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Near optimal decoding of good error control codes is generally a difficult task. However, for a certain type of (sufficiently) good codes an efficient decoding algorithm with near optimal performance exists. These codes are defined via a…
We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes and message-passing decoding. The asymptotic (in the length) performance of such a combination for a fixed number of…
This paper presents generalized channel coding theorems for a time-slotted distributed communication system where a transmitter-receiver pair is communicating in parallel with other transmitters. Assume that the channel code of each…
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,…
Machine learning based approaches are being increasingly used for designing decoders for next generation communication systems. One widely used framework is neural belief propagation (NBP), which unfolds the belief propagation (BP)…
This work proposes a tractable estimation of the maximum a posteriori (MAP) threshold of various families of sparse-graph code ensembles, by using an approximation for the extended belief propagation generalized extrinsic information…
The performance of the generalized belief propagation algorithm for computing the noiseless capacity and mutual information rates of finite-size two-dimensional and three-dimensional run-length limited constraints is investigated. For each…
We develop a novel framework for proving converse theorems for channel coding, which is based on the analysis technique of multicast transmission with an additional auxiliary receiver, which serves as a genie to the original receiver. The…
New upper and lower bounds for the error probability over an erasure channel are provided, making use of Wei's generalized weights, hierarchy and spectra. In many situations the upper and lower bounds coincide and this allows improvement of…
Belief propagation is a fundamental message-passing algorithm for numerous applications in machine learning. It is known that belief propagation algorithm is exact on tree graphs. However, belief propagation is run on loopy graphs in most…
The Poltyrev bound provides a very tight upper bound on the decoding error probability when using binary linear codes for transmission over the binary symmetric channel and the additive white Gaussian noise channel, making use of the code's…
Transformer channel decoders, such as the Error Correction Code Transformer (ECCT), have shown strong empirical performance in channel decoding, yet their generalization behavior remains theoretically unclear. This paper studies the…
This paper considers the performance of Reed-Muller (RM) codes transmitted over binary memoryless symmetric (BMS) channels under bitwise maximum-a-posteriori (bit-MAP) decoding. Its main result is that, for a fixed BMS channel, the family…
When information is to be transmitted over an unknown, possibly unreliable channel, an erasure option at the decoder is desirable. Using constant-composition random codes, we propose a generalization of Csiszar and Korner's Maximum Mutual…
An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g. notably for the quantum low-density parity check (LDPC) code class of…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
We consider the Additive White Gaussian Noise channel with Binary Phase Shift Keying modulation. Our aim is to enable an algebraic hard decision Bounded Minimum Distance decoder for a binary block code to exploit soft information obtained…
We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a…