15 research outputs found
Lossy compression of discrete sources via Viterbi algorithm
We present a new lossy compressor for discrete-valued sources. For coding a
sequence , the encoder starts by assigning a certain cost to each possible
reconstruction sequence. It then finds the one that minimizes this cost and
describes it losslessly to the decoder via a universal lossless compressor. The
cost of each sequence is a linear combination of its distance from the sequence
and a linear function of its order empirical distribution.
The structure of the cost function allows the encoder to employ the Viterbi
algorithm to recover the minimizer of the cost. We identify a choice of the
coefficients comprising the linear function of the empirical distribution used
in the cost function which ensures that the algorithm universally achieves the
optimum rate-distortion performance of any stationary ergodic source in the
limit of large , provided that diverges as . Iterative
techniques for approximating the coefficients, which alleviate the
computational burden of finding the optimal coefficients, are proposed and
studied.Comment: 26 pages, 6 figures, Submitted to IEEE Transactions on Information
Theor
Universal Sampling Rate Distortion
We examine the coordinated and universal rate-efficient sampling of a subset
of correlated discrete memoryless sources followed by lossy compression of the
sampled sources. The goal is to reconstruct a predesignated subset of sources
within a specified level of distortion. The combined sampling mechanism and
rate distortion code are universal in that they are devised to perform robustly
without exact knowledge of the underlying joint probability distribution of the
sources. In Bayesian as well as nonBayesian settings, single-letter
characterizations are provided for the universal sampling rate distortion
function for fixed-set sampling, independent random sampling and memoryless
random sampling. It is illustrated how these sampling mechanisms are
successively better. Our achievability proofs bring forth new schemes for joint
source distribution-learning and lossy compression
Compression-Based Compressed Sensing
Modern compression algorithms exploit complex structures that are present in
signals to describe them very efficiently. On the other hand, the field of
compressed sensing is built upon the observation that "structured" signals can
be recovered from their under-determined set of linear projections. Currently,
there is a large gap between the complexity of the structures studied in the
area of compressed sensing and those employed by the state-of-the-art
compression codes. Recent results in the literature on deterministic signals
aim at bridging this gap through devising compressed sensing decoders that
employ compression codes. This paper focuses on structured stochastic processes
and studies the application of rate-distortion codes to compressed sensing of
such signals. The performance of the formerly-proposed compressible signal
pursuit (CSP) algorithm is studied in this stochastic setting. It is proved
that in the very low distortion regime, as the blocklength grows to infinity,
the CSP algorithm reliably and robustly recovers instances of a stationary
process from random linear projections as long as their count is slightly more
than times the rate-distortion dimension (RDD) of the source. It is also
shown that under some regularity conditions, the RDD of a stationary process is
equal to its information dimension (ID). This connection establishes the
optimality of the CSP algorithm at least for memoryless stationary sources, for
which the fundamental limits are known. Finally, it is shown that the CSP
algorithm combined by a family of universal variable-length fixed-distortion
compression codes yields a family of universal compressed sensing recovery
algorithms
State–of–the–art report on nonlinear representation of sources and channels
This report consists of two complementary parts, related to the modeling of two important sources of nonlinearities in a communications system. In the first part, an overview of important past work related to the estimation, compression and processing of sparse data through the use of nonlinear models is provided. In the second part, the current state of the art on the representation of wireless channels in the presence of nonlinearities is summarized. In addition to the characteristics of the nonlinear wireless fading channel, some information is also provided on recent approaches to the sparse representation of such channels
Rate-Distortion via Markov Chain Monte Carlo
We propose an approach to lossy source coding, utilizing ideas from Gibbs
sampling, simulated annealing, and Markov Chain Monte Carlo (MCMC). The idea is
to sample a reconstruction sequence from a Boltzmann distribution associated
with an energy function that incorporates the distortion between the source and
reconstruction, the compressibility of the reconstruction, and the point sought
on the rate-distortion curve. To sample from this distribution, we use a `heat
bath algorithm': Starting from an initial candidate reconstruction (say the
original source sequence), at every iteration, an index i is chosen and the
i-th sequence component is replaced by drawing from the conditional probability
distribution for that component given all the rest. At the end of this process,
the encoder conveys the reconstruction to the decoder using universal lossless
compression. The complexity of each iteration is independent of the sequence
length and only linearly dependent on a certain context parameter (which grows
sub-logarithmically with the sequence length). We show that the proposed
algorithms achieve optimum rate-distortion performance in the limits of large
number of iterations, and sequence length, when employed on any stationary
ergodic source. Experimentation shows promising initial results. Employing our
lossy compressors on noisy data, with appropriately chosen distortion measure
and level, followed by a simple de-randomization operation, results in a family
of denoisers that compares favorably (both theoretically and in practice) with
other MCMC-based schemes, and with the Discrete Universal Denoiser (DUDE).Comment: 35 pages, 16 figures, Submitted to IEEE Transactions on Information
Theor