1,555 research outputs found
Source-Channel Diversity for Parallel Channels
We consider transmitting a source across a pair of independent, non-ergodic
channels with random states (e.g., slow fading channels) so as to minimize the
average distortion. The general problem is unsolved. Hence, we focus on
comparing two commonly used source and channel encoding systems which
correspond to exploiting diversity either at the physical layer through
parallel channel coding or at the application layer through multiple
description source coding.
For on-off channel models, source coding diversity offers better performance.
For channels with a continuous range of reception quality, we show the reverse
is true. Specifically, we introduce a new figure of merit called the distortion
exponent which measures how fast the average distortion decays with SNR. For
continuous-state models such as additive white Gaussian noise channels with
multiplicative Rayleigh fading, optimal channel coding diversity at the
physical layer is more efficient than source coding diversity at the
application layer in that the former achieves a better distortion exponent.
Finally, we consider a third decoding architecture: multiple description
encoding with a joint source-channel decoding. We show that this architecture
achieves the same distortion exponent as systems with optimal channel coding
diversity for continuous-state channels, and maintains the the advantages of
multiple description systems for on-off channels. Thus, the multiple
description system with joint decoding achieves the best performance, from
among the three architectures considered, on both continuous-state and on-off
channels.Comment: 48 pages, 14 figure
Multiple-Description Coding by Dithered Delta-Sigma Quantization
We address the connection between the multiple-description (MD) problem and
Delta-Sigma quantization. The inherent redundancy due to oversampling in
Delta-Sigma quantization, and the simple linear-additive noise model resulting
from dithered lattice quantization, allow us to construct a symmetric and
time-invariant MD coding scheme. We show that the use of a noise shaping filter
makes it possible to trade off central distortion for side distortion.
Asymptotically as the dimension of the lattice vector quantizer and order of
the noise shaping filter approach infinity, the entropy rate of the dithered
Delta-Sigma quantization scheme approaches the symmetric two-channel MD
rate-distortion function for a memoryless Gaussian source and MSE fidelity
criterion, at any side-to-central distortion ratio and any resolution. In the
optimal scheme, the infinite-order noise shaping filter must be minimum phase
and have a piece-wise flat power spectrum with a single jump discontinuity. An
important advantage of the proposed design is that it is symmetric in rate and
distortion by construction, so the coding rates of the descriptions are
identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has
been fixed. Accepted for publication in the IEEE Transactions on Information
Theor
On moduli of rings and quadrilaterals: algorithms and experiments
Moduli of rings and quadrilaterals are frequently applied in geometric
function theory, see e.g. the Handbook by K\"uhnau. Yet their exact values are
known only in a few special cases. Previously, the class of planar domains with
polygonal boundary has been studied by many authors from the point of view of
numerical computation. We present here a new -FEM algorithm for the
computation of moduli of rings and quadrilaterals and compare its accuracy and
performance with previously known methods such as the Schwarz-Christoffel
Toolbox of Driscoll and Trefethen. We also demonstrate that the -FEM
algorithm applies to the case of non-polygonal boundary and report results with
concrete error bounds
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