Related papers: Asymptotics and Non-asymptotics for Universal Fixe…
This paper sheds light on universal coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and non-decreasing hazard rate. We prove that the auto-censuring AC code…
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…
Shaping codes are used to encode information for use on channels with cost constraints. Applications include data transmission with a power constraint and, more recently, data storage on flash memories with a constraint on memory cell wear.…
The zero-error channel capacity is the maximum asymptotic rate that can be reached with error probability exactly zero, instead of a vanishing error probability. The nature of this problem, essentially combinatorial rather than…
In this paper we consider the use of variable length non prefix-free codes for coding constrained sequences of symbols. We suppose to have a Markov source where some state transitions are impossible, i.e. the stochastic matrix associated…
Variable-to-variable length (VV) codes are a class of lossless source coding. As their name implies, VV codes encode a variable-length sequence of source symbols into a variable-length codeword. This paper will give a complete proof of an…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
We investigate the maximum coding rate achievable on a two-user broadcast channel for the case where a common message is transmitted with feedback using either fixed-blocklength codes or variable-length codes. For the fixed-blocklength-code…
Traditional asymptotic information-theoretic studies of the fundamental limits of wireless communication systems primarily rely on some ideal assumptions, such as infinite blocklength and vanishing error probability. While these assumptions…
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…
In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on…
Given a probability distribution over a set of n words to be transmitted, the Huffman Coding problem is to find a minimal-cost prefix free code for transmitting those words. The basic Huffman coding problem can be solved in O(n log n) time…
Large alphabet source coding is a basic and well-studied problem in data compression. It has many applications such as compression of natural language text, speech and images. The classic perception of most commonly used methods is that a…
We apply so-called tree straight-line programs to the problem of lossless compression of binary trees. We derive upper bound on the maximal pointwise redundancy (or worst-case redundancy) that improve previous bounds obtained by Zhang,…
Lossless variable-length source coding with codeword cost is considered for general sources. The problem setting, where we impose on unequal costs on code symbols, is called the variable-length coding with codeword cost. In this problem,…
A property of prefix codes called strong monotonicity is introduced, and it is proven that for a given source, a prefix code is optimal if and only if it is complete and strongly monotone.
We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that…
We describe an algorithm computing an optimal prefix free code from $N$ unsorted positive integer weights in time linear in the number of machine words holding those weights. This algorithm takes advantage of common non-algebraic…
We investigate the upper and lower bounds on the quantization distortions for independent and identically distributed sources in the finite block-length regime. Based on the convex optimization framework of the rate-distortion theory, we…
The asymptotic rate vs. distance problem is a long-standing fundamental problem in coding theory. The best upper bound to date was given in 1977 and has received since then numerous proofs and interpretations. Here we provide a new,…