Related papers: Stable Source Coding
We study the stabilization of an unpredictable linear control system where the controller must act based on a rate-limited observation of the state. More precisely, we consider the system $X_{n+1} = A_n X_n + W_n - U_n$, where the $A_n$'s…
Traditionally, ensembles of Slepian-Wolf (SW) codes are defined such that every bin of each $n$-vector of each source is randomly drawn under the uniform distribution across the sets $\{0,1,\ldots,2^{nR_X}-1\}$ and…
The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…
When is a nonlinear filter stable with respect to its initial condition? In spite of the recent progress, this question still lacks a complete answer in general. Currently available results indicate that stability of the filter depends on…
Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical…
It was recently shown that the lossless compression of a single source $X^n$ is achievable with a notion of strong locality; any $X_i$ can be decoded from a constant number of compressed bits, with a vanishing in $n$ probability of error.…
Open source software (OSS) generates trillions of dollars in economic value and has become essential to the technical infrastructures that power organizations worldwide. As these systems increasingly depend on OSS, understanding the…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbolwise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
Distribution matching transforms independent and Bernoulli(1/2) distributed input bits into a sequence of output symbols with a desired distribution. Fixed-to-fixed length, invertible, and low complexity encoders and decoders based on…
The geometric measure, the logarithmic robustness and the relative entropy of entanglement are proved to be equal for a stabilizer quantum codeword. The entanglement upper and lower bounds are determined with the generators of code. The…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects…
We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show…
The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in applications of networked control systems. Although the work of Schulman and Sahai over the past two decades, and…
Bi-modal (respectively, multi-modal) constrained coding refers to an encoding model whereby a user input block can be mapped to two (respectively, multiple) codewords. In current storage applications, such as optical disks, multi-modal…
Consider a general quantum stochastic source that emits at discrete time steps quantum pure states which are chosen from a finite alphabet according to some probability distribution which may depend on the whole history. Also, fix two…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
Source coding is the canonical problem of data compression in information theory. In a locally encodable source coding, each compressed bit depends on only few bits of the input. In this paper, we show that a recently popular model of…
Over the past few decades, open source software has been continuously integrated into software supply chains worldwide, drastically increasing reliance and dependence. Because of the role this software plays, it is important to understand…
We consider the problem of lossy source coding with a mismatched distortion measure. That is, we investigate what distortion guarantees can be made with respect to distortion measure $\tilde{\rho}$, for a source code designed such that it…