25,022 research outputs found
Universal Source Coding in the Non-Asymptotic Regime
abstract: Fundamental limits of fixed-to-variable (F-V) and variable-to-fixed (V-F) length universal source coding at short blocklengths is characterized. For F-V length coding, the Type Size (TS) code has previously been shown to be optimal up to the third-order rate for universal compression of all memoryless sources over finite alphabets. The TS code assigns sequences ordered based on their type class sizes to binary strings ordered lexicographically.
Universal F-V coding problem for the class of first-order stationary, irreducible and aperiodic Markov sources is first considered. Third-order coding rate of the TS code for the Markov class is derived. A converse on the third-order coding rate for the general class of F-V codes is presented which shows the optimality of the TS code for such Markov sources.
This type class approach is then generalized for compression of the parametric sources. A natural scheme is to define two sequences to be in the same type class if and only if they are equiprobable under any model in the parametric class. This natural approach, however, is shown to be suboptimal. A variation of the Type Size code is introduced, where type classes are defined based on neighborhoods of minimal sufficient statistics. Asymptotics of the overflow rate of this variation is derived and a converse result establishes its optimality up to the third-order term. These results are derived for parametric families of i.i.d. sources as well as Markov sources.
Finally, universal V-F length coding of the class of parametric sources is considered in the short blocklengths regime. The proposed dictionary which is used to parse the source output stream, consists of sequences in the boundaries of transition from low to high quantized type complexity, hence the name Type Complexity (TC) code. For large enough dictionary, the -coding rate of the TC code is derived and a converse result is derived showing its optimality up to the third-order term.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201
Efficiently Extracting Randomness from Imperfect Stochastic Processes
We study the problem of extracting a prescribed number of random bits by
reading the smallest possible number of symbols from non-ideal stochastic
processes. The related interval algorithm proposed by Han and Hoshi has
asymptotically optimal performance; however, it assumes that the distribution
of the input stochastic process is known. The motivation for our work is the
fact that, in practice, sources of randomness have inherent correlations and
are affected by measurement's noise. Namely, it is hard to obtain an accurate
estimation of the distribution. This challenge was addressed by the concepts of
seeded and seedless extractors that can handle general random sources with
unknown distributions. However, known seeded and seedless extractors provide
extraction efficiencies that are substantially smaller than Shannon's entropy
limit. Our main contribution is the design of extractors that have a variable
input-length and a fixed output length, are efficient in the consumption of
symbols from the source, are capable of generating random bits from general
stochastic processes and approach the information theoretic upper bound on
efficiency.Comment: 2 columns, 16 page
Optimality in Quantum Data Compression using Dynamical Entropy
In this article we study lossless compression of strings of pure quantum
states of indeterminate-length quantum codes which were introduced by
Schumacher and Westmoreland. Past work has assumed that the strings of quantum
data are prepared to be encoded in an independent and identically distributed
way. We introduce the notion of quantum stochastic ensembles, allowing us to
consider strings of quantum states prepared in a more general way. For any
identically distributed quantum stochastic ensemble we define an associated
quantum Markov chain and prove that the optimal average codeword length via
lossless coding is equal to the quantum dynamical entropy of the associated
quantum Markov chain
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