Abstract To ensure the reliable transmission with increased spectral efficiency of the small information block, this article proposes the novel distributed generalized Reed‐Solomon coded differential spatial modulation (DGRSC‐DSM) scheme in the relay cooperation manner. Two different generalized Reed‐Solomon (GRS) codes with identical lengths are deployed at the source and relay, respectively, where the relay utilizes the subcode of the GRS code, which can construct an ultimate code having a unique algebraic structure at the destination. In addition, the Global search algorithm (Algorithm 1) is developed to obtain an optimal selection mode at the relay, resulting in the final code with an optimal code weight enumeration. Since the complexity of this algorithm is extremely high, the low‐complexity Parity‐position local search algorithm (Algorithm 2) is then proposed to get the suboptimal mode. Monte‐Carlo results indicate that there is a minimal disparity in performance between the two proposed algorithms that both effectively enhance the system performance. Moreover, based on the optimized final code and the special construction of GRS code, the novel Smart‐joint decoding algorithm is first presented at the destination which can fully exploit two‐way information data and further lower the bit error rate (BER) of the DGRSC‐DSM scheme. Also, the analytical union bound of the proposed scheme is formulated over the quasi‐static Rayleigh fading channel, which illustrates a tight fit at the high signal‐to‐noise ratio (SNR) regions.

This paper introduces an adaptive technique for grouping variable nodes in decoding non-binary LDPC codes that involve symbol flipping. The technique considers both the individual symbol reliability and majority-based voting when grouping variable nodes in each iteration. Groups are formed based on the cumulative density of the variable nodes, with the least reliable variable nodes given the highest priority. The decoding algorithm then proceeds to decode subsequent groups in order of decreasing priority. The results of numerical analysis demonstrate that this approach strikes a balance between computational complexity and bit error rate performance, making it suitable for various applications, such as data storage and mobile networks.

Abstract The distributed Goppa coded spatial modulation (DGC‐SM) scheme is proposed in cooperative scenarios. In the proposed DGC‐SM scheme, the relay chooses the partial information from the source by using the idea of information selection, and then re‐encodes the selected information. At the destination, a distributed Goppa code is obtained corresponding to each selection. In order to get the best possible code, an optimal information selection algorithm is proposed at the relay. In the proposed optimal algorithm, all selections and source message sequences are considered, which results in high complexity. Thus, another optimized information selection algorithm with low complexity is proposed at the relay. To further enhance the capability to get the source information, two efficient joint decoding algorithms called smart decoding algorithm and improved smart decoding algorithm are proposed. Moreover, the bit error rate (BER) performance bound of the proposed DGC‐SM scheme is derived. Through the simulations, the effectiveness of the proposed two optimized information selection algorithms is confirmed. Also, it is observed that the simulation and analytical results closely match at high signal‐to‐noise ratio (SNR).

To achieve reliable and green communication in the internet of things (IoT) networks, the authors extend the traditional half‐duplex quantise‐and‐forward (QF) cooperation into the simultaneous wireless information and power transfer (SWIPT) regime. This study investigates the achievable rate of the SWIPT‐based half‐duplex QF cooperation with the channel state information available only at the receivers. The source and destination are provided by the external power supply and the relay simultaneously implements the information transmission and the energy harvesting by SWIPT technology with the power‐splitting protocol. The achievable rate of the proposed system over the additive white Gaussian noise channels is analysed and further maximised by optimising the power‐splitting factor. Furthermore, the expected rate of the proposed system over the slow‐fading channels is analysed. Theoretical analysis and simulation results show that the achievable rate or expected rate of the SWIPT‐based QF cooperation is obviously superior to that of the SWIPT‐based amplify‐and‐forward or SWIPT‐based decode‐and‐forward cooperation. Meanwhile, the SWIPT‐based QF cooperation can achieve similar performance to the traditional QF cooperation when the external power supply at the relay is not provided.

This research article proposes a multiple relay‐based Reed–Muller network‐coded cooperative (MR‐RMNCC) scheme for wireless communication. In the MR‐RMNCC scheme, Hadamard transform construction is adopted to build Reed–Muller (RM) codes that effectively achieve network coded‐cooperation among multiple sources and multiple relays over slow and fast Rayleigh fading channels. In any network coded‐cooperative system, a proper encoding strategy at the relay nodes is vital for achieving an optimum code construction at the destination node. Therefore, the authors have proposed an efficient message bit selection algorithm at relay‐2 that optimally selects the message bits. The supremacy of the message bit selection algorithm is demonstrated by Monte–Carlo simulation. Furthermore, the performance bound for average error‐probability is also derived for the MR‐RMNCC scheme that validates its simulated bit‐error‐rate performance over a fast Rayleigh fading channel. At the destination node, the MR‐RMNCC scheme is jointly decoded by two different decoding strategies, i.e. joint soft maximum likelihood decoding and joint majority logic decoding. Monte–Carlo simulations suggest that the MR‐RMNCC scheme not only provides a significant bit‐error‐rate performance gain over its corresponding coded non‐cooperative scheme but also to the existing state‐of‐the‐art RM network‐coded cooperative scheme under identical conditions.

A Plotkin‐based polar coded space–time spatial modulation scheme is proposed and its bit error rate (BER) performance over quasi‐static Rayleigh fading channel is evaluated. The exacerbated complexity in receiver design is ameliorated by employing a low complexity soft demapper for their proposed Plotkin‐based polar coded scheme. As there is a natural split present in the design of the considered Plotkin's construction, therefore the authors effectively extended their proposed scheme to coded‐cooperative scenarios. In any coded‐cooperative communication, the relay node always plays a pivotal role in determining the BER performance of communication system. Therefore, a rational selection criterion for selecting the information bits at the relay node is presented. The authors have also devised nested polar coded‐cooperative space–time spatial modulation (NPCCST‐SM) scheme as a useful benchmark. Monte‐Carlo simulated results revealed that their proposed coded‐cooperative scheme has triumphed conventional NPCCST‐SM scheme by a gain of 0.6–0.8 dB under identical conditions. Moreover, the proposed cooperative scheme outperforms its corresponding non‐cooperative counterpart scheme by a gain of 1–1.2 dB under identical conditions.

A multi‐level construction of polar‐coded single carrier frequency division multiple access (SC‐FDMA) with multiple input multiple output (MIMO) antennas scheme is proposed and its bit error rate performance over frequency selective Rayleigh fading channels has been evaluated. The existence of a parallel split in the design of multi‐level construction of polar code has enabled the authors to effectively extend the proposed scheme in coded cooperative scenarios. As in coded cooperation communication, the relay plays a crucial role in the design of communication system; therefore, an efficient selection criterion for reinforcing the bad channels has been adopted at the relay node. Moreover, the joint successive cancellation decoding is employed at the destination node. To check the efficacy in the performance of the proposed coded cooperative scheme, the authors have also upgraded the traditional nested polar‐coded cooperative scheme in the context of SC‐FDMA with MIMO antennas as a useful benchmark. Monte Carlo simulated results revealed that the proposed coded cooperative scheme have triumphed the conventional nested polar coded cooperative scheme based on SC‐FDMA system by gain of 0.5 dB under identical conditions. Moreover, the proposed cooperative schemes outperform their corresponding non‐cooperative counterpart schemes by the gain of 1 dB under identical conditions.

Recently, it is shown that the channel polarisation phenomenon of Arikan's polar codes with their original multilevel construction happens in several levels with perfect, partially perfect and useless bit channels. On the basis of this construction, this study aims to illustrate design principles and decoding steps of cooperative decode‐and‐forward polar coding schemes for half‐duplex relay channel. In these schemes, the authors consider the use of relay retransmission of partially perfect bit channels in time‐division process. The source node transmits its polar‐coded information to both the relay and the destination nodes during the first time slot. For the second transmission period, the relay first decodes the source signal then after reconstruction of the polarisation matrix, the extracted partially perfect bit channels are recoded using another polar code and finally transmitted to the destination node. At destination, the signals received from both source and relay nodes are processed by using multi‐stage successive cancellation decoding for retrieving the original information bits. They demonstrate via numerical results that by carefully constructed polarisation matrix at relay node, their cooperative polar coding schemes can achieve better performances than other previous schemes.

This study proposes an low density party check (LDPC)‐coded multi‐relay cooperation with receive multi‐antenna in the destination over a Rayleigh‐fading channel, where maximal ratio combining and belief propagation algorithm (BP)‐based joint iterative decoding based on the introduced multi‐layer Tanner graph are effectively designed to detect and decode the corrupted received sequence at the destination. The overall code rate from the destination is derived mathematically in relation to all the constituent LDPC codes employed by source and multiple relays. Theoretical analysis and numerical simulation show that the proposed approach can well combine diversity and coding gains, which consequently result in significant advantage over the conventional cooperations under the same conditions.

This paper describes a coded cooperative multiple-input multiple-output (MIMO) scheme, where structured low-density parity-check (LDPC) codes belonging to a family of repeat-accumulate (RA) codes are employed. The outage probability of the scheme over Rayleigh fading channels is deduced. In an unknown channel state information (CSI) scenario, adaptive transversal filters based on a spatio-temporal recursive least squares (ST-RLS) algorithm are adopted in the destination to realize receive diversity gain. Also, a joint ‘Min-Sum’ iterative decoding is effectively carried out in the destination. Such a decoding algorithm agrees with the bilayer Tanner graph that can be used to fully characterize two distinct structured LDPC codes employed by the source and relay. Simulation results verify the effectiveness of the adopted filter in the coded cooperative MIMO scheme. Theoretical analysis and numerical simulations show that the LDPC coded cooperative MIMO scheme can well combine cooperation diversity, multi-receive diversity, and channel coding gains, and clearly outperforms coded noncooperation schemes under the same conditions.

This letter proposes a strategy using a generalized Gaussian distribution (GGD) to characterize the extrinsic information generated from the constituent maximum a posteriori (MAP) decoders in order to improve the performance of an iterative turbo decoder for finite block lengths. A matching technique based on the measured moments and distance criterion is introduced to dynamically select the appropriate parameters of the GGD model for the extrinsic information in each iteration. The simulation results indicate that the proposed strategy can offer performance gain in medium block lengths over both additive white Gaussian noise and Rayleigh-fading channels.

A new strategy for iterative turbo decoding is proposed, where a class of symmetric Gaussian-like probability distributions are used to estimate the conditional probabilities of extrinsic values generated from branch detectors. A specific probability with a unique parameter is finally determined based on a proposed likelihood criterion of minimum estimated error bits for any detector in each iterative decoding. In this sense, the optimum distributions of the extrinsic values of iterative decoding are unveiled over AWGN, Rician and Rayleigh fading channels. The simulation results show that the decoding with this new technique has superior error performance to the traditional approach based on the conventional Gaussian law for the extrinsic values under the same channel conditions.