相关论文: A General Framework for Codes Involving Redundancy…
This paper presents new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to various nonlinear codeword length objectives. Like the most well-known redundancy bounds for…
Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not…
Consider the set of source distributions within a fixed maximum relative entropy with respect to a given nominal distribution. Lossless source coding over this relative entropy ball can be approached in more than one way. A problem…
In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where…
This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of…
We deal with the minimization of the ${\mathcal H}_\infty$-norm of the transfer function of a parameter-dependent descriptor system over the set of admissible parameter values. Subspace frameworks are proposed for such minimization problems…
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
The problem of detecting and removing redundant constraints is fundamental in optimization. We focus on the case of linear programs (LPs), given by $d$ variables with $n$ inequality constraints. A constraint is called \emph{redundant}, if…
In this paper we study the redundancy of Huffman codes. In particular, we consider sources for which the probability of one of the source symbols is known. We prove a conjecture of Ye and Yeung regarding the upper bound on the redundancy of…
Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems…
We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for…
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result,…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…
We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
In this paper, we study the problem of designing prefix-free encoding schemes having minimum average code length that can be decoded efficiently under a decode cost model that captures memory hierarchy induced cost functions. We also study…