Related papers: Resolvability on Continuous Alphabets
Csisz\'ar's channel coding theorem for multiple codebooks is generalized allowing the codeword lenghts differ across codebooks. Also in this case, for each codebook an error exponent can be achieved that equals the random coding exponent…
We derive a simple lower bound for the multi-version coding problem formulated in [1]. We also propose simple algorithms that almost match the lower bound derived. Another lower bound is proven for an extended version of the multi-version…
We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…
The list-decodable code has been an active topic in theoretical computer science.There are general results about the list-decodability to the Johnson radius and the list-decoding capacity theorem. In this paper we show that rates,…
Many graph coloring proofs proceed by showing that a minimal counterexample to the theorem being proved cannot contain certain configurations, and then showing that each graph under consideration contains at least one such configuration;…
The zero-error capacity of channels with a countably infinite input alphabet formally generalises Shannon's classical problem about the capacity of discrete memoryless channels. We solve the problem for three particular channels. Our…
In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
In this paper, the authors provide a weak decoding version of the traditional source coding theorem of Claude Shannon. The central bound that is obtained is \[ \chi>\log_{\epsilon}(2^{-n(H(X)+\epsilon)}) \] where \[…
Capacity analysis for channels with side information at the receiver has been an active area of interest. This problem is well investigated for the case of finite alphabet channels. However, the results are not easily generalizable to the…
The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be…
This article emphasizes an extension of the study of metric and par- tition dimension to hypergraphs. We give a sharp lower bounds for the metric and partition dimension of hypergraphs in general and give exact values under specified…
This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…
The problem of joint universal source coding and identification is considered in the setting of fixed-rate lossy coding of continuous-alphabet memoryless sources. For a wide class of bounded distortion measures, it is shown that any…
The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem the optimum mean codeword length of variable-length codes has already been determined. On the…
Solomonoff's uncomputable universal prediction scheme $\xi$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $\mu$. This scheme will be…
We consider the average-case complexity of some otherwise undecidable or open Diophantine problems. More precisely, consider the following: (I) Given a polynomial f in Z[v,x,y], decide the sentence \exists v \forall x \exists y f(v,x,y)=0,…
The likelihood encoder with a random codebook is demonstrated as an effective tool for source coding. Coupled with a soft covering lemma (associated with channel resolvability), likelihood encoders yield simple achievability proofs for…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…