Design and Analysis of Joint Group Shuffled Scheduling Decoding Algorithm for Double LDPC Codes System.

In a joint source-channel coding (JSCC) system, excessive source compression can cause an error floor. In the original JSCC scheme based on double protograph LDPC (DP-LDPC) codes, only connections exist between check nodes (CNs) of the source protograph and variable nodes (VNs) of the channel protograph, and error floors are observed. In this paper, we investigate the joint protograph that forms the basis of a DP-LDPC code. The joint protograph consists of a source protograph, a channel protograph, and connections between the two protographs. Our main focus is on the complete-source-variable-linking (CSVL) protomatrix of the joint protograph, which determines the error floor of the DP-LDPC code. We propose a generalized source protograph extrinsic information transfer (GSP-EXIT) algorithm for evaluating the source decoding thresholds of the CSVL protomatrix. Based on the proposed algorithm, we analyze CSVL protomatrices with regular or irregular source protographs. We present design criteria for connections between VNs of the source protograph and CNs of the channel protograph. Such design rules will result in a higher source decoding threshold, which implies a lower error floor. We also propose a differential evolution algorithm for optimizing the source protograph. We present/compare analytical results and/with simulation results, and conclude that they are consistent.

Polar codes [1] are a class of provably capacity-achieving error correcting codes (ECC) for memoryless symmetric channels with low-complexity code structures; they have been shown to enjoy better decoding performance over LDPC and Turbo codes under certain scenarios. In this work, we study the application of polar codes for NAND-based SSDs, and mainly focus on the joint source channel coding (JSCC) aspect of polar codes for flash data protection. In a practical SSD system, in addition to the host data, both flash translation layer (FTL) and host side will write on NAND a small amount of non-host data (a.k.a. metadata) for system managing purposes. We demonstrate that the metadata information can be readily and efficiently utilized by polar codes, whereas such property is lacking in LDPC-based systems. With the help of the side information provided by metadata, the decoding capability of polar codes can be further enhanced with little or no modifications on the decoder side. Simulation results verify the performance improvement of metadata-based JSCC scheme, and indicate that polar codes have competitive advantages over LDPC codes on flash memories.

An image pre-processing approach is proposed for joint source-channel coding (JSCC) scheme based on double protograph low-density parity-check (DP-LDPC) codes. Firstly, discrete cosine transform (DCT) and quantization are applied to the transmitted images. Different from the data processing of the previous approach for the quantized DCT coefficients, the representation of true form takes the place of complement form. Meanwhile, the high entropy frames will be pre-processed into low entropy frames through frame decomposition procedure due to the entropy of source frame limited by the code-rate of source code. Simulation results indicate that the JSCC scheme with the proposed image pre-processing approach improves the transmission efficiency and can recover the images with good quality at a very low signal-to-noise ratio (SNR).

In this paper, we study two problems of providing reliable data transmission and developing aggregation techniques for correlated data in wireless sensor networks. A system with forward error correction (FEC) can provide an objective reliability while using less transmission power than a system without FEC. Because of the additional parity bits and encoding/decoding energy consumptions, we study the effect of FEC on energy efficiency. We propose to use LDPC codes for FEC. We show that wireless sensor networks using LDPC codes are almost 45% more energy efficient than those that use BCH codes, which were shown to be 15% more energy efficient than the best performing convolutional codes. Then we study the problem of providing aggregation for two and three correlated nodes in wireless sensor networks. We propose to use LDPC codes in wireless sensor networks for source and channel coding to obtain a two-fold energy savings. For two correlated nodes, we study both distributed source coding and joint source-channel coding. While distributed source coding using LDPC codes was studied before, joint source-channel coding using LDPC codes is introduced for the first time. The difference between our work in distributed source coding using LDPC codes and the previous work lies in the LDPC code design procedure. The simulation results show that our proposed design criteria improves the performance of the source coding. The convergence of the non-uniform LDPC code of our design technique is almost 60% closer to the Slepian-Wolf limit. For three correlated nodes, we study distributed source coding using LDPC codes. We simplified the problem of design procedure to randomly punctured LDPC codes. This is a new approach for designing LDPC codes and the simulation results for code of length 1000 shows that the convergence of the LDPC code is achieved at compression rate 0.3174 which is only 0.08 away from the Slepian-Wolf limit.

Day by day the internet traffic is increasing rapidly. Challenges to improve these internet traffic requirements leads to evolution of 5G NR LDPC (New Radio Low Density Parity Check) codes which provides high coding gain and energy efficiency. BER Vs Eb/No dB curve defines the energy efficiency and coding gain of the any error correcting codes. LDPC codes which are adopted by 5G Standard are called 5G NR LDPC codes.In the design of the decoder,Message Passing Approach reduces the decoding complexity due to the sparsity of the parity check matrix. An efficient decoding algorithm is the key to the successful code. In this paper an iterative minsum approximation message passing decoding algorithm has been implemented for both BG1 and BG2. Results show that the coding gain can be improved up to 9dB.

A modified joint source-channel decoding (JSCD) algorithm based on low-density parity-check (LDPC) codes and hidden Markov estimation has been presented and extended to applying over Rayleigh fading channels. The proposed algorithm utilizes the source residual redundancy lack of any priori information of the source parameters, and the modifications employ the self-checking and convergence mechanisms of LDPC codes in adjusting the error probability of the hidden Markov model (HMM). To show the validation of the proposed JSCD methods, we also give a framework for the density evolution analysis for JSCD. Simulation results show that the joint decoding scheme on Rayleigh fading channels greatly reduces the number of iterations and improves the system performance more than 0.7 dB. Moreover, the modified JSCD algorithm leads to the joint decoder to converge at least 10% faster than the unmodified method without any degradation in the decoding performance

Although the joint source-channel coding (JSCC) system based on double protograph low-density parity-check (DP-LDPC) codes has been shown to possess excellent error performance over additive white Gaussian noise (AWGN) channels, it cannot perform well over one-dimensional inter-symbol-interference (OD-ISI) magnetic recording channels. In this study, a new JSCC system with a three-stage serially concatenated framework of Turbo equalization is firstly proposed for OD-ISI magnetic recording channels. Then, a modified joint protograph extrinsic information transfer (M-JPEXIT) algorithm is put forward to analyze the convergence-performance of the proposed system. By applying the M-JPEXIT algorithm, the channel codes are redesigned for this system to improve the error performance. Both the M-JPEXIT analysis and the bit-error-rate (BER) simulation results show the performance improvement of the proposed channel codes, especially in the water-fall region.

In high density patterned media storage system, the “multiple islands per read head” model is taken into account for inter-track interference (ITI) in bit-patterned media (BPM). It has been proposed that low-density parity-check (LDPC) codes could improve the symbol error rate (SER) performance significantly when only considering AWGN noise alone over the storage channel. LDPC decoding algorithm could be applied in LDPC joint decoder of patterned media storage system. In this paper, we proposed a decoding algorithm of serial belief propagation (SBP) with a stop updating criterion for LDPC decoder. Simulation results show that the proposed decoding algorithm could reduce the times of generating and propagating the message in decoding with negligible error rate performance loss over AWGN channels when appropriately choosing the parameter that determines which variable node has been converged. By taking advantage of extrinsic information transfer (EXIT) charts, it is demonstrated that the proposed decoding algorithm could maintain superior SER performance and convergence rate compared with the traditional SBP decoding algorithm. To further explore the performance of the proposed decoding algorithm in “multiple islands per read head” model, we performed a large number of simulations over this channel model with different distribution percentages between the AWGN and the island position jitter noise. Simulation results show that the LDPC codes could improve the SER performance when considering jitter noise while the proposed decoding algorithm behaves excellently over the patterned media storage channel and over the AWGN channel.

Low-density parity-check (LDPC) codes have been widely considered as error-correcting codes for next generation communication systems. A good LDPC decoder design requires both implementation friendly LDPC codes and efficient decoder architectures. The quality of LDPC code is crucial in determining the coding gain and implementation complexity of LDPC hardware decoders. This paper presented a genetic algorithm (GA) based LDPC code search algorithm with hardware considerations. Regular quasi-cyclic LDPC codes are used due to its friendliness to hardware implementation. Our hardware architecture design schedules pipeline LDPC decoding operation to boost the hardware utilization efficiency (HUE) of LDPC decoder. A LDPC decoder with a block size of 12288 is implemented in FPGA to validate our code and architecture design.

In the case of short code, polar code demonstrates superior performance compared with Low Density Parity Check (LDPC) code. Particularly in low coding rate scenario, the complexity of Polar code encoding and decoding is significantly lower than that of LDPC code. The technological advantage of Polar code makes it of great value in special application scenarios such as satellite communication and ocean communication. The polar coding scheme can significantly improve the transmission reliability of the communication system, because the satellite spread spectrum communication system generally adopts short code design.In the research of decoding algorithm, the original Serial Cancellation (SC) decoding algorithm has simple rules, but the decoding effect is not ideal under the limited code length, and the serial decoding mechanism leads to large decoding delay. The Successive Cancellation List (SCL) decoding algorithm improves decoding performance by increasing the number of decoding search path. However, maintaining multiple decoding paths can multiply the decoding complexity. Fast node-based decoding algorithm aims to accelerate decoding and reduce latency by defining and simplifying the decoding process for specific nodes, yet they do not optimize the decoding paths. In view of the above problems, this paper proposes a Simplified Parity Check-based Cyclic Redundancy Check (CRC)-Aided Successive Cancellation List (S-PC-CASCL) decoding algorithm. Simulation results demonstrate that the proposed S-PC-CASCL maintains excellent error correction performance while reducing the average list size by up to 16 % under low Signal Noise Ratio (SNR) conditions, thereby lowering computational complexity and decoding latency compared with other widely used polar decoding methods.

Terrestrial digital multimedia TV/handle broadcasting (DMB-TH) is a newly upcoming framing structure, channel coding and modulation for digital television terrestrial broadcasting system standard of China, which is recently drafted and is ready to be verified in order to deploy mobile multimedia broadcasting services for the public. The adoption of strong channel coding techniques appears to be of key importance for mobile operators and broadcasters. Low-density parity-check (LDPC) codes have been widely considered as error-correcting codes for next generation communication systems. A good LDPC decoder design requires both implementation friendly LDPC codes and efficient decoder architectures. The quality of LDPC code is crucial in determining the coding gain and implementation complexity of LDPC hardware decoders. This paper presents a turbo-decoding message-passing algorithm (TDMP) based LDPC code search algorithm with hardware considerations. The main advantages of the proposed algorithm over the DMB-TH standard decoding algorithm are 1) improvement in coding gain by an order of magnitude at high signal-to-noise ratio (SNR), 2) reduced decoder complexity. The performance of the proposed TDMP architecture is shown by the comparison of simulation results.

In this paper, we analyze the sequential message- passing decoding algorithm of low-density parity-check (LDPC) codes by partitioning check nodes. This decoding algorithm shows better bit error rate (BER) performance than the conventional message-passing decoding algorithm, especially for the small number of iterations. Analytical results indicate that as the number of partitioned subsets of check nodes increases, the BER performance is improved. We also derive the recursive equations for mean values of messages at check and variable nodes by using density evolution with a Gaussian approximation. From these equations, the mean values are obtained at each iteration of the sequential decoding algorithm and the corresponding BER values are calculated. They show that the sequential decoding algorithm converges faster than the conventional one. Finally, the analytical results are confirmed by the simulation results.

In mobile communications, the quality of signal is deteriorated by fading. The spatial diversity technique is used to reduce the degradation of the signal by fading. There are several techniques to realize the spatial diversity gain, such as Single- Input Multiple-Output (SIMO), Space-Time Block Code (STBC), and so on. The SIMO system realizes the receive diversity. The error correcting code can be combined with spatial diversity gain. Low-Density Parity Check (LDPC) codes can achieve good performance approaching Shannon limit. In particular, an irregular LDPC code with optimum degree distribution achieves better performance than a regular LDPC code. The optimum degree distribution of the irregular LDPC code depends both on the channel and the system. In this paper, we derive the Eb/No thresholds of a regular LDPC codes and the irregular LDPC codes for SIMO systems with several diversity orders. The Eb/No threshold is the smallest Eb/No that the decoder can achieve the error free. We also derive the optimum degree distributions of the irregular LDPC codes for SIMO systems with several diversity orders. We show that with low diversity order, the optimum degree distributions of the irregular LDPC code depends on the diversity order largely, while with high diversity order, the optimum degree distribution depends both on the diversity order and the combining scheme largely. We also show that comparing the optimum degree distributions for MRC and STBC, when the diversity orders are the same, the optimum degree distributions are also the same.

Neural prosthetic systems seek to improve the lives of severely disabled people by decoding neural activity into useful behavioral commands. These systems and their decoding algorithms are typically developed "offline," using neural activity previously gathered from a healthy animal, and the decoded movement is then compared with the true movement that accompanied the recorded neural activity. However, this offline design and testing may neglect important features of a real prosthesis, most notably the critical role of feedback control, which enables the user to adjust neural activity while using the prosthesis. We hypothesize that understanding and optimally designing high-performance decoders require an experimental platform where humans are in closed-loop with the various candidate decode systems and algorithms. It remains unexplored the extent to which the subject can, for a particular decode system, algorithm, or parameter, engage feedback and other strategies to improve decode performance. Closed-loop testing may suggest different choices than offline analyses. Here we ask if a healthy human subject, using a closed-loop neural prosthesis driven by synthetic neural activity, can inform system design. We use this online prosthesis simulator (OPS) to optimize "online" decode performance based on a key parameter of a current state-of-the-art decode algorithm, the bin width of a Kalman filter. First, we show that offline and online analyses indeed suggest different parameter choices. Previous literature and our offline analyses agree that neural activity should be analyzed in bins of 100- to 300-ms width. OPS analysis, which incorporates feedback control, suggests that much shorter bin widths (25-50 ms) yield higher decode performance. Second, we confirm this surprising finding using a closed-loop rhesus monkey prosthetic system. These findings illustrate the type of discovery made possible by the OPS, and so we hypothesize that this novel testing approach will help in the design of prosthetic systems that will translate well to human patients.

This chapter discusses fundamentals of information theory and channel coding (error correction coding ECC, Forward error correction FEC). First, key results of Shannon, including channel capacity and the relationship between transmit power and bandwidth, are discussed. Block codes multiply a block of data with an encoding matrix. For systematic codes, the resulting codeword consists of systematic bits and parity check bits. Decoding is achieved by multiplication with a parity check matrix and determination of the syndrome vector. Correction of errors within the correction sphere can be done, e.g., through lookup tables. Convolutional codes send the source data stream through shift registers and adders, a process described by a trellis diagram. Maximum-likelihood sequence estimation (Viterbi algorithm) determines the (transmit) bit sequence with best distance metric (Hamming or Euclidean) from the received signal. Methods for combining coding and higher-order modulation include trellis coded modulation (using set partitioning for code design) and bit-interleaved coded modulation (BICM). Turbo codes are close to capacity-achieving. They are based on transmitting differently interleaved convolutional codes; receivers use soft decoding of the constituent codes and iterative exchange of soft information (log-likelihood ratios). Low-density parity check codes (LDPCC) are decoded by belief propagation (message passing), where variable nodes and constraint nodes exchange beliefs about the codeword. In fading channels, (block or convolutional) interleaving is essential to provide diversity. From an information-theoretic point of view, in fading channels we can distinguish between the ergodic capacity and the outage capacity. If the channel state information is known at the transmitter, waterfilling is the optimum power allocation strategy. Automatic Repeat Request ARQ) and Hybrid ARQ (including chase combining or incremental redundancy) are described in the appendix.