The problem of low complexity, close to optimal, channel decoding linear codes with short moderate block length is considered. It shown that deep learning methods can be used improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for min-sum algorithm. also tying parameters decoders across iterations, so as form recurrent neural network architecture, implemented comparable results. advantage significantly less required. We introduce...

A novel deep learning method for improving the belief propagation algorithm is proposed. The generalizes standard by assigning weights to edges of Tanner graph. These are then trained using techniques. well-known property independence performance on transmitted codeword. crucial our new that decoder preserved this property. Furthermore, allows us learn only a single codeword instead exponential number codewords. Improvements over demonstrated various high density parity check codes.

The problem of efficient maximum-likelihood soft decision decoding binary BCH codes is considered. It known that those primitive whose designed distance one less than a power two, contain subcodes high dimension which consist direct-sum several identical codes. authors show the same kind structure exists in all codes, as well composite block length. They also introduce related termed "concurring-sum", and then establish its existence Both structures are employed to upper bound number states...

Maximum-likelihood soft-decision decoding of linear block codes is addressed. A binary multiple-check generalization the Wagner rule presented, and two methods for its implementation, one which resembles suboptimal Forney-Chase algorithms, are described. Besides efficient soft small codes, generalized enables utilization subspaces a wide variety, thereby yielding maximum-likelihood decoders with substantially reduced computational complexity some larger codes. More sophisticated choice...

In this paper, deep neural network (DNN) is utilized to improve message passing detectors (MPDs) for massive multiple-input multiple-output (MIMO) systems. A general framework construct DNN architecture MIMO detection first introduced by unfolding iterative MPDs. are then proposed based on modified MPDs including damped belief propagation (BP), max-sum (MS) BP, and simplified channel hardening-exploiting (CHEMP). The correction factors optimized via learning better performance. Numerical...

A Reed-Solomon decoder that makes use of bit-level soft-decision information is presented. generator matrix possesses a certain inherent structure in GF(2) derived. This allows the code to be represented as union cosets, each coset being an interleaver several binary BCH codes. Such partition into cosets provides clue for efficient decoding. Two decoding algorithms are In development first algorithm memoryless channel assumed, making value this more conceptual than practical. The second...

An approach for efficient utilization of fast Hadamard transform in decoding binary linear block codes is presented. Computational gain obtained by employing various types concurring codewords, and memory reduction also achieved appropriately selecting rows the generator matrix. The availability these codewords general, particularly some most frequently encountered codes, discussed.

Designing a practical, low complexity, close to optimal, channel decoder for powerful algebraic codes with short moderate block length is an open research problem. Recently it has been shown that feed-forward neural network architecture can improve on standard belief propagation decoding, despite the large example space. In this paper we introduce recurrent decoding linear codes. Our method shows comparable bit error rate results compared significantly less parameters. We also demonstrate...

Recently, deep learning methods have shown significant improvements in communication systems. In this paper, we study the equalization problem over nonlinear channel using neural networks. The joint equalizer and decoder based on networks are proposed to realize blind decoding process without knowledge of state information (CSI). Different from previous methods, use two instead one. First, convolutional network (CNN) is used adaptively recover transmitted signal impairment distortions. Then...

An iterative algorithm for soft-input soft-output (SISO) decoding of classical algebraic cyclic block codes is presented below. Inspired by other approaches high performance belief propagation (BP) decoding, this requires up to 10 times less computational complexity than methods that achieve similar performance. By utilizing multiple BP decoders, and using random permutation taken from the group code, reaches near maximum likelihood A comparison proposed versus as well. This includes...

High quality data is essential in deep learning to train a robust model. While other fields sparse and costly collect, error decoding it free query label thus allowing potential exploitation. Utilizing this fact inspired by active learning, two novel methods are introduced improve Weighted Belief Propagation (WBP) decoding. These incorporate machine-learning concepts with measures. For BCH(63,36), (63,45) (127,64) codes, cycle-reduced parity-check matrices, improvement of up 0.4dB at the...

In this paper, deep neural network (DNN) is utilized to improve the belief propagation (BP) detection for massive multiple-input multiple-output (MIMO) systems. A architecture suitable task firstly introduced by unfolding BP algorithms. DNN MIMO detectors are then proposed based on two modified detectors, damped and max-sum BP. The correction factors in these algorithms optimized through learning techniques, aiming at improved performance. Numerical results presented demonstrate performance...

An algorithm for maximum likelihood decoding of the Leech lattice is presented. The involves projecting points directly onto codewords (6,3,4) quaternary code-the hexacode. Projection on hexacode induces a partition into four cosets certain sublattice 24. Such enables with 3595 real operations in worst case and only 2955 average. This about half average complexity best previously known algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML"...

An algorithm for maximum-likelihood soft-decision decoding of the binary (24,12,8) Golay code is presented. The involves projecting codewords onto (6,3,4) over GF(4)-the hexacode. complexity proposed at most 651 real operations. Along similar lines, tetracode may be employed ternary (12,6,6) with only 530 also implies a reduction in number computations required Leech lattice.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents deep learning (DL) methods to optimize polar belief propagation (BP) decoding and concatenated LDPC-polar codes. First, two-dimensional offset Min-Sum (2-D OMS) is proposed improve the error-correction performance of existing normalized (NMS) decoding. Two optimization used in DL, namely back-propagation stochastic gradient descent, are exploited derive parameters algorithms. Numerical results demonstrate that there no gap between 2-D OMS exact BP on various code lengths....

Multilevel constructions of the binary Golay code and Leech lattice are described. Both based upon projection onto (6,3,4) hexacode over GF(4). However, unlike previously reported constructions, new multilevel make three levels independent by way using a different set coset representatives for one quaternary coordinates. Based structure lattice, efficient bounded-distance decoding algorithms devised. The decoder requires at most 431 operations. As compared to 651 operations best known...

The size of minimal trellis representation linear block codes is addressed. Two general upper bounds on the size, based zero-concurring codewords and contraction index subcodes, are presented. related permutations for attaining exhibited. These evidently improve previously published bound. Additional certain code constructions derived. focus squaring construction, specific constructive Reed-Muller repeated-root cyclic obtained. In particular, recursive construction explored exact this design...

An efficient algorithm is presented for maximum-likelihood soft-decision decoding of the Leech lattice. The superiority this decoder with respect to both computational and memory complexities demonstrated in comparison previously published methods. Gain factors range 2-10 are achieved. authors conclude some more advanced ideas achieving a further reduction complexity based on generalization Wagner method two parity constraints. A trellis-coded modulation schemes discussed. seems achieve...

Ensemble models are widely used to solve complex tasks by their decomposition into multiple simpler tasks, each one solved locally a single member of the ensemble. Decoding error-correction codes is hard problem due curse dimensionality, leading consider ensembles-of-decoders as possible solution. Nonetheless, must take complexity account, especially in decoding. We suggest low-complexity scheme where participates decoding word. First, distribution feasible words partitioned non-overlapping...

Geometric interpretation of turbo decoding has founded an analytical basis, and provided tools for the analysis this algorithm. We focus on product codes, based geometric framework, we extend results show how can be practically adapted case. Specifically, investigate algorithm's stability its convergence rate. present new concerning structure properties matrices algorithm, develop upper bounds prove that any 2/spl times/2 (information bits) there is a unique stable fixed point. For general...

A novel and efficient neural decoder algorithm is proposed. The proposed based on the Belief Propagation Automorphism Group. By combining belief propagation with permutations from Group we achieve near maximum likelihood performance for High Density Parity Check codes. Moreover, significantly improves decoding complexity, compared to our earlier work topic. We also investigate training process show how it can be accelerated. Simulations of hessian condition number why learning demonstrate...

The problem of maximum likelihood decoding with a neural decoder for error-correcting code is considered. It shown that the can be improved two novel loss terms on node's activations. first term imposes sparse constraint Whereas, second tried to mimic activations from teacher which has better performance. proposed method same run time complexity and model size as Belief Propagation decoder, while improving performance by up <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML"...