Related papers: Lower Bounds on the Redundancy of Huffman Codes wi…
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…
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…
In this paper we consider the class of anti-uniform Huffman codes and derive tight lower and upper bounds on the average length, entropy, and redundancy of such codes in terms of the alphabet size of the source. The Fibonacci distributions…
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…
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…
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…
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…
Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
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…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
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 investigate the redundancy of universal coding schemes on smooth parametric sources in the finite-length regime. We derive an upper bound on the probability of the event that a sequence of length $n$, chosen using…
This paper deals with the problem of universal lossless coding on a countable infinite alphabet. It focuses on some classes of sources defined by an envelope condition on the marginal distribution, namely exponentially decreasing envelope…
We define the AWGNC, BSC, and max-fractional pseudocodeword redundancy of a code as the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance. We show that…
This paper considers the problem of guessing the realization of a finite alphabet source when some side information is provided. The only knowledge the guesser has about the source and the correlated side information is that the joint…
Binary AIFV codes are lossless codes that generalize the class of instantaneous FV codes. The code uses two code trees and assigns source symbols to incomplete internal nodes as well as to leaves. AIFV codes are empirically shown to attain…
This paper describes universal lossless coding strategies for compressing sources on countably infinite alphabets. Classes of memoryless sources defined by an envelope condition on the marginal distribution provide benchmarks for coding…
A framework with two scalar parameters is introduced for various problems of finding a prefix code minimizing a coding penalty function. The framework encompasses problems previously proposed by Huffman, Campbell, Nath, and Drmota and…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…