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.

This letter concentrates on the problem of spectral compressed sensing in impulsive noise, which aims to recover a spectrally sparse signal from its contaminated and undersampled measurements. We propose a robust formulation for joint sparse signal and frequency recovery, which includes the generalized ℓpnorm(02approach via majorizing the original objective function by a quadratic surrogate function. Simulation results illustrate that the proposed approach attains a significant performance improvement over the existing methods under impulsive noise.

This paper considers the sparse recovery problem of multiple measurement vector (MMV) model corrupted in impulsive noise. To ensure outlier-robust sparse recovery, we formulate an MMV problem that includes the generalized ℓp-norm (12,0joint sparsity-promoting regularizer. The joint sparse penalty, however, is non-continuous and hence non-differentiable, which inevitably raises difficulty in optimization when using a gradient-based method. To address this, we build a smooth approximation for the ℓ2,0-based sparse metric via the log-sum based sparse-encouraging surrogate function. Then, we propose a block successive upper-bound minimization algorithm for the smooth MMV problem by solving a series of subproblems based on the block coordinate descent (BCD) method. Furthermore, local convergence of the proposed algorithm to a stationary point of the smooth problem is proved. Experiments demonstrate its efficiency and robust recovery performance for suppressing impulsive noise.

This paper proposes two new cycle-optimized algorithms, called the multi-step progressive edge-growth (PEG) algorithm and the multi-step approximate cycle extrinsic message degree (ACE) constrained PEG algorithm, to design an LDPC code with larger girth and better cycle-connectivity. In addition, an efficient method is developed to calculate the distances between the variable nodes (VNs) and the check nodes (CNs) in the proposed algorithms. Simulation results show that compared to the conventional cycle-optimized algorithms, the proposed algorithms can achieve both better cycle-connectivity and foreseeable lower error floors.

From the co-array perspective, sparse spatial sampling can significantly increase the degrees-of-freedom (DOFs), enabling us to perform underdetermined direction-of-arrival (DOA) estimation. By leveraging the increased DOFs from the sparse spatial sampling, we develop a new underdetermined DOA estimation method for wideband signals, named wideband sparse spectrum fitting (W-SpSF) estimator. In W-SpSF, we formulate a sparse reconstruction problem that includes a quadratic$({\ell_2})$weighted covariance fitting term added to a sparsity-promoting$({\ell _{2, 1}})$regularizer. Meanwhile, the optimal regularization parameter of W-SpSF is studied to ensure robust sparse recovery. Numerical results enabled nested arrays demonstrate that the W-SpSF estimator outperforms the spatial smoothing based MUSIC algorithm and works well in nonuniform noise environment.

The authors consider the problem of energy consumption in a multiband cognitive radio network, in which a secondary user can sense multiple frequency bands authorised to the primary user (PU) before it decides to access some frequency bands and keep the interference introduced to the PU under a certain threshold. The sensing time and power allocation need to be designed carefully to reduce the energy consumption. Therefore they identify the optimal sensing time and accessing power to minimise the energy consumption of the cognitive radio that simultaneously senses and accesses multiple bands under the multiband sensing‐based spectrum sharing scheme. To obtain the optimal solution, they transform the original problem formulated as the ratio of two functions into another parametric formulation. The interference power is considered as one of constraints in the author's scheme in order to protect the PU. The algorithm of optimal sensing time and power allocation is proposed for the multiband cognitive radio system. Furthermore, they discuss the effect of channel number, interference power and gain estimation of channels on energy consumption and optimal sensing time and validate their schemes and analysis by simulation results.

In this study, the authors focus on energy efficiency of a cognitive radio (CR) system, in which a secondary user (SU) senses periodically and accesses opportunistically a specific band authorised to a primary user (PU). Based on a generalised expression of energy consumption, we jointly optimise sensing, transmission and frame durations to maximise the energy efficiency for a CR system and investigate the performance of the proposed design over Rayleigh fading channels. The problem of energy efficiency is formulated as a function of sensing and transmission durations with the constraints on the interference to the PU. To protect the PU, we limit the detection probability as well as restrict the interference caused by the SU because of the re‐occupancy of the PU. In a generalised model, energy consumptions of sensing, transmission and idling state need to be considered for the SU. The optimal sensing and transmission durations are obtained by a sub‐optimal iterative algorithm. The performance of energy efficiency and duration of the SU over a Rayleigh‐faded channel is investigated. Numerical results show that the proposed reduced‐complexity approach performs comparably with that of the exhaustive search algorithm.

We consider the joint exploitation of coding and diversity techniques to achieve efficient, reliable wireless transmission. The system of interest comprises a powerful non-binary low-density parity-check (LDPC) code that will be soft-decoded to supply strong error protection, a quadratic amplitude modulator (QAM) that directly takes in the non-binary LDPC symbols and will be soft-demodulated, and a modulation diversity (or signal space diversity, SSD) operator that will provide power- and bandwidth-efficient diversity gain. By relaxing the rate of the SSD rotation matrices to below 1, we show that a better rate allocation can be arranged between the LDPC codes and the SSD, which brings significant performance gain over previous systems. To facilitate the design and evaluation of the relaxed SSD rotation matrices, three types of efficient constructions are demonstrated and a set of four criteria are developed. Through analysis and simulations, we show that our strategies are very effective in combating random fading and strong noise on Rayleigh fading channels.