arXiv subjects

David Burshtein

Publications and source records attributed to David Burshtein.

At least 19 recordsLinked to original sources

arXiv2025

GDiffuSE: Diffusion-based speech enhancement with noise model guidance

This paper introduces a novel speech enhancement (SE) approach based on a denoising diffusion probabilistic model (DDPM), termed Guided diffusion for speech enhancement (GDiffuSE). In contrast to conventional methods that directly map noisy speech to clean speech, our method employs a lightweight helper model to estimate the noise distribution, which is then incorporated into the diffusion denoising process via a guidance mechanism. This design improves robustness by enabling seamless adaptation to unseen noise types and by leveraging large-scale DDPMs originally trained for speech generation in the context of SE. We evaluate our approach on noisy signals obtained by adding noise samples from the BBC sound effects database to LibriSpeech utterances, showing consistent improvements over state-of-the-art baselines under mismatched noise conditions. Examples are available at our project webpage.

cs.SD↗

arXiv2025

On the error correction of iterative bounded distance decoding of generalized LDPC codes

Consider an ensemble of regular generalized LDPC (GLDPC) codes and assume that the same component code is associated with each parity check node. To decode a GLDPC code from the ensemble, we use the bit flipping bounded distance decoding algorithm, which is an extension of the bit flipping algorithm for LDPC codes. Previous work has shown conditions, under which, for a typical code in the ensemble with blocklength sufficiently large, a positive constant fraction of worst case errors can be corrected. In this work we first show that these requirements can be relaxed for ensembles with small left degrees. While previous work on GLDPC codes has considered expander graph arguments, our analysis formulates a necessary condition that the Tanner graph needs to satisfy for a failure event and then shows that the probability of this event vanishes for a sufficiently large blocklength. We then extend the analysis to random error correction and derive a lower bound on the fraction of random errors that can be corrected asymptotically. We discuss the extension of our results to non-binary GLDPC codes and present numerical examples.

cs.IT↗

arXiv2023

Semi-Supervised Variational Inference over Nonlinear Channels

Deep learning methods for communications over unknown nonlinear channels have attracted considerable interest recently. In this paper, we consider semi-supervised learning methods, which are based on variational inference, for decoding unknown nonlinear channels. These methods, which include Monte Carlo expectation maximization and a variational autoencoder, make efficient use of few pilot symbols and the payload data. The best semi-supervised learning results are achieved with a variational autoencoder. For sufficiently many payload symbols, the variational autoencoder also has lower error rate compared to meta learning that uses the pilot data of the present as well as previous transmission blocks.

eess.SP↗

arXiv2021

Efficient Belief Propagation List Ordered Statistics Decoding of Polar Codes

New algorithms for efficient decoding of polar codes (which may be CRC-augmented), transmitted over either a binary erasure channel (BEC) or an additive white Gaussian noise channel (AWGNC), are presented. We start by presenting a new efficient exact maximum likelihood decoding algorithm for the BEC based on inactivation decoding and analyze its computational complexity. This algorithm applies a matrix triangulation process on a sparse polar code parity check matrix, followed by solving a small size linear system over GF(2). We then consider efficient decoding of polar codes, transmitted over the AWGNC. The algorithm applies CRC-aided belief propagation list (CBPL) decoding, followed by ordered statistics decoding (OSD) of low order. Even when the reprocessing order of the OSD is as low as one, the new decoder is shown to significantly improve on plain CBPL. To implement the OSD efficiently, we adapt the matrix triangulation algorithm from the BEC case. We also indicate how the decoding algorithms can be implemented in parallel for low latency decoding. Numerical simulations are used to evaluate the performance and computational complexity of the new algorithms.

cs.IT↗

arXiv2021

Efficient Maximum Likelihood Decoding of Polar Codes Over the Binary Erasure Channel

A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar code parity check matrix, followed by solving a small size linear system over GF(2). To implement the matrix triangulation, we apply belief propagation decoding type operations. We also indicate how this decoder can be implemented in parallel for low latency decoding. Numerical simulations are used to evaluate the performance and computational complexity of the new algorithm.

cs.IT↗

arXiv2021

Belief Propagation List Ordered Statistics Decoding of Polar Codes

It is shown how to combine ordered statistics decoding (OSD) with CRC-aided belief propagation list (CBPL) decoding of polar codes. Even when the reprocessing order of the OSD is as low as one, the new decoder is shown to significantly improve on CBPL. For reprocessing orders higher than one, we suggest partial reprocessing, where only error patterns associated with the least reliable part of the belief propagation decoded most reliable independent bits are considered. This type of partial reprocessing offers a trade-off between performance and computational complexity.

cs.IT↗

arXiv2020

Feedback Channel Communication with Low Precision Arithmetic

The problem of communicating over an additive white Gaussian noise channel with feedback, using low precision arithmetic, is considered. The Schalkwijk-Kailath (SK) scheme is known to achieve an error probability that decays double exponentially in the number of interaction rounds, for any rate below channel capacity. However, SK is also known to suffer from numerical issues. Transmission close to channel capacity requires a moderate number of interaction rounds. This may lead to a huge constellation size. Furthermore, the internal variables of the scheme decay to zero exponentially fast. As a result, the SK scheme fails when implemented with low precision variables, which are widely used in hardware implementations. In this work we propose a new, modified scheme termed Zoom-in SK (ZSK), which breaks the SK protocol into several stages. Each stage comprises several SK iterations followed by a synchronized zoom step. The zoom-in allows the receiver and transmitter to keep the scheme's parameters relatively large such that low precision arithmetic can be used even for a large rate or a large number of interaction rounds. We prove that the new scheme achieves approximately the same error probability as SK while not suffering from numerical issues. We further verify our results in simulation and compare ZSK to the original SK scheme.

cs.IT↗

arXiv2019

Unsupervised Linear and Nonlinear Channel Equalization and Decoding using Variational Autoencoders

A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, without using pilot symbols. We derive an approximate maximum likelihood estimate to the channel parameters and reconstruct the transmitted data. We demonstrate significant and consistent improvements in the error rate of the reconstructed symbols, compared to existing blind equalization methods such as constant modulus, thus enabling faster channel acquisition. The VAE equalizer uses a convolutional neural network with a small number of free parameters. These results are extended to blind equalization over a noisy nonlinear ISI channel with unknown parameters. We then consider coded communication using low-density parity-check (LDPC) codes transmitted over a noisy linear or nonlinear ISI channel. The goal is to reconstruct the transmitted message from the channel observations corresponding to a transmitted codeword, without using pilot symbols. We demonstrate improvements compared to the expectation maximization (EM) algorithm using turbo equalization. Furthermore, unlike EM, the computational complexity of our method does not have exponential dependence on the size of the channel impulse response.

cs.LG↗

arXiv2019

On Polar Coding for Binary Dirty Paper

The problem of communication over binary dirty paper (DP) using nested polar codes is considered. An improved scheme, focusing on low delay, short to moderate blocklength communication is proposed. Successive cancellation list (SCL) decoding with properly defined CRC is used for channel coding, and SCL encoding without CRC is used for source coding. The performance is compared to the best achievable rate of any coding scheme for binary DP using nested codes. A well known problem with nested polar codes for binary DP is the existence of frozen channel code bits that are not frozen in the source code. These bits need to be retransmitted in a second phase of the scheme, thus reducing transmission rate. We observe that the number of these bits is typically either zero or a small number, and provide an improved analysis, compared to that presented in the literature, on the size of this set and on its scaling with respect to the blocklength when the power constraint parameter is sufficiently large or the channel crossover probability sufficiently small.

cs.IT↗

arXiv2018

Blind Channel Equalization using Variational Autoencoders

A new maximum likelihood estimation approach for blind channel equalization, using variational autoencoders (VAEs), is introduced. Significant and consistent improvements in the error rate of the reconstructed symbols, compared to constant modulus equalizers, are demonstrated. In fact, for the channels that were examined, the performance of the new VAE blind channel equalizer was close to the performance of a nonblind adaptive linear minimum mean square error equalizer. The new equalization method enables a significantly lower latency channel acquisition compared to the constant modulus algorithm (CMA). The VAE uses a convolutional neural network with two layers and a very small number of free parameters. Although the computational complexity of the new equalizer is higher compared to CMA, it is still reasonable, and the number of free parameters to estimate is small.

eess.SP↗

arXiv2018

Near Maximum Likelihood Decoding with Deep Learning

A novel and efficient neural decoder algorithm is proposed. The proposed decoder is based on the neural Belief Propagation algorithm and the Automorphism Group. By combining neural belief propagation with permutations from the Automorphism Group we achieve near maximum likelihood performance for High Density Parity Check codes. Moreover, the proposed decoder significantly improves the decoding complexity, compared to our earlier work on the topic. We also investigate the training process and show how it can be accelerated. Simulations of the hessian and the condition number show why the learning process is accelerated. We demonstrate the decoding algorithm for various linear block codes of length up to 63 bits.

cs.IT↗

arXiv2017

Performance Bounds of Concatenated Polar Coding Schemes

A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first bound is obtained using outer codes which are typical linear codes from the ensemble of parity check matrices whose elements are chosen independently and uniformly. As a byproduct of this bound, it determines the required rate split of the total rate to the rates of the outer codes. A lower bound on the error exponent that holds for all BMS channels with a given capacity is then derived. Improved bounds and approximations for finite blocklength codes using channel dispersions (normal approximation), as well as converse and approximate converse results, are also obtained. The bounds are compared to actual simulation results from the literature. For the cases considered, when transmitting over the binary input additive white Gaussian noise channel, there was only a small gap between the normal approximation prediction and the actual error rate of concatenated BCH-polar codes.

cs.IT↗

arXiv2017

Deep Learning Methods for Improved Decoding of Linear Codes

The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for the min-sum algorithm. It is also shown that tying the parameters of the decoders across iterations, so as to form a recurrent neural network architecture, can be implemented with comparable results. The advantage is that significantly less parameters are required. We also introduce a recurrent neural decoder architecture based on the method of successive relaxation. Improvements over standard belief propagation are also observed on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the neural belief propagation decoder can be used to improve the performance, or alternatively reduce the computational complexity, of a close to optimal decoder of short BCH codes.

cs.IT↗

arXiv2017

Simplified End-to-End MMI Training and Voting for ASR

A simplified speech recognition system that uses the maximum mutual information (MMI) criterion is considered. End-to-end training using gradient descent is suggested, similarly to the training of connectionist temporal classification (CTC). We use an MMI criterion with a simple language model in the training stage, and a standard HMM decoder. Our method compares favorably to CTC in terms of performance, robustness, decoding time, disk footprint and quality of alignments. The good alignments enable the use of a straightforward ensemble method, obtained by simply averaging the predictions of several neural network models, that were trained separately end-to-end. The ensemble method yields a considerable reduction in the word error rate.

cs.LG↗

arXiv2017

RNN Decoding of Linear Block Codes

Designing a practical, low complexity, close to optimal, channel decoder for powerful algebraic codes with short to moderate block length is an open research problem. Recently it has been shown that a feed-forward neural network architecture can improve on standard belief propagation decoding, despite the large example space. In this paper we introduce a recurrent neural network architecture for decoding linear block codes. Our method shows comparable bit error rate results compared to the feed-forward neural network with significantly less parameters. We also demonstrate improved performance over belief propagation on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the RNN decoder can be used to improve the performance or alternatively reduce the computational complexity of the mRRD algorithm for low complexity, close to optimal, decoding of short BCH codes.

cs.IT↗

arXiv2016

Learning to Decode Linear Codes Using Deep Learning

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

cs.IT↗

arXiv2015

On the Finite Length Scaling of Ternary Polar Codes

The polarization process of polar codes over a ternary alphabet is studied. Recently it has been shown that the scaling of the blocklength of polar codes with prime alphabet size scales polynomially with respect to the inverse of the gap between code rate and channel capacity. However, except for the binary case, the degree of the polynomial in the bound is extremely large. In this work, it is shown that a much lower degree polynomial can be computed numerically for the ternary case. Similar results are conjectured for the general case of prime alphabet size.

cs.IT↗

arXiv2013

Improved Bounds on the Finite Length Scaling of Polar Codes

Improved bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is obtained. The main result is that the blocklength required to communicate reliably scales at most as $O((I(W)-R)^{-5.77})$ where $R$ is the code rate and $I(W)$ the symmetric capacity of the channel, $W$. The results are then extended to polar lossy source coding at rate $R$ of a source with symmetric distortion-rate function $D(\cdot)$. The blocklength required scales at most as $O((D_N-D(R))^{-5.77})$ where $D_N$ is the actual distortion.

cs.IT↗