Block Markov Superposition Transmission Research Articles

Spatially Coupled Codes via Bidirectional Block Markov Superposition Transmission

Spatially Coupled Codes via Bidirectional Block Markov Superposition Transmission

CRC-Aided Sparse Regression Codes for Unsourced Random Access

This letter considers a coding scheme for unsourced random access (URA) based on sparse regression codes (SPARCs). In particular, an efficient concatenated coding scheme is proposed, which concatenates SPARCs and cyclic redundancy check-based block Markov superposition transmission (CRC-BMST) codes. A hybrid decoder consisting of a successive cancellation algorithm and a simplified approximated message passing (AMP) algorithm is presented for inner SPARCs, and an improved tree decoder is proposed for outer CRC-BMST codes by introducing a pruning technique. Simulation results show the proposed coding scheme outperforms the coded compressed sensing (CCS) scheme with lower computational complexity.

Block Markov superposition transmission of LDPC codes

In this paper, based on the block Markov superposition transmission (BMST) technique, we present a new class of coupled low-density parity-check (LDPC) codes for the transport block (TB)-based transmission to improve the error-correcting performance. For encoding, the previous LDPC codewords corresponding to a TB (at prior time slot) are interleaved and superimposed onto the current LDPC codewords, resulting in the transmitted codewords. For decoding, the sliding window decoding algorithm with sum-product or min-sum implementations can be employed, inheriting a relatively low-latency decoding. A distinguished advantage of the proposed coded transmission over spatially coupled LDPC (SC-LDPC) codes is that the encoder/decoder of the proposed codes can be designed by reusing the encoder/decoder architecture of component block LDPC codes. To analyze the waterfall performance of BMST-LDPC code ensembles, we present the protograph-based EXIT chart analysis, which can efficiently predict the error-correcting performance in waterfall region. To analyze the error-floor performance of BMST-LDPC codes, we employ the genie-aided (GA) lower bound, which can efficiently predict the error-correcting performance in error-floor region. For ease of implementation, the BMST-LDPC codes are constructed by taking the (2, 4)-raptor-like LDPC codes or the 5G LDPC codes as the basic components. The numerical results reveal that the proposed codes can have capacity-approaching performance, exhibiting a gap of 0.007 ​dB away from the corresponding Shannon limit. They also reveal that, by using the proposed BMST construction, the error-correcting performance of the original 5G block LDPC codes can be significantly improved, achieving coding gains up to one dB over the AWGN channels and two dB over the fast fading channels.

A Low-Complexity Decoder With Non-Uniform Quantization for Recursive BMST Codes

Recursive block Markov superposition transmission (rBMST) can be used to construct high-performance spatially coupled codes. When used in power-limited scenarios, low-complexity quantized decoders are required for the rBMST codes. In this letter, we introduce an efficient decoder for rBMST codes by incorporating non-uniform quantization (NUQ) into the threshold attenuated min-sum algorithm (TAMSA). The resulting decoder is referred to as the NUQ-TAMSA. We use the hierarchical dynamic quantization algorithm to design the non-uniform quantizer. To show the effectiveness of the NUQ-TAMSA, we carry out comprehensive comparisons. Our results show that, for low-resolution quantization, performance gains as large as 0.3 dB can be obtained with the NUQ-TAMSA. Numerical results also show that, for a wide range of coding rates, 5-bits non-uniform quantization is sufficient for NUQ-TAMSA to approach the performances of the floating-point based TAMSA.

Spatially Coupled LDPC Codes via Partial Superposition and Their Application to HARQ

This paper proposes a new class of spatially coupled codes, which are constructed by sending codewords of a low-density parity-check block code (LDPC-BC) in a block Markov superposition transmission (BMST) manner, resulting in the BMST-LDPC codes. Different from the conventional spatially coupled LDPC (SC-LDPC) codes, the proposed BMST-LDPC codes can have encoder/decoder implemented using the structure of the corresponding LDPC-BCs. The proposed construction is universal , which is applicable to any existing LDPC-BCs including the 5 G New Radio (5G-NR) LDPC-BCs to obtain extra coding gains. The proposed BMST-LDPC codes are also a special class of BMST codes, which have lower error floors even with an encoding memory of one, inheriting a low decoding latency. Moreover, partial superposition , where a fraction of the coded bits are superimposed onto the following codewords, is introduced to alleviate the decoding error propagation. The construction can be optimized, for random long codes, by a protograph-based extrinsic information transfer (EXIT) chart analysis, or by a one-dimensional search for structured block codes. Furthermore, the BMST-LDPC scheme is integrated with the hybrid automatic retransmission request (HARQ) over the block fading channel, improving the throughput performance. Numerical results are presented to validate our analysis and demonstrate the performance advantage of the BMST-LDPC codes over the LDPC-BCs. They also show that the proposed HARQ scheme can yield a throughput improvement of up to 10% over the conventional HARQ scheme.

Spatially Coupled Codes via Partial and Recursive Superposition for Industrial IoT With High Trustworthiness

For industrial Internet of Things (IIoT), data trustworthiness should be maintained both at the time of sensing and at the time of transmission. This article is concerned with trustworthiness during transmission, which is determined by transmission reliability. We present a low-complexity and flexible method via partial and recursive superposition to improve the transmission reliability of IIoT, resulting in an IIoT with high trustworthiness. In our method, a portion of the previously transmitted data are superimposed onto the current transmitted data to introduce memory among different transmissions, which are then exploited by the windowed decoder to obtain performance gain. The proposed method is referred to as partially recursive block Markov superposition transmission of low-density parity-check (PrBMST-LDPC) codes. This article is focused on the construction of low-complexity PrBMST-LDPC codes since IIoT is resource-limited in nature. The first construction is the memory-one PrBMST-LDPC code. We present a simplified density evolution algorithm to optimize the superposition ratio for memory-one PrBMST-LDPC code. Both the analytical and numerical results show that PrBMST with memory one can be used to reduce the packet loss ratio (PLR) of IIoT using LDPC codes. Particularly, around 1.0 dB performance gain is obtained by PrBMST. We then present a low-complexity construction for PrBMST-LDPC codes with encoding memory larger than one. Simulation results show that compared with memory-one PrBMST, a further PLR reduction of around one order of magnitude can be obtained.

Rate-Compatible Codes via Recursive BMST for Content-Sharing in Intelligent Vehicular Network

Content-sharing is one of the major applications of vehicular networks. To fully utilize the spectrum and the connection time, rate-compatible codes are required when sharing content. In this paper, we present a simple and flexible method to construct low-complexity rate-compatible codes for content sharing. We first present a novel construction framework for rate-compatible codes via recursive block Markov superposition transmission (rBMST). In the proposed construction, the shared content is partitioned into equal-length data chunks and transmitted directly, while their replicas are taken as the inputs of a given number of parallel systematic encoders to generate parity-check chunks. These parity-check chunks are then transmitted in parallel in a recursive block Markov superposition transmission manner. The proposed construction is flexible in the sense that codes with arbitrary rates can be obtained by adjusting the number of parallel rBMST encoders and the number of randomly punctured bits. We show that the simplest construction, using repetition to generate the parity-check chunks, leads to high-performance and low-complexity rate-compatible rBMST (RC-rBMST) codes. Specifically, the extrinsic information transfer (EXIT) chart analysis shows that asymptotic thresholds of the repetition-based RC-rBMST (RB-RC-rBMST) codes are within 0.25 dB of the channel capacities for a wide range of coding rates. Numerical results are presented to confirm the advantages of the RB-RC-rBMST codes in performance and complexity. Particularly, the RB-RC-rBMST codes perform as well as BMST-R codes but with much lower computational complexities.

Doubly-Recursive Block Markov Superposition Transmission: A Low-Complexity and Flexible Coding Scheme

In this paper, we introduce a novel method, called doubly-recursive block Markov superposition transmission (DrBMST), to construct high-performance spatially coupled codes. An important characteristic of DrBMST codes is that the degrees of the constraint nodes in their normal graphs are at most three. As a result, DrBMST codes can be decoded with low complexity. We first prove that the error probability of an enlarged DrBMST code ensemble can be made arbitrarily small under windowed maximum-likelihood decoding (MLD) by increasing the decoding window size. This result partially explains the superior performances of DrBMST codes. Then we propose to use the extrinsic information transfer (EXIT) chart analysis to estimate the iterative windowed decoding thresholds of DrBMST codes. The EXIT chart analyses show that, with such a simple structure, DrBMST codes are comparable to BMST codes with large encoding memories in terms of decoding thresholds. Finally, we carry out comparisons to validate the advantages of DrBMST codes in terms of error performances and decoding complexities. In particular, for a decoding latency of 20,000 bits, the DrBMST code performs better than the (4, 8)-regular spatially coupled low-density parity-check (SC-LDPC) code, but with lower computational complexity. Hence, DrBMST codes can be used in communication systems with limited computational resources. In addition, we show that DrBMST can be used to construct multiple-rate codes.

Spatial-modulated physical-layer network coding based on block Markov superposition transmission for maritime relay communications

As an alternative to satellite communications, multi-hop relay networks can be deployed for maritime long-distance communications. Distinct from terrestrial environment, marine radio signals are affected by many factors, e.g., weather conditions, evaporation ducting, and ship rocking caused by waves. To ensure the data transmission reliability, the block Markov superposition transmission (BMST) codes, which are easily configurable and have predictable performance, are applied in this study. Meanwhile, the physical-layer network coding (PNC) scheme with spatial modulation (SM) is adopted to improve the spectrum utilization. For the BMST-SM-PNC system, we propose an iterative algorithm, which utilizes the channel observations and the a priori information from BMST decoder, to compute the soft information corresponding to the XORed bits constructed by the relay node. The results indicate that the proposed scheme outperforms the convolutional coded SM-PNC over fast-fading Rician channels. Especially, the performance can be easily improved in high spatial correlation maritime channel by increasing the memory m.

Application of block Markov superposition transmission to physical-layer network coding for maritime communications

Physical-layer network coding (PNC) is a promising technology that can improve the throughput of two-way relay networks. This paper focus on designing physical-layer network coding schemes for maritime communication systems. Unlike terrestrial environment, radio propagation at sea is seriously affected by wave movement, ship shaking and other complicated environmental factors. In order to improve the transmission reliability, we apply block Markov superposition transmission (BMST) to PNC schemes. Simulation results show that the proposed schemes outperform the existing convolutional coded PNC schemes over Rician channels, suggesting that the proposed schemes are more appropriate for marine applications.

Block Markov Superposition Transmission of BCH Codes With Iterative Erasures-and-Errors Decoders

In this paper, we present the block Markov superposition transmission of BCH (BMST-BCH) codes, which can be constructed to obtain a very low error floor. To reduce the implementation complexity, we design a low complexity iterative sliding-window decoding algorithm, in which only binary and/or erasure messages are processed and exchanged between processing units. The error floor can be predicted by the proposed genie-aided lower bounds, while the waterfall performance can be analyzed by the density evolution method. To evaluate the error floor of the constructed BMST-BCH codes at a very low bit error rate (BER) region, we propose a fast simulation approach. Numerical results show that, at a target BER of $10^{-15}$ , the proposed BMST-BCH code with hard-decision can achieve a net coding gain (NCG) of 10.55 dB with 25% overhead, while a soft-decision design can yield an NCG of 10.74 dB. The construction of BMST-BCH codes is flexible to trade off latency against performance at all overheads of interest and may find applications in optical transport networks as an attractive candidate.

Block Markov Superposition Transmission with Color Shift Keying

Block Markov Superposition Transmission with Color Shift Keying

Recursive Block Markov Superposition Transmission of Short Codes: Construction, Analysis, and Applications

Extensive studies have demonstrated the effectiveness and the flexibility of constructing capacity-approaching codes by block Markov superposition transmission (BMST). However, to achieve high performance, BMST codes typically require large encoding memories and large decoding window sizes, which result in high decoding complexity and high decoding latency. To address these issues, we introduce the recursive BMST (rBMST), in which the block-oriented feedback convolutional code is used instead of the block-oriented feedforward convolutional code of BMST. We propose to use a modified extrinsic information transfer chart analysis, which relates the mutual information to the bit error rate, to study the convergence behaviors of rBMST codes. On one hand, rBMST code shares most merits of BMST code, including near-capacity performance, low-complexity encoding, and flexible construction. On the other hand, compared with BMST code, rBMST code requires a smaller encoding memory, hence a lower decoding complexity, to approach the capacity. In particular, both analytical and simulation results show that rBMST code with encoding memory three reveals a lower error floor than the BMST code with encoding memory twelve. Furthermore, we show by analysis and simulations that rBMST with fixed encoding memory ( $m = 3$ ) and fixed decoding delay ( $d = 12$ ) can be used to construct capacity-approaching multiple-rate codes. Finally, the comparison between rBMST codes and spatially coupled low-density parity-check codes is carried out, which shows the advantages of rBMST codes in terms of performances and decoding complexities.

MIMO visible light communication system with block Markov superposition transmission

This study is concerned with coded multiple-input multiple-output (MIMO) visible light communication (VLC) system, where unipolar M-level pulse amplitude modulation is assumed along with MIMO transmission techniques, including repetition coding, spatial multiplexing and spatial modulation. In order to evaluate the performance of MIMO-VLC system, the authors analyse the mutual information of the MIMO techniques, based on which the block Markov superposition transmission (BMST) codes are constructed to improve the bit-error rate (BER) performance of the system. In addition, they present a genie-aided lower bound to predict the performance of the BMST-VLC system in the low-BER region. Simulation results demonstrate that the proposed scheme can achieve significant coding gain compared with Reed-Solomon-coded MIMO-VLC system adopted in IEEE standard 802.15.7.

Systematic Block Markov Superposition Transmission of Repetition Codes

In this paper, we propose systematic block Markov superposition transmission of repetition (BMST-R) codes, which can support a wide range of code rates but maintain essentially the same encoding/decoding hardware structure. The systematic BMST-R codes resemble the classical rate-compatible punctured convolutional codes, except that they are typically non-decodable by the Viterbi algorithm due to the huge constraint length induced by the block-oriented encoding process. The information sequence is partitioned equally into blocks and transmitted directly, while their replicas are interleaved and transmitted in a block Markov superposition manner. By taking into account that the codes are systematic, we derive both upper and lower bounds on the bit-error-rate (BER) under maximum a posteriori decoding. The derived lower bound reveals connections among BER, encoding memory and code rate, which provides a way to design good systematic BMST-R codes and also allows us to make trade-offs among efficiency, performance, and complexity. Numerical results show that: 1) the proposed bounds are tight in the high signal-to-noise ratio region; 2) systematic BMST-R codes perform well in a wide range of code rates; and 3) rate 1/2 systematic BMST-R codes outperform the considered (3,6)- and (4,8)-regular spatially coupled low-density parity-check codes under an equal decoding latency constraint.

Block Markov superposition transmission with pulse position modulation over free-space optical links

In FSO (Free-Space Optical) communications, performance of the communication systems is severely degraded by atmospheric turbulence. PPM (Pulse Position Modulation) is widely used in FSO communication systems owing to its high power effciency. In this paper, we present a combination of the BMST (Block Markov Superposition Transmission) technique and the PPM scheme to improve the reliability of the transmission over FSO links. Based on analyzing an equivalent system, a lower bound on the bit-error-rate of the proposed scheme is presented. Extensive simulations are performed which show that the BMST-PPM system performs well under a wide range of turbulence conditions and improves the performance of the basic code. Simulation results also show that, the performance of the system with the sliding-window detection/decoding algorithm matches well with the lower bound in the low-error-rate region.

Generalized block Markov superposition transmission over free-space optical links

In free-space optical (FSO) communications, the performance of the communication systems is severely degraded by atmospheric turbulence. Channel coding and diversity techniques are commonly used to combat channel fading induced by atmospheric turbulence. In this paper, we present the generalized block Markov superposition transmission (GBMST) of repetition codes to improve time diversity. In the GBMST scheme, information sub-blocks are transmitted in the block Markov superposition manner, with possibly different transmission memories. Based on analyzing an equivalent system, a lower bound on the bit-error-rate (BER) of the proposed scheme is presented. Simulation results demonstrate that, under a wide range of turbulence conditions, the proposed scheme improves diversity gain with only a slight reduction of transmission rate. In particular, with encoding memory sequence (0, 0, 8) and transmission rate 1/3, a diversity order of eleven is achieved under moderate turbulence conditions. Numerical results also show that, the GBMST systems with appropriate settings can approach the derived lower bound, implying that full diversity is achievable.

Coded transceive spatial modulation with block Markov superposition transmission

A new multiple-input multiple-output system, referred to as transceive spatial modulation (TRSM), which integrates transmit spatial modulation (SM) and receive SM. In the TRSM system, information bits are carried by the conventional amplitude–phase modulation as well as by the indices of both the transmit and the receive antennas. To improve the bit-error-rate performance, block Markov superposition transmission (BMST) is applied to the TRSM, resulting in BMST-TRSM, where BMST is a recently proposed coding scheme and can be easily designed according to the spectral efficiency requirement. To reduce the computational complexity, a layered (suboptimal) soft detection algorithm is presented, which delivers a list of candidate spatial points (antenna combinations) first. Numerical results show that the proposed TRSM system performs well over the Rayleigh fading channels.

Partially Block Markov Superposition Transmission of a Gaussian Source With Nested Lattice Codes

This paper studies the transmission of Gaussian sources through additive white Gaussian noise channels in bandwidth expansion regime, i.e., the channel bandwidth is greater than the source bandwidth. To mitigate the error propagation phenomenon of conventional digital transmission schemes, we propose in this paper a new capacity-approaching joint source channel coding (JSCC) scheme based on partially block Markov superposition transmission (BMST) of nested lattice codes. In the proposed scheme, first, the Gaussian source sequence is discretized by a lattice-based quantizer, resulting in a sequence of lattice points. Second, these lattice points are encoded by a short systematic group code. Third, the coded sequence is partitioned into blocks of equal length and then transmitted in the BMST manner. The main characteristics of the proposed JSCC scheme include: 1) entropy coding is not used explicitly and 2) only parity-check sequence is superimposed, hence, termed partially BMST. This is different from the original BMST. To show the superior performance of the proposed scheme, we present extensive simulation results which show that the proposed scheme performs within 1 dB of the Shannon limits. Hence, the proposed scheme provides an attractive candidate for transmission of Gaussian sources.

A Low-Complexity Delay-Tunable Coding Scheme for Visible Light Communication Systems

Visible light communication (VLC) systems are expected to support a variety of applications, such as common-information broadcasting, real-time multimedia streaming, and large file downloading. Typically, these applications have different delay requirements. Hence, it is desirable to design high-performance coding scheme capable of supporting a wide range of delays but with acceptable hardware complexity. To achieve this, we propose a delay-tunable coding scheme for VLC systems based on block Markov superposition transmission of short non-binary low-density parity-check (NBLDPC) codes. The proposed coding scheme includes the following advantages: 1) it is easily configurable to fulfill different delay requirements while keeping the code rate constant; 2) it requires essentially the same hardware modules to implement the encoder/decoder as the involved short NBLDPC code; and 3) it can have a larger coding gain if a longer delay is tolerated. Numerical results are presented to show the expected tradeoff between delay and energy in a VLC system.