Related papers: Linear Programming based Converses for Finite Bloc…
We present a hardware-based implementation of Linear Program (LP) decoding for binary linear codes. LP decoding frames error-correction as an optimization problem. In contrast, variants of Belief Propagation (BP) decoding frame…
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…
We show how to efficiently compute the derivative (when it exists) of the solution map of log-log convex programs (LLCPs). These are nonconvex, nonsmooth optimization problems with positive variables that become convex when the variables,…
Guruswami and Indyk showed in [1] that Forney's error exponent can be achieved with linear coding complexity over binary symmetric channels. This paper extends this conclusion to general discrete-time memoryless channels and shows that…
Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of…
This paper proposes two approaches for reducing the impact of the error floor phenomenon when decoding quantum low-density parity-check codes with belief propagation based algorithms. First, a low-complexity syndrome-based linear…
Given a nonlinear, univariate, bounded, and differentiable function $f(x)$, this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of $f(x)$ and its…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both…
Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs…
We derive upper bounds on the rate of transmission of classical information over quantum channels by block codes with a given blocklength and error probability, for both entanglement-assisted and unassisted codes, in terms of a unifying…
We show that linear codes combined with rejection sampling can yield a capacity-achieving scheme for simulating additive exchangeable noise channels. Specifically, our scheme achieves an amount of communication within $\log e + 1$ bits from…
For quasi-linear interface problems with discontinuous diffusion coefficients, the nonconvex objective functional often leads to optimization stagnation in randomized neural network approximations. This paper Proposes a…
Decentralized optimization for non-convex problems are now demanding by many emerging applications (e.g., smart grids, smart building, etc.). Though dramatic progress has been achieved in convex problems, the results for non-convex cases,…
Lattice reduction is a NP-hard problem well known in computer science and cryptography. The Lenstra-Lenstra-Lovasz (LLL) algorithm based on the calculation of orthogonal Gram-Schmidt (GS) bases is efficient and gives a good solution in…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
We consider the problem of Linear Programming (LP) decoding of binary linear codes. The LP excess lemma was introduced by the first author, B. Ghazi, and R. Urbanke (IEEE Trans. Inf. Th., 2014) as a technique to trade crossover probability…
The lift-and-project closure is the relaxation obtained by computing all lift-and-project cuts from the initial formulation of a mixed integer linear program or equivalently by computing all mixed integer Gomory cuts read from all tableau's…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…