Related papers: Applications of Universal Source Coding to Statist…
The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal…
We study the following one-way asymmetric transmission problem, also a variant of model-based compressed sensing: a resource-limited encoder has to report a small set $S$ from a universe of $N$ items to a more powerful decoder (server). The…
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…
We study source compression with a helper in the fully quantum regime, extending our earlier result on classical source compression with a quantum helper [arXiv:1501.04366, 2015]. We characterise the quantum resources involved in this…
In this paper, source coding or data compression is viewed as a measurement problem. Given a measurement device with fewer states than the observable of a stochastic source, how can one capture the essential information? We propose modeling…
A general method of coding over expansion is proposed,which allows one to reduce the highly non-trivial problems of coding over analog channels and compressing analog sources to a set of much simpler subproblems, coding over discrete…
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a…
Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…
We have recently established a strong connection between the Tent map (also known as Generalized Luroth Series or GLS which is a chaotic, ergodic and lebesgue measure preserving non-linear dynamical system) and Arithmetic coding which is a…
We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…
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…
Locally decodable channel codes form a special class of error-correcting codes with the property that the decoder is able to reconstruct any bit of the input message from querying only a few bits of a noisy codeword. It is well known that…
The problem of joint universal source coding and modeling, addressed by Rissanen in the context of lossless codes, is generalized to fixed-rate lossy coding of continuous-alphabet memoryless sources. We show that, for bounded distortion…
We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of…
The problem of classical data compression when the decoder has quantum side information at his disposal is considered. This is a quantum generalization of the classical Slepian-Wolf theorem. The optimal compression rate is found to be…
This paper studies a Shannon-theoretic version of the generalized distribution preserving quantization problem where a stationary and memoryless source is encoded subject to a distortion constraint and the additional requirement that the…
Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This work treats and solves the…
We address the problem of constructing a fast lossless code in the case when the source alphabet is large. The main idea of the new scheme may be described as follows. We group letters with small probabilities in subsets (acting as super…
The presence of smart objects is increasingly widespread and their ecosystem, also known as Internet of Things, is relevant in many different application scenarios. The huge amount of temporally annotated data produced by these smart…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…