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IEEE East-West Design & Test Symposium (EWDTS)

Hyper Neural Network as the Diffeomorphic Domain for Short Code Soft Decision Beyound Belief Propagation Decoding Problem

Vasiliy S. Usatyuk, Егоров Сергей Иванович

Published Sep 1, 2020• 2 citations
Publisher

Abstract

We proposed topological interpretation of the Tanner-Forney-Gross-Nachmani's Hyper Graph soft decoders based on Sourlas's Spin Glass reduction and Mezard's Replica Symmetry Breaking. Using it, we demonstrated reasons for uncertainty of the Neural Network loss function landscape and efficiency of replacing the arctanh neural network activation function with the Nishimori Temperature arctanh Taylor approximation. We compare the performance of short-length best known linear binary codes from Brouwer-Grassl codetable, Polar codes with sequence of frozen bits designed by Gaussian approximation and 5G eMBB Multi-Edge Type LDPC code with Base Graph 2 protograph on the AWGN-channel. The Sum-Product Flooding Scheduler decoder 50 iteration, Afterburn Saturated Min-Sum decoder, Ordered Statistics Decoder, Successive Cancellation Decoder with List size 32, Hyper Graph Neural Network under unfolding Belief Propagation decoder with Activation function Continues Metric Space relaxation according Nishimura temperature are used. The obtained simulation results are compared with the Finite-Length Polyanskiy theoretical boundary.

DOI
10.1109/ewdts50664.2020.9224643

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We proposed topological interpretation of the Tanner-Forney-Gross-Nachmani's Hyper Graph soft decoders based on Sourlas's Spin Glass reduction and Mezard's Replica Symmetry Breaking. Using it, we demonstrated reasons for uncertainty of the Neural Network loss function landscape and efficiency of replacing the arctanh neural network activation function with the Nishimori Temperature arctanh Taylor approximation. We compare the performance of short-length best known linear binary codes from Brouwer-Grassl codetable, Polar codes with sequence of frozen bits designed by Gaussian approximation and 5G eMBB Multi-Edge Type LDPC code with Base Graph 2 protograph on the AWGN-channel. The Sum-Product Flooding Scheduler decoder 50 iteration, Afterburn Saturated Min-Sum decoder, Ordered Statistics Decoder, Successive Cancellation Decoder with List size 32, Hyper Graph Neural Network under unfolding Belief Propagation decoder with Activation function Continues Metric Space relaxation according Nishimura temperature are used. The obtained simulation results are compared with the Finite-Length Polyanskiy theoretical boundary.
Neural decoders were shown to outperform classical message passing techniques for short BCH codes. In this work, we extend these results to much larger families of algebraic block codes, by performing message passing with graph neural networks. The parameters of the sub-network at each variable-node in the Tanner graph are obtained from a hypernetwork that receives the absolute values of the current message as input. To add stability, we employ a simplified version of the arctanh activation that is based on a high order Taylor approximation of this activation function. Our results show that for a large number of algebraic block codes, from diverse families of codes (BCH, LDPC, Polar), the decoding obtained with our method outperforms the vanilla belief propagation method as well as other learning techniques from the literature.
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with the codelength, thus they can only support short to moderate codelengths. From the point view of practicality, we propose a high-performance neural min-sum (MS) decoding method that makes full use of the lifting structure of protograph low-density parity-check (LDPC) codes. By this means, the size of the parameter array of each layer in the neural decoder only equals the number of edge-types for arbitrary codelengths. In particular, for protograph LDPC codes, the proposed neural MS decoder is constructed in a special way such that identical parameters are shared by a bundle of edges derived from the same edge-type. To reduce the complexity and overcome the vanishing gradient problem in training the proposed neural MS decoder, an iteration-by-iteration (i.e., layer-by-layer in neural networks) greedy training method is proposed. With this, the proposed neural MS decoder tends to be optimized with faster convergence, which is aligned with the early termination mechanism widely used in practice. To further enhance the generalization ability of the proposed neural MS decoder, a codelength/rate compatible training method is proposed, which randomly selects samples from a set of codes lifted from the same base code. As a theoretical performance evaluation tool, a trajectory-based extrinsic information transfer (T-EXIT) chart is developed for various decoders. Both T-EXIT and simulation results show that the optimized MS decoding can provide faster convergence and up to 1dB gain compared with the plain MS decoding and its variants with only slightly increased complexity. In addition, it can even outperform the sum-product algorithm for some short codes.
Spiking neural networks (SNNs) are neural networks that enable energy-efficient signal processing due to their event-based nature. This letter proposes a novel decoding algorithm for low-density parity-check (LDPC) codes that integrates SNNs into belief propagation (BP) decoding by approximating the check node update equations using SNNs. For the (273,191) and (1023,781) finite-geometry LDPC code, the proposed decoder outperforms sum-product decoder at high signal-to-noise ratios (SNRs). The decoder achieves a similar bit error rate to normalized sum-product decoding with successive relaxation. Furthermore, the novel decoding operates without requiring knowledge of the SNR, making it robust to SNR mismatch.
BP decoding algorithm is one of the commonly used decoding algorithms for LDPC codes. To adapt LDPC codes to different 5G scenarios and further improve the decoding performance of short LDPC codes, a scheme combining model-driven deep learning with a traditional BP decoding algorithm is proposed. With the advantages of model-driven, this solution expands the decoding iteration process between the check node and the variable node into a neural network and proposes a parameter normalization optimization solution to solve the problem of the program with many training parameters, the edge weights of the optimized Tanner graph are re-assigned and bound. Simulation results show that the proposed scheme can improve the decoding performance of LDPC codes with short lengths.
In this paper, we present a sparse neural network decoder (SNND) of polar codes based on belief propagation (BP) and deep learning. At first, the conventional factor graph of polar BP decoding is converted to the bipartite Tanner graph similar to low-density parity-check (LDPC) codes. Then the Tanner graph is unfolded and translated into the graphical representation of deep neural network (DNN). The complex sum-product algorithm (SPA) is modified to min-sum (MS) approximation with low complexity. We dramatically reduce the number of weight by using single weight to parameterize the networks. Optimized by the training techniques of deep learning, proposed SNND achieves comparative decoding performance of SPA and obtains about 0.5 dB gain over MS decoding on (128,64) and (256,128) codes. Moreover, 60% complexity reduction is achieved and the decoding latency is significantly lower than the conventional polar BP.
In this work, we propose a fully differentiable graph neural network (GNN)-based architecture for channel decoding and showcase a competitive decoding performance for various coding schemes, such as low-density parity-check (LDPC) and BCH codes. The idea is to let a neural network (NN) learn a generalized message passing algorithm over a given graph that represents the forward error correction (FEC) code structure by replacing node and edge message updates with trainable functions. Contrary to many other deep learning-based decoding approaches, the proposed solution enjoys scalability to arbitrary block lengths and the training is not limited by the curse of dimensionality. We benchmark our proposed decoder against state-of-the-art in conventional channel decoding as well as against recent deep learning-based results. For the (63,45) BCH code, our solution outperforms weighted belief propagation (BP) decoding by approximately 0.4 dB with significantly less decoding iterations and even for 5G NR LDPC codes, we observe a competitive performance when compared to conventional BP decoding. For the BCH codes, the resulting GNN decoder can be fully parametrized with only 9640 weights.