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When we try to solve a system of linear equations, we can consider a simple iterative algorithm in which an equation including only one variable is chosen at each step, and the variable is fixed to the value satisfying the equation. The…
The article reviews different definitions for a convolutional code which can be found in the literature. The algebraic differences between the definitions are worked out in detail. It is shown that bi-infinite support systems are dual to…
We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…
Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods. In this paper, we develop an encoding that allows for logical properties to be preserved and is…
In this paper, we introduce an efficient iterative solver for the joint linear-programming (LP) decoding of low-density parity-check (LDPC) codes and finite-state channels (FSCs). In particular, we extend the approach of iterative…
Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…
We study the general integer programming (IP) problem of optimizing a separable convex function over the integer points of a polytope: $\min \{f(\mathbf{x}) \mid A\mathbf{x} = \mathbf{b}, \, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \,…
Motivated by the sequence reconstruction problem from traces in DNA-based storage, we consider the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder. We propose simple…
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…
We describe a successive-cancellation \emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\i}kan. In the proposed list decoder, up to $L$ decoding paths are considered…
Polar codes under cyclic redundancy check aided successive cancellation list (CA-SCL) decoding can outperform the turbo codes and the LDPC codes when code lengths are configured to be several kilobits. In order to reduce the decoding…
In recent years, neural network-based image compression techniques have been able to outperform traditional codecs and have opened the gates for the development of learning-based video codecs. However, to take advantage of the high temporal…
A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
In this paper, a construction of $(n,k,\delta)$ LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and the later work of Tong is provided. The sets of integers forming a…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
In this paper, we introduce a deep learning-based decoder designed for concatenated coding schemes over a deletion/substitution channel. Specifically, we focus on serially concatenated codes, where the outer code is either a convolutional…
We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.
This paper characterizes and discusses devolutionary genetic algorithms and evaluates their performances in solving the minimum labeling Steiner tree (MLST) problem. We define devolutionary algorithms as the process of reaching a feasible…
We tackle the problems of latent variables identification and ``out-of-support'' image generation in representation learning. We show that both are possible for a class of decoders that we call additive, which are reminiscent of decoders…