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The residual belief propagation (RBP) algorithm, which is the most classic informed dynamic scheduling strategy, achieves outstanding performance in error correction and can drastically accelerate convergence speed. However, the greedy algorithmic property of this iterative decoding will inevitably cause loss of decoding performance. To address this, a novel algorithm called the partial average bundle residual belief propagation (PABRBP) is proposed in this paper. According to the construction characteristics of a base matrix of protograph‐LDPC codes, informed dynamic scheduling (IDS) strategies are applied to an edge bundle of base matrices for the first time. This edge bundle of the base matrix can be applied to a corresponding cyclic permutation matrix. Furthermore, the update level of each bundle is determined by the value of the Partially Average Bundle Residual (PABR). Therefore, the edge message with the maximum residual in each bundle is updated in order, and the process of iterative decoding is less likely to become trapped in a local optimum. Additionally, the generation of silent nodes is reduced as much as possible. To further improve the PABRBP decoding performance for medium and long codes over the fading channel, the adjusted compensation term is periodically introduced. Analysis and simulation results show that PABRBP demonstrates a notable convergence quality and decoding performance improvement over the fading channels compared to existing state‐of‐art IDS algorithms. [ABSTRACT FROM AUTHOR]

Polar codes have received widespread attention because of their excellent performance. However, although successive cancellation (SC)‐based decoding algorithms have achieved excellent error correction performance, they still encounter large time delays in decoding because a serial decoding structure is employed. At present, a cyclic redundancy check (CRC) is used to judge whether the decoding result of a frame is erroneous. To obtain such a result, the decoder has to wait until the end of decoding. In this work, a judgement strategy for error frames using frozen bits is proposed. With the proposed strategy, the recognition of erroneously decoded frames can be achieved based on the error state of the frozen bits in this frame. Accordingly, early termination of decoding can be realized. By using this mechanism, the strategy can also be applied in the SC List algorithm to prune the path. In addition, the SC Flip decoding algorithm can also use the proposed strategy to help find the first error message bit. The experimental results show that at least 85% of the frames decoded erroneously can be recognized by the proposed strategy so that decoding can be terminated in advance and computational resources can be saved. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

A latest coding scheme named polarization‐adjusted convolutional (PAC) codes is shown to approach the dispersion bound for the code (128,64) under list decoding. However, to achieve the near‐bound performance, the list size of list decoding needs to be excessively large, which leads to insufferable time complexity. In this paper, to improve the speed of list decoding, fast list decoders for PAC codes are proposed. Four types of constituent nodes are defined and fast list decoding algorithms are provided for each of them. Simulation results present that fast list decoding with three types of constituent nodes can yield exactly the same error‐correction performance as list decoding, and reduce more than 50% time steps for the code (128,64). Moreover, fast list decoding with four types of constituent nodes can further reduce decoding complexity with negligible performance degradation. [ABSTRACT FROM AUTHOR]

Frequency‐time selective fading degrades the performance of communication systems, but it also provides an opportunity to collect multipath diversity and Doppler diversity. In this paper, an oversampled grouped‐linear‐constellation‐precoding (GLCP) scheme is proposed for orthogonal frequency division multiplexing (OFDM) systems to extract the diversity inherent in doubly selective fading channels. In the proposed scheme, GLCP is employed to precode the information symbols of OFDM at the transmitter, and the precoded OFDM symbols are oversampled in the time domain at the receiver. A full‐groups maximum likelihood (ML) decoder and a successive group decoder to decode the oversampled OFDM symbols with diversity gains are developed. The successive group decoder combines the group ML decoding algorithm with a block‐decision‐feedback‐equalization (BDFE) algorithm. The proposed scheme can take advantage of both the GLCP scheme and the oversampling scheme to achieve multipath diversity gains and Doppler diversity gains in doubly selective fading channels. Simulation results show that the proposed scheme can significantly improve the performance of OFDM systems in the frequency selective fading channel and the doubly selective fading channel in terms of bit error ratio, indicating that the diversity gains can be greatly enhanced by the proposed scheme in doubly selective fading channels. [ABSTRACT FROM AUTHOR]

This work studies the equalization methods for the reduced zero‐padding version of the orthogonal time frequency space modulation. Here, the focus is on applications in low data rate scenarios such as the Internet of Things, and the case where the number of subcarriers and time slots are small will be considered. First, the system equation is established to model the inter‐subcarrier and inter‐slot interference phenomena. Based on the system model, three sphere‐decoding based equalization methods are proposed. The first method is to directly apply the sphere‐decoding algorithm on the full‐scale system model; for the second method, the transmitter needs to perform the triangular precoding; and for the third method, the transmitter needs to perform the diagonal precoding. Simulation results show that the proposed sphere‐decoding based methods achieve better bit error rate performance than the state‐of‐the‐art methods like message passing, unitary approximate message passing, and variational approximate message passing, especially when the channel has severe inter‐slot interference. [ABSTRACT FROM AUTHOR]

The successive cancellation flip (SC Flip) decoding algorithm was recently suggested for decoding polar codes, which could improve the performance of the frame error rate (FER). The performance of the SC Flip (SCF) decoding algorithm is strong, and its computational complexity tends to be the same as that of the SC decoder at medium to high signal‐to‐noise ratios (SNRs). However, the decoding latency of the SCF decoding algorithm is large. In this paper, a new method for detecting whether or not the flipped bit is correct is proposed. The proposed method makes a decision according to the changing log likelihood ratio (LLR) value caused by the flipped bit to ensure that the decoding process can be terminated in advance and the decoding latency is reduced. The simulation results show that the proposed Latency‐Reduced SCF decoding algorithm can decrease computational complexity and decoding latency, while also achieving similar decoding performance compared to its counterpart. [ABSTRACT FROM AUTHOR]

The informed dynamic scheduling (IDS) strategies, in which the edge message with the maximum message‐residual is updated preferentially, achieve remarkable error‐correction performance when applied to low‐density parity‐check (LDPC) codes. However, the IDS strategies incur inferior convergence in iterative decoding owing to the greedy problem, which is called the update‐relayed trend here. In order to solve the greediness, two locally informed dynamic scheduling algorithms based on the law of large numbers are proposed. The proposed decoding algorithms use random select of check nodes over a predefined update range (RSPUR) which effectively suppresses the propagation of the update‐relayed trend and accordingly restrains the forming of multi‐update cycles. Moreover, the decoding algorithm is further improved based on random select of check nodes over an adjustable update range (RSCAR). The update ranges are selected based on the law of large numbers. Therefore, the computational resources can be allocated more equitably by increasing iterations. Simulation results show that both the proposed algorithms achieve excellent performance in terms of throughput and convergence with low decoding complexity over the Additive White Gaussian Noise (AWGN) and the fading channels compared to the previous IDS strategies. Hence, the proposed algorithms behave excellently over the wireless channels. [ABSTRACT FROM AUTHOR]

Hollmann built a theoretical framework for subspace regenerating storage code. In this framework, a storage node is equipped with a constant dimension subspace chosen from an overall message space Fqm${\bm{F}}_{\bm{q}}^{\bm{m}}$. The projection of user message on the subspace is stored on the corresponding node. A subspace code needs to fulfil decoding and repairing functionality. The framework stipulates the property for subspace storage code, but a simple implementable construction is still missing. To decrease the complexity of code design as well as encoding and decoding, this article proposed a subspace code implementation over F2 with the parameters of (m,m,2,⌈m2⌉,r,β)$({\bm{m}},{\bm{m}},2,\lceil {\frac{{\bm{m}}}{2}} \rceil ,{\bm{\ r}},{\bm{\beta }})$. It is proved theoretically the code is characterized by minimum decoding bandwidth, minimum storage, and exact repair. Still, the code is explicit, feasible and lightweight. A series of examples are given to elucidate the encoding, decoding and repairing procedures, which show in cases of m ≤ 5, the code could achieve high repair efficiency by combining with network coding. [ABSTRACT FROM AUTHOR]

Luby transform (LT) codes have received less attention in larger non-binary fields. Robust soliton distribution (RSD) was designed to provide universal optimality over the binary erasure channel in terms of minimising the overhead. In this study, the authors introduce a fundamental degree distribution (FDD), which when used with non-binary LT codes, outperforms their binary counterparts using the RSD in terms of error rate and realised code rate. For instance, over an additive white Gaussian noise (AWGN) channel at Eb/N0 of 12 dB and a rateless criteria (zero error probability), a non-systematic 4-ary LT code using the FDD can achieve a code rate of 0.75, compared to its binary counterpart which only achieves a code rate of 0.7. [ABSTRACT FROM AUTHOR]

In this study, the authors investigate the use of combined belief propagation (BP), mean field (MF) and expectation propagation (EP) message passing to achieve joint channel estimation and decoding (JCED) for orthogonal frequency division multiplexing where the channel sparsity is exploited, and a low-complexity BP-MF-EP-based JCED receiver is designed. Moreover, comparisons in message updating of state-of-the-art message passing-based JCED receivers are provided to illustrate the merits of the proposed one. In addition, message passing schedules are optimised to achieve better system performance. Simulation results verify the superiority of the proposed combined message passing receiver in terms of both bit-error-rate performance and convergence speed. [ABSTRACT FROM AUTHOR]

Sparse code multiple access (SCMA) is a promising candidate air interface of the next generation mobile networks. However, the decoding complexity of current message passing algorithm for SCMA is very high. In this study, the authors map SCMA constellation to q-order Galois field (GF(q)) and introduce a trellis representation to SCMA. Based on the trellis representation, they propose low-complexity decoding algorithms for SCMA by using truncated messages, which is referred as extended max-log (EML) algorithm. As the truncated length of EML is unitary for each user, they further propose a channel-adaptive EMLalgorithm to truncate the messages with a rule that can be adaptive to the channel state. Simulation results show that the proposed schemes obtain a low computational complexity with only a slight performance degradation when the truncated length is selected appropriately. [ABSTRACT FROM AUTHOR]

The Luby transform (LT) code is the first practical implementation of the digital fountain code, and its utilisation over a noisy channel invokes iterative decoding with soft information. For a good decoding performance, the role of the encoder degree distribution is vital. Especially, when utilising the soft iterative decoder, the bit error rate (BER) performance of the LT code can be improved by increasing the number of the degree-1 encoding nodes and reducing the number of lower-degree variable nodes. This study proposes an efficient LT-code encoding algorithm that satisfies the conditions for improving the BER performance. The proposed scheme applies different priorities for selecting the neighbouring source nodes for given degrees of the encoding nodes. The simulation results demonstrate that the proposed scheme outperforms the existing schemes. [ABSTRACT FROM AUTHOR]

By multiplexing waveform mapped with shifting and weighted symbols, overlapped x domain multiplexing (OVXDM) encoding scheme can obtain high spectral efficiency under a low signal-to-noise ratio. Though the maximum likelihood sequence detection decoders can obtain the optimal decoding performance, their computational complexities which increase exponentially with spectral efficiency in OVXDM are unbearable for practical implementations. In this study, a low-complexity multiple-signal joint decoding (MSJD) algorithm for OVXDM signalling is proposed over additive white Gaussian noise (AWGN) channel and extended to frequency selective fading (FSF) channel. Based on a novel joint information-based metric, the proposed algorithm utilises information of each transmitted symbol contained in multiple received signals, and selects the proper number of received signals for decoding to achieve performance maximisation. Moreover, theoretical analysis is provided for the proposed algorithm in both AWGN and FSF channels, which indicates the relationship between performance and number of received signals under different OVXDM encoding parameters including multiplexing waveform and overlapping fold. Simulation results confirm the superior performance of the MSJD algorithm in terms of decoding performance and computational complexity compared with the present approaches. [ABSTRACT FROM AUTHOR]

A novel concatenated physical-layer encryption (CPLE) scheme is proposed in this study, where better security can be achieved as well as reliability advantage. In CPLE scheme, the encryption is embedded in rateless encoding. The secret key, which is generated from wireless channel, controls the random degree and random linear combination. The rateless codes are also concatenated with other conventional channel codes, which can achieve better reliability. Different from security codes, both the security and reliability in the proposed scheme can be improved. Furthermore, there is no extra computation requirement on decoding process. Security analysis is presented including time complexity comparison and attacks resistance in practical application. Compared to other PLE schemes, the proposed scheme achieves lower complexity, and higher channel adaptation and performance advantage. On the basis of National Institute of Standards and Technology statistical test suite, CPLE scheme can achieve randomness as the traditional cipher system such as advanced encryption standard. Furthermore, simulation results show that the CPLE scheme outperforms the conventional concatenated codes at the same coderate. [ABSTRACT FROM AUTHOR]

The authors study the problem of two-user Gaussian multiple access channel (GMAC) in the presence of an external eavesdropper, where all transmitted messages should be kept confidential against the eavesdropper. For this purpose, they propose a secure coding scheme on this channel which utilises low-density parity-check (LDPC) codes by employing random bit insertion and puncturing techniques. At each encoder, the confidential message with some random bits as a random message are systematically encoded, and then the associated bits to the confidential message are punctured. Next, the encoders send their unpunctured bits over a Gaussian multiple access wiretap channel (GMAC-WT). The puncturing distribution applied to the LDPC code is considered in random and optimised cases. They utilise a modified extrinsic information transfer chart analysis to optimise the puncturing distributions. The security gap is used as a measure of secrecy. They compared the achieved secure rate pair with an achievable secrecy rate region of GMAC-WT to show the effective performance of the proposed scheme. In this study, equal and unequal power conditions at the transmitters are investigated. For both cases, they attain a fairly small security gap which is equivalent to achieve the points near the secrecy rate region of GMAC-WT. [ABSTRACT FROM AUTHOR]

Unequal error protection (UEP) divides the data into different levels of importance in order to ensure that the most important parts of the source information have more protection than the less important parts. In this study, the authors investigate the application of UEP using polar codes and propose a technique that utilises the channel polarisation property of these codes to achieve UEP without any significant modification. They demonstrate the error bounds of the proposed technique particularly within the context of JPEG2000. In addition, they propose a joint source-channel decoding method that is based on iterative decoding. This method takes the advantage of the error resilience tools that already exist in the JPEG2000 decoder. It will be shown that the proposed technique offers better performance than the conventional transmission with equal error protection. [ABSTRACT FROM AUTHOR]

Expanding window fountain (EWF) codes use a windowing technique to achieve unequal error protection (UEP) and unequal recovery time. UEP affords significant performance improvement of the more important bits (MIB), but at the cost of performance deterioration of the less important bits (LIB), resulting in poor intermediate performance of the EWF coding. In this study, the authors propose the utilisation of intermediate feedback in EWF coding to terminate the encoding of the MIB after their recovery, with the purpose of enhancing the intermediate performance of EWF codes over binary input additive white Gaussian noise (BIAWGN) channels. The effectiveness of the proposed coding scheme is analysed and evaluated by using extrinsic information transfer functions to investigate the theoretical performance and obtain the closed-form formula of the bit error rate (BER) of the LIB after the intermediate feedback. The results of the theoretical analysis and simulation of the scheme using additive white Gaussian noises with different signal-to-noise ratios reveal an improvement in the BER performance of the LIB compared to the case of conventional EWF coding, and also show that the scheme significantly enhances the intermediate performance of the EWF codes and improves the transmission efficiency. [ABSTRACT FROM AUTHOR]

A rate adaption scheme is given at the receiver using rateless codes and log-likelihood ratio (LLR) threshold-based adaptive demodulation (ADM). The received bits with LLR absolute values higher than the preset threshold are demodulated by the receiver, otherwise, deleted. Through the theoretical analysis of the average mutual information (MI) of the demodulated bits, the method is obtained to calculate the LLR demodulation threshold under the required error performance after decoding and the constraint of codeword length for decoding. Then, the rate adaption scheme is applied in a parallel multiple relay wireless communication system. The LLR threshold is set according to the instantaneous SNR of the received signals in order to keep the average MI per demodulated bit of each relay link the same. The demodulated bits coming from all links are combined for decoding. The 256-QAM constellation and Raptor code are then considered as a special case to design a sample scheme. Simulation results prove the correctness of the theoretical analysis and the feasibility of the proposed scheme, and when it is employed by a multi-relay transmission system, the diversity gain can be obtained, and the anti-fading and the antijamming abilities of the system are promoted. [ABSTRACT FROM AUTHOR]

The physical layer security in the up-link of the wireless communication systems is often modelled as the multiple access wiretap channel (MAC-WT), and recently it has received a lot attention. In this paper, the MAC-WT has been re-visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC-WT with noiseless feedback. Inner and outer bounds on the secrecy capacity region of this feedback model are provided. To be specific, we first present a decode-and-forward (DF) inner bound on the secrecy capacity region of this feedback model, and this bound is constructed by allowing each transmitter to decode the other one's transmitted message from the feedback, and then each transmitter uses the decoded message to reencode his own messages, i.e. this DF inner bound allows the independent transmitters to co-operate with each other. Then, we provide a hybrid inner bound which is strictly larger than the DF inner bound, and it is constructed by using the feedback as a tool not only to allow the independent transmitters to co-operate with each other but also to generate two secret keys, respectively, shared between the legitimate receiver and the two transmitters. Finally, we give a sato-type outer bound on the secrecy capacity region of this feedback model. The results of this paper are further explained via a Gaussian example, and from this example, we see that the noiseless feedback helps to enhance the achievable secrecy rate region of the Gaussian MAC-WT without feedback. [ABSTRACT FROM AUTHOR]

In this study, the authors propose a new two-stage decoding scheme for low-density parity-check codes to lower the error-floor, which consists of the conventional belief propagation (BP) decoding algorithm as the first-stage decoding and the redecodings with manipulated log-likelihood ratios (LLRs) of variable nodes as the second-stage decoding. In the first-stage decoding, an early stopping criterion is proposed for early detection of decoding failure and the candidate set of the variable nodes are determined, which can be partly included in the small trapping sets. In the second-stage decoding, the scores of the variable nodes in the candidate set are computed by the proposed unreliable path search algorithm and the variable nodes are sorted in ascending order by their scores for the re-decoding trials. Each re-decoding trial is performed by BP decoding algorithm with manipulated LLR of a selected variable node in the candidate set one at a time with the second early stopping criterion. The parallel unreliable path search algorithm is also proposed for practical application of the proposed algorithm. Numerical results show that the proposed early stopping criteria and the proposed decoding algorithms for the second-stage decoding can correct most of the unsuccessfully decoded codewords by the first-stage decoding in the error-floor region. [ABSTRACT FROM AUTHOR]

A new decoding strategy of belief propagation (BP) for low-density parity-check codes is presented by serially concatenating the traditional simultaneous decoding (also known as flooding) and the informed dynamic decoding (IDD) (e.g. node-wise residual belief propagation (NW RBP) or informed variable-to-check (IVC) RBP). The frame error rates (FER) and bit error rates (BER) of the concatenated BP decoder outperform that of the non-concatenated single decoder. In addition, as the signal-to-noise ratio (SNR) increases, the average number of decoding iterations required for the concatenated BP decoder decreases, and tends to merge with that of the first sub-decoder in the high SNR region. Moreover, since the IDD strategies concerned in this paper require extra effort for the residual computation, and the sequential updating of IDD is much more time consuming than the simultaneous updating of flooding. Therefore, compared with using a single IDD, serially concatenating flooding and IDD reduces both the approximate decoding complexity and the decoding latency because the concatenated decoder is still dominated by the sub-decoder flooding. [ABSTRACT FROM AUTHOR]

For iterative detection and decoding (IDD) in multiple-input multiple-output systems, the maximum a posteriori probability (MAP) detector would be ideal in terms of the performance. However, due to its high computational complexity, various suboptimal low-complexity approximate MAP detectors have been studied. In this study, a lattice reduction (LR)-based detector is considered for a near-optimal performance for IDD. The authors improve further the performance by employing a partial bit-wise minimum mean square error (MMSE) approach with randomised sampling, which has a lower complexity than that of the full bit-wise MMSE method. Moreover, the list of candidate vectors obtained by randomised sampling is extended using a MAP-aided integer perturbation algorithm for a better performance with low additional complexity. Through simulation results, it is shown that a near-optimal performance can be obtained which is better than that of the LR-based randomised successive interference cancellation and the full bit-wise MMSE methods. [ABSTRACT FROM AUTHOR]

The authors study the performance of protograph low-density parity-check (LDPC) codes over two-dimensional (2D) intersymbol interference (ISI) channels in this study. To begin with, the authors propose a modified version of finite-length (FL) extrinsic information transfer (EXIT) algorithm so as to facilitate the convergence analysis of protograph codes. Exploiting the FL-EXIT analyses, the authors observe that the protograph codes optimised for 1D ISI channels, e.g. the 1D ISI protograph code, cannot maintain their advantages in the 2D-ISI scenarios. To address this problem, the authors develop a simple design scheme for constructing a family of rate-compatible improved protograph (RCIP) codes particularly for 2D-ISI channels, which not only outperform the 1D-ISI protograph code, but also are superior to the regular column-weight-3 code and optimised irregular LDPC codes in terms of the convergence speed and error performance. More importantly, such RCIP codes benefit from relatively lower error-floor as well as linear encoding and fast decoding. Thanks to these advantages, the proposed RCIP codes stand out as better alternatives in comparison with other error-correction codes for ultra-high-density data storage systems. [ABSTRACT FROM AUTHOR]

In shifted Luby transform (SLT) codes, robust soltion distribution (RSD) degree distribution was conducted with shifted rounding to derive shifted RSD (SRSD) degree distribution based on partial information. In shifted rounding process, the large shift of corresponding probability distribution destroyed belief propagation decoding rule, so the decoding symbols increased. Meanwhile, the overlarge probability distribution value of degree k resulted in the increase of decoding symbols. In this work, traditional SRSD degree distribution was developed to improved SRSD (I-SRSD) degree distribution function by decreasing degree shift of rounding and limiting probability distribution of degree k. Theoretical analysis and experimental results show that SLT codes by I-SRSD degree distribution can decrease decoding symbols as well as encoding and decoding complexity. [ABSTRACT FROM AUTHOR]

In this study, the authors propose a polar coding (PC) scheme for the power line communication (PLC) system to cope with the impulsive noise and thereby promote the transmission performance. This new error-correcting coding scheme is essentially inspired on a novel conception of channel polarisation. To be specific, via recursively channel combing and splitting, a group of channels with ideal transmission conditions, that is having a capacity of 1, will be constructed to carry the useful information, while the other band sub-channels bear useless information. The decoding performance of PC under realistic impulsive noises is investigated under the condition that the impulsive noise is modelled by a well-known Middleton Class-A model. To mitigate the error propagation caused by sudden strong impulsive noises and further enhance the decoding performance, a matrix interleave operator is integrated. Simulations validate the suggested PC scheme in PLC systems. Compared with another commonly used low-density parity-check (LDPC) coding scheme, the suggested PC scheme, which has the low complexity, can significantly improve the bit error rate (BER) performance of PLC transmissions with impulsive interference. The PC scheme, as demonstrated by simulation results, can be of great importance to practical PLC systems. [ABSTRACT FROM AUTHOR]

The distribution of information bits and frozen bits on the decoder graph can be exploited to simplify the successive-cancellation (SC) decoding of polar codes. In this study, the authors establish a general simplified SC decoding framework for polar codes with arbitrary block-length, which is independent of any specific or explicit generator matrices and considerably reduces decoding complexity while retaining the same error performance. Then, based on the fact that the complexity reduction depends on the distribution of information bits, a so-called m-radius reselection scheme is proposed to construct multiple feasible information sets which are different from the original one defined by Arıkan. In this way, flexible tradeoffs between performance and complexity could be achieved. [ABSTRACT FROM AUTHOR]

Spectral efficiency of turbo code can be improved by use of coded modulation methods such as bit-interleaved coded modulation (BICM) with iterative decoding (BICM-ID). On the other hand, the performance of the turbo-BICM can be further improved by iteratively exchanging information between a decoder and a demodulator within a receiver and this scheme is known as the turbo-BICM-ID. Unfortunately, the required complexity of the turbo-BICM-ID is much higher than that of the turbo bit-interleaved coded modulation with iterative decoding turbo-BICM-ID. In this study, the authors propose a complexity reduced turbo-BICM-ID by optimising the mapping of coded bits to modulation symbols and the amount of information fed back from the decoder to the demodulator. [ABSTRACT FROM AUTHOR]

In this study, a new weighted bit-flipping (WBF) algorithm called mixed modified WBF (MM-WBF) decoding is proposed for low-density parity-check codes. The new algorithm is built by mixing two WBF algorithms, one acting as the main decoding algorithm and the other acting as the auxiliary. Simulation results show that the new algorithm achieves a notable performance gain over reliability ratio-based WBF, improved M-WBF and low-complexity WBF algorithms with almost the same computational complexity. Compared with some belief-propagation-based algorithms, MM-WBF also provides an appealing performance against complexity trade-off. [ABSTRACT FROM AUTHOR]