enable the multi-data-stream-based UEP transmission.

Anytime code is a new class of error-correcting code that has very long coding memory and is decodable with flexible decoding window size (decoding delay). It is designed for real-time reliable applications, such as tracking and controlling unstable systems. In this paper, we construct a family of rate-compatible (RC) Anytime code ensembles with code rate from 0 to 1 based on spatially coupled repeat-accumulate (SC-RA) codes and apply them to the automatic-repeat-request (ARQ) communication with incremental redundancy. Using density evolution (DE) analysis, we prove that each element code within the RC family has superior Anytime-reliable properties over the binary erasure channel (BEC) and the binary-input additive white Gaussian noise (BI-AWGN) channel. In addition, we develop an expanding-window IR-HARQ (incremental redundancy hybrid automatic-repeat-request) scheme for the proposed RC Anytime codes. Simulation results testify that our proposed RC Anytime codes have better decoding performance than the prior-art RC Anytime codes. Furthermore, when combined with the proposed expanding-window IR-HARQ scheme, our proposed RC Anytime codes show significant advantages over the conventional RC low-density parity-check (LDPC) codes and RC polar codes in the conventional CRC-based IR-HARQ communication systems.

In our early work, we proposed a class of joint source channel anytime coding (JSCAC) scheme based on spatially coupled repeat-accumulate (SC-RA) codes, in addition to an improved partial joint expanding window decoding (PJEWD) algorithm. In this paper, we extend our preliminary results and make a comprehensive theoretical analysis for this system. First, we propose an improved density evolution (DE) algorithm for the SC-RA based JSCAC with PJEWD scheme. Based on the proposed DE algorithm, we systematically analyze the anytime property, the belief propagation (BP) decoding threshold, and the decoding complexity of this system over binary additive white Gaussian noise channel (BIAWGN), as well as the effects of code parameters on performances of the above three aspects. Moreover, we explore some application scenarios for JSCAC schemes, where it could maximize its advantages over the prior-art JSCC schemes. Both numerical and simulation results demonstrate the potentials of the proposed JSCAC scheme for high reliability and low latency communications. The proposed DE algorithm could also provide a good reference for the analysis of other JSCAC systems.

Algebraic codes such as BCH code are receiving renewed interest as their short block lengths and low/no error floors make them attractive for ultra-reliable low-latency communications (URLLC) in 5G wireless networks. This article aims at enhancing the traditional adaptive belief propagation (ABP) decoding, which is a soft-in-soft-out (SISO) decoding for high-density parity-check (HDPC) algebraic codes, such as Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem (BCH) codes, and product codes. The key idea of traditional ABP is to sparsify certain columns of the parity-check matrix corresponding to the least reliable bits with small log-likelihood-ratio (LLR) values. This sparsification strategy may not be optimal when some bits have large LLR magnitudes but wrong signs. Motivated by this observation, we propose a Perturbed ABP (P-ABP) to incorporate a small number of unstable bits with large LLRs into the sparsification operation of the parity-check matrix. In addition, we propose to apply partial layered scheduling or hybrid dynamic scheduling to further enhance the performance of P-ABP. Simulation results show that our proposed decoding algorithms lead to improved error correction performances and faster convergence rates than the prior-art ABP variants.

Joint source channel coding (JSCC) is an effective technique in the non-asymptotic and low latency regime, while suffers from high error floor for sequences with high source probabilities and short block-lengths (HSP-SB). Aiming to address this issue, a joint source channel anytime coding (JSCAC) based on the anytime spatially coupled repeat-accumulate (ASC-RA) codes is presented. In the proposed JSCAC scheme, the adopted exponential distributed coupling (EDC) and partial joint expanding window decoding (PJEWD) can efficiently recover the early transmitted HSP-SB messages that are not fully corrected. Meanwhile, the updating mechanisms in the proposed PJEWD mitigate the complexity of expanding window decoding and the error propagation between the source and channel decoders, attributing to a better error performance. The proposed JSCAC is suitable for HSP-SB source transmission, which is a competitive candidate for communications with high reliability and low delay demands, such as streaming source and control applications, etc.