783 research outputs found
First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources with General Mixture
The first- and second-order optimum achievable exponents in the simple
hypothesis testing problem are investigated. The optimum achievable exponent
for type II error probability, under the constraint that the type I error
probability is allowed asymptotically up to epsilon, is called the
epsilon-optimum exponent. In this paper, we first give the second-order
epsilon-exponent in the case where the null hypothesis and the alternative
hypothesis are a mixed memoryless source and a stationary memoryless source,
respectively. We next generalize this setting to the case where the alternative
hypothesis is also a mixed memoryless source. We address the first-order
epsilon-optimum exponent in this setting. In addition, an extension of our
results to more general setting such as the hypothesis testing with mixed
general source and the relationship with the general compound hypothesis
testing problem are also discussed.Comment: 23 page
Second-Order Asymptotics of Visible Mixed Quantum Source Coding via Universal Codes
This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TIT.2016.2571662The simplest example of a quantum information source with memory is a mixed
source which emits signals entirely from one of two memoryless quantum sources
with given a priori probabilities. Considering a mixed source consisting of a
general one-parameter family of memoryless sources, we derive the second order
asymptotic rate for fixed-length visible source coding. Furthermore, we
specialize our main result to a mixed source consisting of two memoryless
sources. Our results provide the first example of second order asymptotics for
a quantum information-processing task employing a resource with memory. For the
case of a classical mixed source (using a finite alphabet), our results reduce
to those obtained by Nomura and Han [IEEE Trans. on Inf. Th. 59.1 (2013), pp.
1-16]. To prove the achievability part of our main result, we introduce
universal quantum source codes achieving second order asymptotic rates. These
are obtained by an extension of Hayashi's construction [IEEE Trans. on Inf. Th.
54.10 (2008), pp. 4619-4637] of their classical counterparts
Guessing Revisited: A Large Deviations Approach
The problem of guessing a random string is revisited. A close relation
between guessing and compression is first established. Then it is shown that if
the sequence of distributions of the information spectrum satisfies the large
deviation property with a certain rate function, then the limiting guessing
exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the
rate function. Other sufficient conditions related to certain continuity
properties of the information spectrum are briefly discussed. This approach
highlights the importance of the information spectrum in determining the
limiting guessing exponent. All known prior results are then re-derived as
example applications of our unifying approach.Comment: 16 pages, to appear in IEEE Transaction on Information Theor
Data Discovery and Anomaly Detection Using Atypicality: Theory
A central question in the era of 'big data' is what to do with the enormous
amount of information. One possibility is to characterize it through
statistics, e.g., averages, or classify it using machine learning, in order to
understand the general structure of the overall data. The perspective in this
paper is the opposite, namely that most of the value in the information in some
applications is in the parts that deviate from the average, that are unusual,
atypical. We define what we mean by 'atypical' in an axiomatic way as data that
can be encoded with fewer bits in itself rather than using the code for the
typical data. We show that this definition has good theoretical properties. We
then develop an implementation based on universal source coding, and apply this
to a number of real world data sets.Comment: 40 page
A vector quantization approach to universal noiseless coding and quantization
A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that “quantizes” the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n -1 log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n-1) when the universe of sources is countable, and as O(n-1+ϵ) when the universe of sources is infinite-dimensional, under appropriate conditions
Tema Con Variazioni: Quantum Channel Capacity
Channel capacity describes the size of the nearly ideal channels, which can
be obtained from many uses of a given channel, using an optimal error
correcting code. In this paper we collect and compare minor and major
variations in the mathematically precise statements of this idea which have
been put forward in the literature. We show that all the variations considered
lead to equivalent capacity definitions. In particular, it makes no difference
whether one requires mean or maximal errors to go to zero, and it makes no
difference whether errors are required to vanish for any sequence of block
sizes compatible with the rate, or only for one infinite sequence.Comment: 32 pages, uses iopart.cl
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