272 research outputs found
Lossy Compression of Exponential and Laplacian Sources using Expansion Coding
A general method of source coding over expansion is proposed in this paper,
which enables one to reduce the problem of compressing an analog
(continuous-valued source) to a set of much simpler problems, compressing
discrete sources. Specifically, the focus is on lossy compression of
exponential and Laplacian sources, which is subsequently expanded using a
finite alphabet prior to being quantized. Due to decomposability property of
such sources, the resulting random variables post expansion are independent and
discrete. Thus, each of the expanded levels corresponds to an independent
discrete source coding problem, and the original problem is reduced to coding
over these parallel sources with a total distortion constraint. Any feasible
solution to the optimization problem is an achievable rate distortion pair of
the original continuous-valued source compression problem. Although finding the
solution to this optimization problem at every distortion is hard, we show that
our expansion coding scheme presents a good solution in the low distrotion
regime. Further, by adopting low-complexity codes designed for discrete source
coding, the total coding complexity can be tractable in practice.Comment: 8 pages, 3 figure
Incremental Refinements and Multiple Descriptions with Feedback
It is well known that independent (separate) encoding of K correlated sources
may incur some rate loss compared to joint encoding, even if the decoding is
done jointly. This loss is particularly evident in the multiple descriptions
problem, where the sources are repetitions of the same source, but each
description must be individually good. We observe that under mild conditions
about the source and distortion measure, the rate ratio Rindependent(K)/Rjoint
goes to one in the limit of small rate/high distortion. Moreover, we consider
the excess rate with respect to the rate-distortion function, Rindependent(K,
M) - R(D), in M rounds of K independent encodings with a final distortion level
D. We provide two examples - a Gaussian source with mean-squared error and an
exponential source with one-sided error - for which the excess rate vanishes in
the limit as the number of rounds M goes to infinity, for any fixed D and K.
This result has an interesting interpretation for a multi-round variant of the
multiple descriptions problem, where after each round the encoder gets a
(block) feedback regarding which of the descriptions arrived: In the limit as
the number of rounds M goes to infinity (i.e., many incremental rounds), the
total rate of received descriptions approaches the rate-distortion function. We
provide theoretical and experimental evidence showing that this phenomenon is
in fact more general than in the two examples above.Comment: 62 pages. Accepted in the IEEE Transactions on Information Theor
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Coding mechanisms for communication and compression : analysis of wireless channels and DNA sequencing
textThis thesis comprises of two related but distinct components: Coding arguments for communication channels and information-theoretic analysis for haplotype assembly. The common thread for both problems is utilizing information and coding theoretic principles in understanding their underlying mechanisms. For the first class of problems, I study two practical challenges that prevent optimal discrete codes utilizing in real communication and compression systems, namely, coding over analog alphabet and fading. In particular, I use an expansion coding scheme to convert the original analog channel coding and source coding problems into a set of independent discrete subproblems. By adopting optimal discrete codes over the expanded levels, this low-complexity coding scheme can approach Shannon limit perfectly or in ratio. Meanwhile, I design a polar coding scheme to deal with the unstable state of fading channels. This novel coding mechanism of hierarchically utilizing different types of polar codes has been proved to be ergodic capacity achievable for several fading systems, without channel state information known at the transmitter. For the second class of problems, I build an information-theoretic view for haplotype assembly. More precisely, the recovery of the target pair of haplotype sequences using short reads is rephrased as the joint source-channel coding problem. Two binary messages, representing haplotypes and chromosome memberships of reads, are encoded and transmitted over a channel with erasures and errors, where the channel model reflects salient features of highthroughput sequencing. The focus is on determining the required number of reads for reliable haplotype reconstruction.Electrical and Computer Engineerin
An Orthogonality Principle for Select-Maximum Estimation of Exponential Variables
It was recently proposed to encode the one-sided exponential source X via K
parallel channels, Y1, ..., YK , such that the error signals X - Yi, i =
1,...,K, are one-sided exponential and mutually independent given X. Moreover,
it was shown that the optimal estimator \hat{Y} of the source X with respect to
the one-sided error criterion, is simply given by the maximum of the outputs,
i.e., \hat{Y} = max{Y1,..., YK}. In this paper, we show that the distribution
of the resulting estimation error X - \hat{Y} , is equivalent to that of the
optimum noise in the backward test-channel of the one-sided exponential source,
i.e., it is one-sided exponentially distributed and statistically independent
of the joint output Y1,...,YK.Comment: 5 pages. Submitted to ISI
A stochastic algorithm for probabilistic independent component analysis
The decomposition of a sample of images on a relevant subspace is a recurrent
problem in many different fields from Computer Vision to medical image
analysis. We propose in this paper a new learning principle and implementation
of the generative decomposition model generally known as noisy ICA (for
independent component analysis) based on the SAEM algorithm, which is a
versatile stochastic approximation of the standard EM algorithm. We demonstrate
the applicability of the method on a large range of decomposition models and
illustrate the developments with experimental results on various data sets.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS499 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Approximate trigonometric expansions with applications to signal decomposition and coding
Signal representation and data coding for multi-dimensional signals have recently received considerable attention due to their importance to several modern technologies. Many useful contributions have been reported that employ wavelets and transform methods. For signal representation, it is always desired that a signal be represented using minimum number of parameters. The transform efficiency and ease of its implementation are to a large extent mutually incompatible. If a stationary process is not periodic, then the coefficients of its Fourier expansion are not uncorrelated. With the exception of periodic signals the expansion of such a process as a superposition of exponentials, particularly in the study of linear systems, needs no elaboration. In this research, stationary and non-periodic signals are represented using approximate trigonometric expansions. These expansions have a user-defined parameter which can be used for making the transformation a signal decomposition tool. It is shown that fast implementation of these expansions is possible using wavelets. These approximate trigonometric expansions are applied to multidimensional signals in a constrained environment where dominant coefficients of the expansion are retained and insignificant ones are set to zero. The signal is then reconstructed using these limited set of coefficients, thus leading to compression. Sample results for representing multidimensional signals are given to illustrate the efficiency of the proposed method. It is verified that for a given number of coefficients, the proposed technique yields higher signal to noise ratio than conventional techniques employing the discrete cosine transform technique
Efficient compression of motion compensated residuals
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