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.

In this paper, we consider pilot-aided channel estimation and equalization for single-carrier and single-carrier frequency division multiple-access (SC-FDMA) transmission over doubly-selective channels (DSC). To reduce the channel estimation (CE) parameters, the DSC is modelled using a complex-exponential basis expansion model (CX-BEM) with non-uniform BEM frequencies. We optimize the CX-BEM basis functions using CE error minimization as the objective. As a result, the channel modelling error is greatly reduced. Next, we propose a BEM-based per-survivor processing (PSP) technique and combine it with a decision-directed channel estimator to obtain a channel-tracking equalizer at the receiver. The resultant BEM-PSP receiver significantly improves the channel estimation mean square error (MSE) and the bit error rates (BER) performance in fast fading multi-path channel, thanks to the channel tracking capability embedded within its Viterbi equalizer. Finally, we employ cross-frame channel interpolation, and power distribution between the data and pilot symbols to further improve the system performance at high fading rates. Extensive simulation results show that our BEM-PSP receiver outperforms many existing methods and approaches close to an ideal receiver with perfectly known CSI under various fading scenarios.