Repeat-accumulate Codes Research Articles

Image Data Compression and Noisy Channel Error Correction Using Deep Neural Network

Everyday an enormous amount of information is stored, processed and transmitted digitally around the world. Neural Networks have been rapidly developed and researched as a solution to image processing tasks and channel error correction control. This paper presents a deep neural network (DNN) for gray image compression and a fault-tolerant transmission system with channel error-correction capabilities. First, a DNN implemented with the Levenberg-Marguardt learning algorithm is proposed for image compression. We demonstrate experimentally that our DNN not only provides better quality reconstructed images but also less computational capacity compared to DCT Zonal coding, DCT Threshold coding, Set Partitioning in Hierarchical Trees (SPIHT) and Gaussian Pyramid. Secondly, a DNN with improved channel error-correction rate is proposed. The experimental results indicate that our implemented network provides a superior error-correction ability by transmitting binary images over the noisy channel using Hamming and Repeat-Accumulate coding. Meanwhile, the network's storage requirement is 64 times less than the Hamming coding and 62 times less than the Repeat-Accumulate coding.

Spatially Coupled Repeater-Combiner-Convolutional Codes

A form of spatially coupled codes is obtained by coupling multiple identical concatenated codes consisting of a block outer code (a repetition code followed by a single-parity code) concatenated with a convolutional inner code of infinite impulse response. The coupling operation involves only the outer code of the block-convolutional concatenated code. Because of the simple outer code and diverse inner code, the proposed codes have simple encoding implementation and flexible designation space. Extrinsic information functions are used to analyze the belief propagation (BP) thresholds of the proposed codes over an additive white Gaussian noise channel. The numerical results demonstrate that the proposed codes have better BP threshold and error correction performances than conventional spatially coupled repeat-accumulate codes and spatially coupled low-density parity-check codes. In particular, the proposed codes with a rate of about 0.5 and length of 15628 have a bit-error-rate (BER) of $10^{-5}$ at Eb/N0 of 1.13 dB that is less than 1 dB away from the Shannon limit.

Performance estimation of finite‐length repeat–accumulate codes

In this paper, the authors study the performance of finite-length repeat–accumulate (RA) codes in the waterfall region. Utilising density evolution technique, the authors present estimation algorithms to predict the error performance of finite-length RA codes over binary memoryless channels. Through comparison with numerical results, the authors show that the finite-length performance of RA codes can be closely estimated by using authors’ proposed approach.

Memory‐efficient quasi‐cyclic spatially coupled low‐density parity‐check and repeat‐accumulate codes

The authors propose the construction of spatially coupled low-density parity-check (SC-LDPC) codes using a periodic time-variant quasi-cyclic (QC) algorithm. The QC-based approach is optimised to obtain memory efficiency in storing the parity-check matrix in the decoders. A hardware model of the parity-check storage units has been designed for a Xilinx field-programmable gate array (FPGA), to compare the logic and memory requirements for various approaches. It is shown that the proposed QC SC-LDPC code (with optimisation) can be stored with reasonable logic resources and without the need of block memory in the FPGA. In addition, a significant improvement in the processing speed is also achieved. This study also proposes a new QC algorithm for constructing spatially coupled repeat-accumulate (SC-RA) codes. The proposed construction reduces the implementation complexity of the encoder and subsequently saves significant computational resources required for storing and accessing the circulants in the decoder. The performance of the proposed code is also compared with the standard RA codes through simulations.

Design of Irregular Repeat Accumulate Codes for Finite Decoder Iterations

This paper deals with the design of non-systematic irregular repeat-accumulate codes that are optimised for a finite number of decoding iterations. In many cases of practical interest, the usual approach for sparse-graph codes, which aims to approach capacity (with arbitrarily many decoder iterations), may not be suitable. This is of particular importance for systems with complexity or delay constraints. In this paper, we provide a design methodology which constrains the number of decoder iterations, as well as other measures of implementation complexity. Our approach uses extrinsic information transfer analysis, and our main contribution is the formulation of code optimisation problems which directly incorporate the number of iterations into the constraints. We focus on the single user binary erasure channel and the two-user binary adder channel, where this transfer analysis is exact. Generalisation to other sparse graph codes and other channels (under usual approximations) is straightforward.

EXIT chart optimization of Repeat-Accumulate codes for an N-Frequency T-User Multiple Access Channel with noise

In this paper we show how a graph-based systemcan be designed for an N-FSK T-user multiple access channel withnoise. The channel is a frequency selective fast fading channelwith additive white Gaussian Noise. The system does not knowor attempt to determine the fading incurred at a given moment.The system is composed of a multiuser detector and T differentRepeat-Accumulate (RA) decoders. The decoders are optimizedas a set and consequently have the same parameters. A structuralvariation between the users’ encoders/decoders is sufficient toallow for multiple access and channel error correction, whileproviding rates close to channel capacity.

Spatially Coupled Repeat-Accumulate Codes

In this paper we propose a new class of spatially coupled codes based on regular repeat-accumulate codes. We show that these codes have several advantages over spatially coupled regular low-density parity-check codes including simpler encoders and slightly higher code rates when the thresholds and decoding complexity (as measured by the Tanner graph edge density) are similar.

An LDPC coded cooperative MIMO scheme over Rayleigh fading channels with unknown channel state information

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.

Local-Optimality Guarantees Based on Paths for Optimal Decoding

This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs. These local-optimality characterizations are based on combinatorial structures embedded in the Tanner graph of the code. Local optimality implies both unique maximum likelihood optimality and unique linear programming (LP) decoding optimality. Also, an iterative message-passing decoding algorithm is guaranteed to find the unique locally optimal codeword if one exists. We demonstrate an instance of this proof technique by considering a definition of local optimality that is based on the simplest combinatorial structures in Tanner graphs, namely, paths of length $h$. We apply the technique of local optimality to binary Tanner codes (including any low-density parity-check code, and in particular any irregular repeat-accumulate code with both even and odd repetition factors). Inverse polynomial bounds in the code length are proved on the word error probability of LP decoding for binary Tanner codes. When the local codes are restricted to single parity-check codes, these bounds also hold for decoding by a certain iterative message-passing decoding algorithm.

Maximum Sum Rate of Repeat-Accumulate Interleave-Division System by Fixed-Point Analysis

A multi-user repeat-accumulate interleave-division (RAID) system is considered for a multiple-access channel (MAC) with binary inputs, equal-power, and symbol synchronization. In the system, a regular repeat-accumulate (RA) code serially concatenated with block spreading is employed for each user. At the receiver, multi-user message-passing decoding is performed on a single factor graph. Over the MAC with additive white Gaussian noise (AWGN), a fixed point analysis is developed to obtain the optimal code rate and the spreading length that give the maximum sum rate for an arbitrary small decoding error rate.

New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes

This paper presents several new construction techniques for low-density parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on specific classes of combinatorial designs, the improved code design focuses on high-rate structured codes with constant column weights 3 and higher. The proposed codes are efficiently encodable and exhibit good structural properties. Experimental results on decoding performance with the sum-product algorithm show that the novel codes offer substantial practical application potential, for instance, in high-speed applications in magnetic recording and optical communications channels.

A Serial Joint Channel and Physical Layer Network Decoding in Two-Way Relay Networks

This paper presents a novel joint channel and physical layer network decoding scheme for a two-way relay communication system. The proposed decoding scheme can be viewed as a serial concatenated decoding scheme with the source codes, different or identical, as the outer codes and the physical network coding (PNC) as the inner code. To achieve good error performance, iteratively decodable codes are used as the source codes. Decoding of the scheme consists of two loops, the inner-loop for which the source codes are decoded with a message-passing decoding algorithm and the outer-loop for which the reliability messages are passed between the source decoders and the PNC decoder for updating message reliabilities. Using two different protograph repeat-accumulate codes as the source codes for low decoder complexity, the proposed scheme achieves a superior performance. In the case that the source codes are identical, the proposed scheme outperforms the previously proposed decoding schemes for two-way relay communication systems with two source nodes.

Hybrid coding scheme based on repeat-accumulate and polar codes

A hybrid coding scheme using repeat-accumulate (RA) code and polar code as subcodes is presented to improve the performance of block error probability. As the simplest turbo-like code, punctured RA code is introduced to improve the reliability of the hybrid scheme. A low complexity algorithm, belief propagation/successive cancellation hybrid decoding algorithm is proposed. Compared with polar code, this hybrid scheme can provide 0.3 dB coding gain with the code length 1024 and code rate 1/2. In contrast with RA code, it has no error floor in the additive white Gaussian noise channel.

An Improved Decoding Algorithm of Repeat Accumulate (RA) Codes

重复累积(RA)码译码使用置信传播(BP)算法，具有接近香农限的性能，但校验节点更新时使用复杂的双曲正切函数和反双曲正切函数，算法复杂度较高。为了降低译码算法的复杂度，且具有较好的性能，该文将查表法和分段函数近似法结合起来，提出了一种改进的译码算法。该算法采用分段的一次函数，去近似BP算法检验节点变换化简后的原函数，采用非常小的查找表得到一个校正值，用校正值去修正近似函数和变换化简后的原函数之间的误差，很好地避免了复杂函数的计算，且误差极小。该算法大大降低了译码算法的复杂度，且具有接近BP算法的译码性能。

Error bounds for repeat-accumulate codes decoded via linear programming

We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a linear-programming based decoder which is an inverse polynomial in the block length. Our bound is valid for any memoryless, binary-input, output-symmetric (MBIOS) channel. This result generalizes the bound derived by Feldman et al., which was for regular RA($2$) codes.

Design of Irregular Weighted Nonbinary Repeat-Accumulate Codes over GF(q) with q-ary Orthogonal Modulation Using a Gaussian Approximation

Using a Gaussian approximation to the distribution of the message vectors under density evolution, we design irregular weighted nonbinary repeat-accumulate codes over GF(q) with q-ary orthogonal modulation. The resulting codes achieve a frame error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> within 0.56 to 0.91 dB of channel capacity under the AWGN channel.

Performance of Weighted Nonbinary Repeat-Accumulate Codes over GF(q) with q-ary Orthogonal Modulation

An approximate upper bound is derived to the maximum likelihood decoding threshold of weighted nonbinary repeat-accumulate (WNRA) codes over GF(q) with q-ary orthogonal modulation and coherent detection over the additive white Gaussian noise channel. As with binary RA codes, WNRA codes show the potential for achieving the channel capacity with decreasing code rate for large enough q.

Performance Comparisons and Improvements of Channel Coding Techniques for Digital Satellite Broadcasting to Mobile Users

Digital satellite multimedia broadcasting services in Europe are specified in the Mobile Satellite Services (MSS) frequency band by two recently developed standards, namely the European Telecommunications Standards Institute (ETSI) Satellite Digital Radio (SDR) and the Digital Video Broadcasting-Satellite services to Handhelds (DVB-SH) standards. Commercial deployment of operational systems based on these standards is foreseen in the coming years targeting mainly six large European markets. For these standards, a state-of-the-art channel code is deployed based on the 3rd Generation Partnership Project 2 (3GPP2) specifications having a wide range of coding rates. The purpose of this paper is twofold: (i) It studies and compares, for the first time, the Bit Error Rate (BER) performance of the 3GPP2 turbo code used in the aforementioned systems, in order to serve as a benchmark for system design engineers; and (ii) It investigates novel alternative channel coding schemes, including other state-of-the-art turbo code configurations and also Low-Density Parity-Check (LDPC) codes with linear-time encoding, such as the Irregular Repeat-Accumulate (IRA) codes, in order to improve the performance and/or reduce the complexity in future mobile satellite broadcasting systems. Extensive performance evaluation results in the Additive White Gaussian Noise (AWGN) and uncorrelated Rayleigh/Rician fading channels have shown that the use of turbo codes with higher number of states improves performance against the 3GPP2 turbo codes of up to 0.25 dB but the decoding complexity is almost doubled. Furthermore, the use of duo-binary turbo codes reduces decoding latency and makes them more robust in puncturing with performance improvement against the 3GPP2 turbo codes of up to 0.3 dB but performance degrades at very low coding rates. On the other hand, the use of Rate Compatible (RC)-IRA codes results in smaller performance improvement against the 3GPP2 turbo codes, i.e. up to 0.1 dB, but rate compatibility is used to obtain different coding rates with simple puncturing/extending method.

Minimum distance lower bounds for girth-constrained RA code ensembles

Minimum distance lower bounds are derived using graphical enumeration and integer programming for girth-constrained repeat-accumulate (RA) code ensembles. Moreover, the worst subgraphs in Tanner graphs leading to the minimum distance lower bounds and the probabilities they occur are analyzed.

Matrix Embedding With Pseudorandom Coefficient Selection and Error Correction for Robust and Secure Steganography

In matrix embedding (ME)-based steganography, the host coefficients are minimally perturbed such that the transmitted bits fall in a coset of a linear code, with the syndrome conveying the hidden bits. The corresponding embedding distortion and vulnerability to steganalysis are significantly less than that of conventional quantization index modulation (QIM)-based hiding. However, ME is less robust to attacks, with a single host bit error leading to multiple decoding errors for the hidden bits. In this paper, we employ the ME-RA scheme, a combination of ME-based hiding with powerful repeat accumulate (RA) codes for error correction, to address this problem. A key contribution of this paper is to compute log likelihood ratios for RA decoding, taking into account the many-to-one mapping between the host coefficients and an encoded bit, for ME. To reduce detectability, we hide in randomized blocks, as in the recently proposed Yet Another Steganographic Scheme (YASS), replacing the QIM-based embedding in YASS by the proposed ME-RA scheme. We also show that the embedding performance can be improved by employing punctured RA codes. Through experiments based on a couple of thousand images, we show that for the same embedded data rate and a moderate attack level, the proposed ME-based method results in a lower detection rate than that obtained for QIM-based YASS.