Related papers: Exact Redundancy for Symmetric Rate-Distortion
We derive a general formula of the minimum achievable rate for fixed-to-variable length coding with a regular cost function by allowing the error probability up to a constant $\varepsilon$. For a fixed-to-variable length code, we call the…
This paper considers the problem of lossy compression for the computation of a function of two correlated sources, both of which are observed at the encoder. Due to presence of observation costs, the encoder is allowed to observe only…
We investigate two source coding problems with secrecy constraints. In the first problem we consider real--time fully secure transmission of a memoryless source. We show that although classical variable--rate coding is not an option since…
We study the problem of rate-distortion-equivocation with side-information only available at the decoder when an independent private random key is shared between the sender and the receiver. The sender compresses the sequence, and the…
We investigate the Wyner-Ziv coding in which the statistics of the principal source is known but the statistics of the channel generating the side-information is unknown except that it is in a certain class. The class consists of channels…
The second-order achievable asymptotics in typical random number generation problems such as resolvability, intrinsic randomness, fixed-length source coding are considered. In these problems, several researchers have derived the first-order…
For any Markov source, there exist universal codes whose normalized codelength approaches the Shannon limit asymptotically as the number of samples goes to infinity. This paper investigates how fast the gap between the normalized codelength…
A lossy source code $\mathcal{C}$ with rate $R$ for a discrete memoryless source $S$ is called subset-universal if for every $0<R'< R$, almost every subset of $2^{nR'}$ of its codewords achieves average distortion close to the source's…
Shannon proved that if we can transmit bits reliably at rates larger than the rate distortion function $R(D)$, then we can transmit this source to within a distortion $D$. We answer the converse question ``If we can transmit a source to…
In this paper, we study rate-distortion theory for general sources with an emphasis on the existence of optimal reconstruction distributions on noncompact alphabets. Classical attainability results typically rely on compactness of the…
Given a sufficient statistic for a parametric family of distributions, one can estimate the parameter without access to the data. However, the memory or code size for storing the sufficient statistic may nonetheless still be prohibitive.…
We study codes that can correct backtracking errors during nanopore sequencing. In this channel, a sequence of length $n$ over an alphabet of size $q$ is being read by a sliding window of length $\ell$, where from each window we obtain only…
We establish two strong senses of universality of logarithmic loss as a distortion criterion in lossy compression: For any fixed length lossy compression problem under an arbitrary distortion criterion, we show that there is an equivalent…
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…
This paper presents a novel approach to address the constrained coding challenge of generating almost-balanced sequences. While strictly balanced sequences have been well studied in the past, the problem of designing efficient algorithms…
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques. An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly…
Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size $m \times n$) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix…
We prove that the diffusion coefficient for the two dimensional asymmetric simple exclusion process diverges as $(\log t)^{2/3}$ to the leading order. The method applies to nearest and non-nearest neighbor asymmetric simple exclusion…
We consider the maximum coding rate achievable by uniformly-random codes for the deletion channel. We prove an upper bound that's within 0.1 of the best known lower bounds for all values of the deletion probability $d,$ and much closer for…
Motivated by the celebrated Beck-Fiala conjecture, we consider the random setting where there are $n$ elements and $m$ sets and each element lies in $t$ randomly chosen sets. In this setting, Ezra and Lovett showed an $O((t \log t)^{1/2})$…