Showing papers on "Sequential decoding published in 2018"

An Iterative BP-CNN Architecture for Channel Decoding

Abstract: Inspired by the recent advances in deep learning, we propose a novel iterative belief propagation – convolutional neural network (BP-CNN) architecture for channel decoding under correlated noise. This architecture concatenates a trained CNN with a standard BP decoder. The standard BP decoder is used to estimate the coded bits, followed by a CNN to remove the estimation errors of the BP decoder and obtain a more accurate estimation of the channel noise. Iterating between BP and CNN will gradually improve the decoding SNR and, hence, result in better decoding performance. To train a well-behaved CNN model, we define a new loss function that involves not only the accuracy of the noise estimation but also the normality test for the estimation errors, i.e., to measure how likely the estimation errors follow a Gaussian distribution. The introduction of the normality test to the CNN training shapes the residual noise distribution and further reduces the bit error rate of the iterative decoding, compared to using the standard quadratic loss function. We carry out extensive experiments to analyze and verify the proposed framework. 1 1 Code is available at https://github.com/liangfei-info/Iterative-BP-CNN .

Dynamic-SCFlip Decoding of Polar Codes

Abstract: This paper proposes a generalization of the recently introduced successive cancellation flip (SCFlip) decoding of polar codes, characterized by a number of extra decoding attempts, where one or several positions are flipped from the standard SC decoding. To make such an approach effective, we first introduce the concept of higher order bit flips and propose a new metric to determine the bit flips that are more likely to correct the trajectory of the SC decoding. We then propose a generalized SCFlip decoding algorithm, referred to as dynamic-SCFlip (D-SCFlip), which dynamically builds a list of candidate bit flips, while guaranteeing that the next attempt has the highest probability of success among the remaining ones. Simulation results show that D-SCFlip is an effective alternative to SC-list decoding of polar codes, by providing very good error correcting performance, with an average computation complexity close to the one of the SC decoder.

Generalized Multiple-Mode OFDM With Index Modulation

Abstract: Multiple-mode orthogonal frequency division multiplexing with index modulation (MM-OFDM-IM), which transmits an OFDM signal with information bits embedded onto multiple distinguishable signal constellations of the same cardinality and their permutations, is a recently proposed IM technique in the frequency domain. It is capable of achieving higher spectral efficiency and better error performance than classical OFDM and existing frequency-domain IM schemes. In this paper, we propose the scheme of generalized (G-) MM-OFDM-IM, which allows a different subcarrier to utilize a signal constellation of a different size while conveying the same number of IM bits. Considering phase shift keying constellations, we present design guidelines for GMM-OFDM-IM to achieve an optimal error performance in the asymptotically high signal-to-noise ratio region. A computationally efficient and near-optimal detector based on the idea of sequential decoding is also tailored to GMM-OFDM-IM, which avoids the detection of an illegitimate constellation permutation. Monte Carlo simulations are conducted to validate the inherent properties and advantages of GMM-OFDM-IM.

A Score Function for Sequential Decoding of Polar Codes

Abstract: A novel score function is proposed for sequential decoding of polar codes. Significant reduction of the average decoding complexity is achieved by biasing the path metrics in the min-sum version of the stack successive cancellation decoding algorithm with its expected value. The proposed approach can be also used for near-ML decoding of short extended BCH codes.

An Iterative Check Polytope Projection Algorithm for ADMM-Based LP Decoding of LDPC Codes

Abstract: Alternating direction method of multipliers (ADMM) is a popular technique for linear-programming decoding of low-density parity-check codes. The computational complexity of ADMM is dominated by the Euclidean projection of a real-valued vector onto a parity-check polytope. Existing algorithms for such a projection all require sorting operations, which happen to be the most complex part of the projection. In this letter, we propose an iterative algorithm, without sorting operation, for projection onto the parity-check polytope. The proposed algorithm has a worst case complexity linear in the input dimension compared with the super-linear complexity of existing algorithms.

A New Construction and an Efficient Decoding Method for Rabin-Like Codes

Abstract: Array codes have been widely used in communication and storage systems. To reduce computational complexity, one important property of the array codes is that only exclusive OR operations are used in the encoding and decoding processes. Cauchy Reed–Solomon codes, Rabin-like codes, and circulant Cauchy codes are existing Cauchy maximum-distance separable (MDS) array codes that employ Cauchy matrices over finite fields, circular permutation matrices, and circulant Cauchy matrices, respectively. All these codes can correct any number of failures; however, a critical drawback of existing codes is the high decoding complexity. In this paper, we propose a new construction of Rabin-like codes based on a quotient ring with a cyclic structure. The newly constructed Rabin-like codes have more supported parameters (prime $p$ is extended to an odd number), such that the world sizes of them are more flexible than the existing Cauchy MDS array codes. An efficient decoding method using LU factorization of the Cauchy matrix can be applied to the newly constructed Rabin-like codes. It is shown that the decoding complexity of the proposed approach is less than that of existing Cauchy MDS array codes. Hence, the Rabin-like codes based on the new construction are attractive to distributed storage systems.

Top-down Tree Structured Decoding with Syntactic Connections for Neural Machine Translation and Parsing

Abstract: The addition of syntax-aware decoding in Neural Machine Translation (NMT) systems requires an effective tree-structured neural network, a syntax-aware attention model and a language generation model that is sensitive to sentence structure. Recent approaches resort to sequential decoding by adding additional neural network units to capture bottom-up structural information, or serialising structured data into sequence. We exploit a top-down tree-structured model called DRNN (Doubly-Recurrent Neural Networks) first proposed by Alvarez-Melis and Jaakola (2017) to create an NMT model called Seq2DRNN that combines a sequential encoder with tree-structured decoding augmented with a syntax-aware attention model. Unlike previous approaches to syntax-based NMT which use dependency parsing models our method uses constituency parsing which we argue provides useful information for translation. In addition, we use the syntactic structure of the sentence to add new connections to the tree-structured decoder neural network (Seq2DRNN+SynC). We compare our NMT model with sequential and state of the art syntax-based NMT models and show that our model produces more fluent translations with better reordering. Since our model is capable of doing translation and constituency parsing at the same time we also compare our parsing accuracy against other neural parsing models.

Randomized chained polar subcodes

Abstract: A generalization of polar subcodes is proposed, which enables a simple construction of codes of arbitrary length. The obtained codes are shown to outperform punctured and shortened polar codes under list/sequential decoding. Furthermore, a simplified Gaussian approximation for polar codes is presented.

Peterson–Gorenstein–Zierler algorithm for skew RS codes

Abstract: We design a non-commutative version of the Peterson–Gorenstein–Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In particular, our decoding algorithm applies for block codes beyond the classical cyclic case.

Simultaneous Partial Inverses and Decoding Interleaved Reed–Solomon Codes

Abstract: This paper introduces the simultaneous partial-inverse problem (SPI) for polynomials and develops its application to decoding interleaved Reed–Solomon codes beyond half the minimum distance. While closely related both to standard key equations and to well-known Pade approximation problems, the SPI problem stands out in several respects. First, the SPI problem has a unique solution (up to a scale factor), which satisfies a natural degree bound. Second, the SPI problem can be transformed (monomialized) into an equivalent SPI problem where all moduli are monomials. Third, the SPI problem can be solved by an efficient algorithm of the Berlekamp–Massey type. Fourth, decoding interleaved Reed–Solomon codes (or subfield-evaluation codes) beyond half the minimum distance can be analyzed in terms of a partial-inverse condition for the error pattern: if that condition is satisfied, then the (true) error locator polynomial is the unique solution of a standard key equation and can be computed in many different ways, including the well-known multi-sequence Berlekamp–Massey algorithm and the SPI algorithm of this paper. Two of the best performance bounds from the literature (the Schmidt–Sidorenko–Bossert bound and the Roth–Vontobel bound) are generalized to hold for the partial-inverse condition and thus to apply to several different decoding algorithms.

Distributed Joint Source-Channel Decoding Using Systematic Polar Codes

Abstract: This letter proposes a novel joint decoding scheme for correlated sources using systematic polar codes. In the proposed scheme, each source independently encodes its message into a systematic polar code word and sends the codeword via a binary-input additive white Gaussian noise channel to the common destination, where adaptive cyclic redundancy check-aided successive cancellation list (CA-SCL) decoders are employed. During the iterative decoding process, the log likelihood ratios (LLRs) fed to each adaptive CA-SCL decoder are iteratively combined with the extrinsic LLRs from other decoders. The correlation among the sources is exploited to improve the decoding performance. Simulation results show that, in comparison with independent decoding, the proposed scheme can achieve significantly improved decoding performance without increased complexity.

Decision-Directed Retention-Failure Recovery With Channel Update for MLC NAND Flash Memory

Abstract: To recover from the retention noise induced errors in nand flash memory, a retention-aware belief-propagation (RABP) decoding scheme for low-density parity-check codes is introduced. The RABP is a two-stage decoding scheme in which the memory cell’s charge-loss effect is systematically compensated. In RABP decoding, instead of read retries for data recovery, the probable victim cells are first determined with the help of read-back voltage signal and the decoded bit decisions. Then, for such suspected victim cells, their log-likelihood-ratio regions are modified in such a way as to absorb the effect of cell voltage downshift caused by retention noise, and then a second round of belief-propagation (BP) decoding is performed afresh, often with decoding failure recovery. Furthermore, leveraging on the RABP decoded bit-error pattern, an RABP assisted channel update (RABP-CU) algorithm is proposed which re-estimates the latest cell voltage distribution parameters without incurring new memory sensing operations. This is achieved by minimizing the mean squared error between the measured and predicted bit error/erasure values. Through simulations, it is shown that the RABP decoder increases the retention time limit by up to 70% compared with single round of BP decoding. The proposed RABP-CU algorithm further extends the data retention time.

Improving Windowed Decoding of SC LDPC Codes by Effective Decoding Termination, Message Reuse, and Amplification

Abstract: In this paper, we address a number of weaknesses of the windowed decoding of spatially coupled low-density parity-check (SC LDPC) codes and propose three modifications that simultaneously improve its performance, complexity, and latency. An effective termination method of the windowed decoding and the reuse of edge messages of previous target symbols provide a good performance-latency tradeoff when compared with the conventional windowed decoder. Also, we propose a scheme that lowers the error floor, in which the amplified edge messages of the previous window are used in the present window. The proposed windowed decoding, consisting of the three schemes, provides a significant performance gain with smaller latency. The validity of the new windowed decoding is verified by the evaluation with codes from different SC LDPC ensembles.

A Low Latency Coding Scheme: Semi-Random Block Oriented Convolutional Code

Abstract: In this paper, we propose a low latency coding scheme called Semi-Random Block Oriented Convolutional Code (SRBO-CC) which is similar to the Block Markov Superposition Transmission (BMST) but has short layer length. The SRBO-CC has a block oriented encoding process, where the input sequence is firstly encoded by a structured code and then superimposed on the random transformation of the previous inputs. The SRBO-CC is typically non-decodable by the Viterbi algorithm. Therefore, we analyze the tree structure of the SRBO-CC and employ the sequential decoding algorithm to decode the SRBO-CC. Simulation results show that the SRBO-CC performs well at low latency, suggesting that the SRBO-CC can be a promising solution for Ultra-Reliable and Low Latency Communication (URLLC).

A 21.66 Gbps Nonbinary LDPC Decoder for High-Speed Communications

Abstract: Compared to binary Low-Density Parity-Check (LDPC) codes, nonbinary LDPC (NB-LDPC) codes have better error correction performance under short-to-moderate block lengths or high-order modulations. Traditional min-sum-based soft decoding algorithms for NB-LDPC codes suffer from large computational complexity, which leads to inefficient hardware implementations. The Multiple-symbol-reliability weighted Bit-Reliability-Based (MwBRB) hard decoding algorithm achieves a good tradeoff between error correction performance and decoding complexity. However, efficient hardware implementations based on the MwBRB algorithm have not been investigated. In this brief, an improved layered MwBRB algorithm is first proposed, which results in faster convergence rate than the MwBRB algorithm. Then, an ultra-high-throughput low-complexity decoder architecture with an efficient partially parallel processing schedule is also presented. Finally, the proposed architecture is coded with RTL and synthesized under the TSMC 90-nm CMOS technology. The synthesis results demonstrate that the proposed decoder for a (837, 726) quasi-cyclic NB-LDPC code over GF(25) achieves a throughput of 21.66 Gbps and an area efficiency of 4.77 Gbps/M-gates under the TSMC 90-nm CMOS technology. The proposed decoder reaches a throughput more than 20 Gbps for the first time among the prior NB-LDPC decoders, and the area efficiency is far beyond the state-of-the-art designs.

Decoding of Decode and Forward (DF) Relay Protocol using Min-Sum Based Low Density Parity Check (LDPC) System

Abstract: Decoding high complexity is a major issue to design a decode and forward (DF) relay protocol. Thus, the establishment of low complexity decoding system would beneficial to assist decode and forward relay protocol. This paper reviews existing methods for the min-sum based LDPC decoding system as the low complexity decoding system. Reference lists of chosen articles were further reviewed for associated publications. This paper introduces comprehensive system model representing and describing the methods developed for LDPC based for DF relay protocol. It is consists of a number of components: (1) encoder and modulation at the source node, (2) demodulation, decoding, encoding and modulation at relay node, and (3) demodulation and decoding at the destination node. This paper also proposes a new taxonomy for min-sum based LDPC decoding techniques, highlights some of the most important components such as data used, result performances and profiles the Variable and Check Node (VCN) operation methods that have the potential to be used in DF relay protocol. Min-sum based LDPC decoding methods have the potential to provide an objective measure the best tradeoff between low complexities decoding process and the decoding error performance, and emerge as a cost-effective solution for practical application.

A Stage-Combined Belief Propagation Decoder for Polar Codes

Abstract: Message-passing decoding algorithm based on belief propagation is a widely used decoding algorithm for error correction codes. For moderate length polar codes, it achieves the error correction performance similar to the successive cancellation algorithm at the cost of high storage and computation requirements. In this paper, a novel modification is introduced for the belief propagation decoder of polar codes, wherein adjacent two processing stages are efficiently combined together to speed up the decoding. Corresponding path based belief estimation method is presented in detail. The proposed decoder halves the number of stages of the conventional decoder and thus can significantly reduce the message memory requirement. The architecture of the proposed decoder is presented. In general, the proposed decoder achieves 50 % memory reduction, more than 77 % throughput gain and significant area reduction without decoding performance degradation.

MDS 2D convolutional codes with optimal 1D horizontal projections

Abstract: Two dimensional (2D) convolutional codes is a class of codes that generalizes standard one-dimensional (1D) convolutional codes in order to treat two dimensional data. In this paper we present a novel and concrete construction of 2D convolutional codes with the particular property that their projection onto the horizontal lines yield optimal [in the sense of Almeida et al. (Linear Algebra Appl 499:1–25, 2016)] 1D convolutional codes with a certain rate and certain Forney indices. Moreover, using this property we show that the proposed constructions are indeed maximum distance separable, i.e., are 2D convolutional codes having the maximum possible distance among all 2D convolutional codes with the same parameters. The key idea is to use a particular type of superregular matrices to build the generator matrix.

Sequential Decoding on Syndrome Trellises for Nonparametric Detection

Abstract: Abstract The following paper adapts the classical Zigangirov-Jelinek algorithm to the decoding of nonbinary block codes under severe mixed jamming. To ensure reliable communications in this scenario we combine reception techniques based on distribution free statistical tests with sequential decoding on syndrome trellises. It will be shown that the proposed approach can ensure relatively high transmission rate with reasonable complexity.

An Integrated SWIPT Receiver Using Non-Coherent Detection Schemes

Abstract: In this paper, we investigate non-coherent detection schemes, for the integrated simultaneous wireless information and power tranfer (SWIPT) receiver. Firstly, we study a symbol by symbol (SBS) detection, while optimization of the transmitted energy pulses, enhances the performance of the receiver, in terms of symbol error rate (SER). In addition, by exploiting the channel coherence time, over $N$ transmitted energy pulses, we study sequential detection and introduce an integrated SEQ- MLSD decoder. With the use of sophisticated techniques such as Viterbi-type trellis-search algorithm and strategic-store strategy, we simplify the complexity of the sequential detection and overcome the error floor problem. Simulation results along with theoretical bounds are provided, validating the enhanced performance of our solution. The proposed sequential decoding scheme outperforms in terms of SER, the integrated SBS decoder and the conventional power-splitting SWIPT receiver, without degrading the energy harvested.

Generation and Decoding of Non-Binary LDPC Codes Using MSA Decoding Algorithm

Abstract: The latest advancements in low density parity check (LDPC) codes have resulted in reducing the decoding complexity. Hence these codes have excelled over BCH and turbo codes in terms of performance in the higher code rate, hence these codes are the trending topic in coding theory. Construction of LDPC codes is being elaborated in this proposed paper which further helps to study encoding and decoding of these NB-low density parity check codes. In the proposed design architecture, we have considered the Min-Sum Decoding Algorithm (MSA) employed here utilizes reliability estimation to improve error performance and it has advantages over bit flipping (BF) algorithms This algorithm can be improved with still more security level by having a trade-off between performance and data transmission. It can also enhanced by implementing it in real-time applications for data decoding and correction, for smaller size datum and these codes are used for medical and signal processing applications. These proposed LDPC codes are also used in the generation of bar codes, which are used in real time applications.

Fast Block Sequential Decoding of Polar Codes

Abstract: A reduced complexity sequential decoding algorithm for polar (sub)codes is described. The proposed approach relies on a decomposition of the polar (sub)code being decoded into a number of outer codes, and on-demand construction of codewords of these codes in the descending order of their probability. Construction of such codewords is implemented by fast decoding algorithms, which are available for many codes arising in the decomposition of polar codes. Further complexity reduction is achieved by taking hard decisions of the intermediate LLRs, and avoiding decoding of some outer codes. Data structures for sequential decoding of polar codes are described. The proposed algorithm can be also used for decoding of polar codes with CRC and short extended BCH\ codes. It has lower average decoding complexity compared with the existing decoding algorithms for the corresponding codes. \end{abstract}

The Fractality of Polar and Reed-Muller Codes.

Abstract: The generator matrices of polar codes and Reed-Muller codes are submatrices of the Kronecker product of a lower-triangular binary square matrix. For polar codes, the submatrix is generated by selecting rows according to their Bhattacharyya parameter, which is related to the error probability of sequential decoding. For Reed-Muller codes, the submatrix is generated by selecting rows according to their Hamming weight. In this work, we investigate the properties of the index sets selecting those rows, in the limit as the blocklength tends to infinity. We compute the Lebesgue measure and the Hausdorff dimension of these sets. We furthermore show that these sets are finely structured and self-similar in a well-defined sense, i.e., they have properties that are common to fractals.

Efficient Multi-User Quantize-Forward Relaying in Massive MIMO HetNets

Abstract: We utilize the orthogonality and channel hardening properties of massive multiple-input multiple- output (MIMO) systems to propose an efficient uplink transmission scheme for a heterogeneous network (HetNet). Such a network consists of multiple user-equipments (UEs) communicating with a macro-cell base station (MCBS) through a small-cell BS (SCBS) where both BSs have a large number of antennas and deploy zero-forcing (ZF) detection. The SCBS helps relay UEs' information using quantize-forward (QF) relaying with Wyner-Ziv (WZ) binning and multiple-timeslot transmission for the binning indices to the MCBS. The MCBS then deploys separate and sequential decoding for each UE's message. To maximize the rate region, we optimize the quantization levels through geometric programming and further obtain the optimal transmission timeslot durations in terms of the optimal quantization. We show that the proposed scheme has linear codebook size and decoding complexity in the number of UEs, while it achieves the same rate region of other QF schemes that employ joint transmission at the SCBS and/or joint decoding at the MCBS, all of which have exponential complexity. Furthermore, simulation results show that the SCBS should employ finer quantization for UE signals that have strong UE-SCBS links compared with the UE-MCBS links, and the proposed scheme can substantially outperform several existing alternatives under a wide range of parameter settings.

A soft-Input Bit-Flipping Decoder for Generalized Concatenated Codes

Abstract: Generalized concatenated (GC) codes with soft-input decoding were recently proposed for error correction in flash memories. This work proposes a soft-input decoder for GC codes that is based on a low-complexity bit-flipping procedure. This bit-flipping decoder uses a fixed number of test patterns and an algebraic decoder for soft-input decoding. An acceptance criterion for the final candidate codeword is proposed. Combined with error and erasure decoding of the outer Reed-Solomon codes, this bit-flipping decoder can improve the decoding performance and reduce the decoding complexity compared to the previously proposed sequential decoding. The bit-flipping decoder achieves a decoding performance similar to a maximum likelihood decoder for the inner codes.

Sequential decoding with stack reordering

Abstract: There is provided a decoder (310) for sequentially decoding a data signal received through a transmission channel in a communication system, the received data signal carrying transmitted symbols, the decoder comprising a symbol estimation unit (311) configured to determine estimated symbols representative of the transmitted symbols carried by the received signal from information stored in a stack, the stack being filled by iteratively expanding child nodes of a selected node of a decoding tree comprising a plurality of nodes, each node of the decoding tree corresponding to a candidate component of a symbol of the received data signal and each node being associated with a predetermined metric, the stack being filled at each iteration with at least some of the expanded child nodes and being ordered by increasing values of the metrics associated with the nodes, the selected node for each iteration corresponding to the node having the lowest metric in the stack. The decoder further comprises a stack reordering activation monitoring unit (313) configured to monitor at least one stack reordering activation condition and, in response to a stack reordering activation condition being verified, to cause the symbol estimation unit to : - reduce the metric associated with each node stored in the stack by a quantity, - reorder the stack by increasing value of the reduced metric, and - remove a set of nodes from the reordered stack so as to maintain a number N of nodes in the reordered stack, the maintained nodes corresponding to the N nodes having the lowest metrics in the reordered stack.

A Generalization of Multiple-Mode OFDM with Index Modulation

Abstract: In this paper, we propose the scheme of generalized multiple-mode orthogonal frequency division multiplexing with index modulation (GMM-OFDM-IM), which allows a different subcarrier to utilize a signal constellation of a different size while conveying the same number of IM bits. Considering phase shift keying (PSK) constellations, we present design guidelines for GMM-OFDM-IM to achieve the optimal error performance in the asymptotically high signal-to-noise ratio region. A computationally efficient and near-optimal detector based on the idea of sequential decoding is also tailored to GMM-OFDM-IM to avoid the detection of an illegimate constellation permutation. Monte Carlo simulations are conducted to examine GMM-OFDM-IM, whose inherent properties and advantages are revealed by the simulation results.

Block Sequential Decoding Techniques for Polar Subcodes

Abstract: A reduced complexity sequential decoding algorithm for polar subcodes is described. The proposed approach relies on a decomposition of the polar (sub)code into a number of outer codes, and on-demand construction of codewords of these codes in the descending order of their probability. The proposed algorithm can be also used for decoding of polar codes with CRC and short extended BCH\ codes. It has lower average decoding complexity compared to the existing decoding algorithms for the corresponding codes.

Reliability Enhancement without Employing STCs of a 3 × 3 MIMO Communication System Using a Parallel Decoding Technique

Abstract: In this paper, the performance analysis of a (3 × 3) Multiple Input Multiple Output (MIMO) communication system is performed to achieve spatial diversity using linear minimum mean square estimation (LMMSE) decoding method at the receiver. We propose an efficient algorithm that achieves both spatial diversity and spatial multiplexing simultaneously. We called it parallel processing decoding technique. The proposed technique increases the rate of decoded symbol, improves the reliability of the transmission without employing STCs, and prevents any possible error propagation that may be presented in other sequential decoding methods. Simulation results demonstrate the advantages of using the proposed novel technique.

Turbo decoding of simple product codes in a two user binary adder channel employing the Bahl–Cocke–Jelinek–Raviv algorithm

Abstract: The main goal in this paper is an investigation of the Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm applied in a turbo decoding scheme. Binary product codes are employed in a turbo coding scheme and the channel model considered is the two user binary adder channel (2-BAC) with additive white Gaussian noise. A trellis for two users is constructed for a pair of product codes tailored for use in the 2-BAC in order to employ the BCJR decoding algorithm. Computer simulation is employed to show that product codes on the 2-BAC, employing low-complexity component codes, produces considerable gain with few iterations under iterative BCJR decoding.