9,845 research outputs found
Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
We deal with zero-delay source coding of a vector-valued Gauss-Markov source
subject to a mean-squared error (MSE) fidelity criterion characterized by the
operational zero-delay vector-valued Gaussian rate distortion function (RDF).
We address this problem by considering the nonanticipative RDF (NRDF) which is
a lower bound to the causal optimal performance theoretically attainable (OPTA)
function and operational zero-delay RDF. We recall the realization that
corresponds to the optimal "test-channel" of the Gaussian NRDF, when
considering a vector Gauss-Markov source subject to a MSE distortion in the
finite time horizon. Then, we introduce sufficient conditions to show existence
of solution for this problem in the infinite time horizon. For the asymptotic
regime, we use the asymptotic characterization of the Gaussian NRDF to provide
a new equivalent realization scheme with feedback which is characterized by a
resource allocation (reverse-waterfilling) problem across the dimension of the
vector source. We leverage the new realization to derive a predictive coding
scheme via lattice quantization with subtractive dither and joint memoryless
entropy coding. This coding scheme offers an upper bound to the operational
zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then
for "r" active dimensions of the vector Gauss-Markov source the gap between the
obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1
bits/vector. We further show that it is possible when we use vector
quantization, and assume infinite dimensional Gauss-Markov sources to make the
previous gap to be negligible, i.e., Gaussian NRDF approximates the operational
zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian
sources of any finite memory under mild conditions. Our theoretical framework
is demonstrated with illustrative numerical experiments.Comment: 32 pages, 9 figures, published in IEEE Journal of Selected Topics in
Signal Processin
Efficient Universal Noiseless Source Codes
Although the existence of universal noiseless variable-rate codes for the class of discrete stationary ergodic sources has previously been established, very few practical universal encoding methods are available. Efficient implementable universal source coding techniques are discussed in this paper. Results are presented on source codes for which a small value of the maximum redundancy is achieved with a relatively short block length. A constructive proof of the existence of universal noiseless codes for discrete stationary sources is first presented. The proof is shown to provide a method for obtaining efficient universal noiseless variable-rate codes for various classes of sources. For memoryless sources, upper and lower bounds are obtained for the minimax redundancy as a function of the block length of the code. Several techniques for constructing universal noiseless source codes for memoryless sources are presented and their redundancies are compared with the bounds. Consideration is given to possible applications to data compression for certain nonstationary sources
A Universal Scheme for Wyner–Ziv Coding of Discrete Sources
We consider the Wyner–Ziv (WZ) problem of lossy compression where the decompressor observes a noisy version of the source, whose statistics are unknown. A new family of WZ coding algorithms is proposed and their universal optimality is proven. Compression consists of sliding-window processing followed by Lempel–Ziv (LZ) compression, while the decompressor is based on a modification of the discrete universal denoiser (DUDE) algorithm to take advantage of side information. The new algorithms not only universally attain the fundamental limits, but also suggest a paradigm for practical WZ coding. The effectiveness of our approach is illustrated with experiments on binary images, and English text using a low complexity algorithm motivated by our class of universally optimal WZ codes
One-shot lossy quantum data compression
We provide a framework for one-shot quantum rate distortion coding, in which
the goal is to determine the minimum number of qubits required to compress
quantum information as a function of the probability that the distortion
incurred upon decompression exceeds some specified level. We obtain a one-shot
characterization of the minimum qubit compression size for an
entanglement-assisted quantum rate-distortion code in terms of the smooth
max-information, a quantity previously employed in the one-shot quantum reverse
Shannon theorem. Next, we show how this characterization converges to the known
expression for the entanglement-assisted quantum rate distortion function for
asymptotically many copies of a memoryless quantum information source. Finally,
we give a tight, finite blocklength characterization for the
entanglement-assisted minimum qubit compression size of a memoryless isotropic
qubit source subject to an average symbol-wise distortion constraint.Comment: 36 page
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
On the Distributed Compression of Quantum Information
The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian–Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction
Lossy joint source-channel coding in the finite blocklength regime
This paper finds new tight finite-blocklength bounds for the best achievable
lossy joint source-channel code rate, and demonstrates that joint
source-channel code design brings considerable performance advantage over a
separate one in the non-asymptotic regime. A joint source-channel code maps a
block of source symbols onto a length channel codeword, and the
fidelity of reproduction at the receiver end is measured by the probability
that the distortion exceeds a given threshold . For memoryless
sources and channels, it is demonstrated that the parameters of the best joint
source-channel code must satisfy , where and are the channel capacity and channel
dispersion, respectively; and are the source
rate-distortion and rate-dispersion functions; and is the standard Gaussian
complementary cdf. Symbol-by-symbol (uncoded) transmission is known to achieve
the Shannon limit when the source and channel satisfy a certain probabilistic
matching condition. In this paper we show that even when this condition is not
satisfied, symbol-by-symbol transmission is, in some cases, the best known
strategy in the non-asymptotic regime
Compressing Sparse Sequences under Local Decodability Constraints
We consider a variable-length source coding problem subject to local
decodability constraints. In particular, we investigate the blocklength scaling
behavior attainable by encodings of -sparse binary sequences, under the
constraint that any source bit can be correctly decoded upon probing at most
codeword bits. We consider both adaptive and non-adaptive access models,
and derive upper and lower bounds that often coincide up to constant factors.
Notably, such a characterization for the fixed-blocklength analog of our
problem remains unknown, despite considerable research over the last three
decades. Connections to communication complexity are also briefly discussed.Comment: 8 pages, 1 figure. First five pages to appear in 2015 International
Symposium on Information Theory. This version contains supplementary materia
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