290 research outputs found
Side-information Scalable Source Coding
The problem of side-information scalable (SI-scalable) source coding is
considered in this work, where the encoder constructs a progressive
description, such that the receiver with high quality side information will be
able to truncate the bitstream and reconstruct in the rate distortion sense,
while the receiver with low quality side information will have to receive
further data in order to decode. We provide inner and outer bounds for general
discrete memoryless sources. The achievable region is shown to be tight for the
case that either of the decoders requires a lossless reconstruction, as well as
the case with degraded deterministic distortion measures. Furthermore we show
that the gap between the achievable region and the outer bounds can be bounded
by a constant when square error distortion measure is used. The notion of
perfectly scalable coding is introduced as both the stages operate on the
Wyner-Ziv bound, and necessary and sufficient conditions are given for sources
satisfying a mild support condition. Using SI-scalable coding and successive
refinement Wyner-Ziv coding as basic building blocks, a complete
characterization is provided for the important quadratic Gaussian source with
multiple jointly Gaussian side-informations, where the side information quality
does not have to be monotonic along the scalable coding order. Partial result
is provided for the doubly symmetric binary source with Hamming distortion when
the worse side information is a constant, for which one of the outer bound is
strictly tighter than the other one.Comment: 35 pages, submitted to IEEE Transaction on Information Theor
Multiuser Successive Refinement and Multiple Description Coding
We consider the multiuser successive refinement (MSR) problem, where the
users are connected to a central server via links with different noiseless
capacities, and each user wishes to reconstruct in a successive-refinement
fashion. An achievable region is given for the two-user two-layer case and it
provides the complete rate-distortion region for the Gaussian source under the
MSE distortion measure. The key observation is that this problem includes the
multiple description (MD) problem (with two descriptions) as a subsystem, and
the techniques useful in the MD problem can be extended to this case. We show
that the coding scheme based on the universality of random binning is
sub-optimal, because multiple Gaussian side informations only at the decoders
do incur performance loss, in contrast to the case of single side information
at the decoder. We further show that unlike the single user case, when there
are multiple users, the loss of performance by a multistage coding approach can
be unbounded for the Gaussian source. The result suggests that in such a
setting, the benefit of using successive refinement is not likely to justify
the accompanying performance loss. The MSR problem is also related to the
source coding problem where each decoder has its individual side information,
while the encoder has the complete set of the side informations. The MSR
problem further includes several variations of the MD problem, for which the
specialization of the general result is investigated and the implication is
discussed.Comment: 10 pages, 5 figures. To appear in IEEE Transaction on Information
Theory. References updated and typos correcte
Integer-Forcing Source Coding
Integer-Forcing (IF) is a new framework, based on compute-and-forward, for
decoding multiple integer linear combinations from the output of a Gaussian
multiple-input multiple-output channel. This work applies the IF approach to
arrive at a new low-complexity scheme, IF source coding, for distributed lossy
compression of correlated Gaussian sources under a minimum mean squared error
distortion measure. All encoders use the same nested lattice codebook. Each
encoder quantizes its observation using the fine lattice as a quantizer and
reduces the result modulo the coarse lattice, which plays the role of binning.
Rather than directly recovering the individual quantized signals, the decoder
first recovers a full-rank set of judiciously chosen integer linear
combinations of the quantized signals, and then inverts it. In general, the
linear combinations have smaller average powers than the original signals. This
allows to increase the density of the coarse lattice, which in turn translates
to smaller compression rates. We also propose and analyze a one-shot version of
IF source coding, that is simple enough to potentially lead to a new design
principle for analog-to-digital converters that can exploit spatial
correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor
On the rate loss and construction of source codes for broadcast channels
In this paper, we first define and bound the rate loss of source codes for broadcast channels. Our broadcast channel model comprises one transmitter and two receivers; the transmitter is connected to each receiver by a private channel and to both receivers by a common channel. The transmitter sends a description of source (X, Y) through these channels, receiver 1 reconstructs X with distortion D1, and receiver 2 reconstructs Y with distortion D2. Suppose the rates of the common channel and private channels 1 and 2 are R0, R1, and R2, respectively. The work of Gray and Wyner gives a complete characterization of all achievable rate triples (R0,R1,R2) given any distortion pair (D1,D2). In this paper, we define the rate loss as the gap between the achievable region and the outer bound composed by the rate-distortion functions, i.e., R0+R1+R2 ≥ RX,Y (D1,D2), R0 + R1 ≥ RX(D1), and R0 + R2 ≥ RY (D2). We upper bound the rate loss for general sources by functions of distortions and upper bound the rate loss for Gaussian sources by constants, which implies that though the outer bound is generally not achievable, it may be quite close to the achievable region. This also bounds the gap between the achievable region and the inner bound proposed by Gray and Wyner and bounds the performance penalty associated with using separate decoders rather than joint decoders. We then construct such source codes using entropy-constrained dithered quantizers. The resulting implementation has low complexity and performance close to the theoretical optimum. In particular, the gap between its performance and the theoretical optimum can be bounded from above by constants for Gaussian sources
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