14 research outputs found
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
Sampling versus Random Binning for Multiple Descriptions of a Bandlimited Source
Random binning is an efficient, yet complex, coding technique for the
symmetric L-description source coding problem. We propose an alternative
approach, that uses the quantized samples of a bandlimited source as
"descriptions". By the Nyquist condition, the source can be reconstructed if
enough samples are received. We examine a coding scheme that combines sampling
and noise-shaped quantization for a scenario in which only K < L descriptions
or all L descriptions are received. Some of the received K-sets of descriptions
correspond to uniform sampling while others to non-uniform sampling. This
scheme achieves the optimum rate-distortion performance for uniform-sampling
K-sets, but suffers noise amplification for nonuniform-sampling K-sets. We then
show that by increasing the sampling rate and adding a random-binning stage,
the optimal operation point is achieved for any K-set.Comment: Presented at the ITW'13. 5 pages, two-column mode, 3 figure
Index assignment for multiple description repair in distributed storage systems
Distributed storage systems have been receiving increasing attention lately due to the developments in cloud and grid computing. Furthermore, a major part of the stored information comprises of multimedia, whose content can be communicated even with a lossy (non-perfect) reconstruction. In this context, Multiple Description Lattice Quantizers (MDLQ) can be employed to encode such sources for distributed storage and store them across distributed nodes. Their inherent properties yield that having access to all nodes gives perfect reconstruction of the source, while the reconstruction quality decreases gracefully with fewer available nodes. If a set of nodes fails, lossy repair techniques could be applied to reconstruct the failed nodes from the available ones. This problem has mostly been studied with the lossless (perfect) reconstruction assumption. In this work, a general model, Multiple Description Lattice Quantizer with Repairs (MDLQR), is introduced that encompasses the lossy repair problem for distributed storage applications. New performance measures and repair techniques are introduced for MDLQR, and a non-trivial identity is derived, which is related to other results in the literature. This enables us to find the optimal encoder for a certain repair technique used in the MDLQR. Furthermore, simulation results are used to evaluate the performance of the different repair techniques. © 2014 IEEE
Multi-Tenant C-RAN With Spectrum Pooling: Downlink Optimization Under Privacy Constraints
Spectrum pooling allows multiple operators, or tenants, to share the same
frequency bands. This work studies the optimization of spectrum pooling for the
downlink of a multi-tenant Cloud Radio Access Network (C-RAN) system in the
presence of inter-tenant privacy constraints. The spectrum available for
downlink transmission is partitioned into private and shared subbands, and the
participating operators cooperate to serve the user equipments (UEs) on the
shared subband. The network of each operator consists of a cloud processor (CP)
that is connected to proprietary radio units (RUs) by means of finite-capacity
fronthaul links. In order to enable interoperator cooperation, the CPs of the
participating operators are also connected by finite-capacity backhaul links.
Inter-operator cooperation may hence result in loss of privacy. Fronthaul and
backhaul links are used to transfer quantized baseband signals. Standard
quantization is considered first. Then, a novel approach based on the idea of
correlating quantization noise signals across RUs of different operators is
proposed to control the trade-off between distortion at UEs and inter-operator
privacy. The problem of optimizing the bandwidth allocation, precoding, and
fronthaul/backhaul compression strategies is tackled under constraints on
backhaul and fronthaul capacity, as well as on per-RU transmit power and
inter-operator privacy. For both cases, the optimization problems are tackled
using the concave convex procedure (CCCP), and extensive numerical results are
provided.Comment: Submitted, 24 pages, 7 figure
Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms
It is well known that Shannon's rate-distortion function (RDF) in the colored
quadratic Gaussian (QG) case can be parametrized via a single Lagrangian
variable (the "water level" in the reverse water filling solution). In this
work, we show that the symmetric colored QG multiple-description (MD) RDF in
the case of two descriptions can be parametrized in the spectral domain via two
Lagrangian variables, which control the trade-off between the side distortion,
the central distortion, and the coding rate. This spectral-domain analysis is
complemented by a time-domain scheme-design approach: we show that the
symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma
modulation and differential pulse-code modulation. Specifically, two source
prediction loops, one for each description, are embedded within a common noise
shaping loop, whose parameters are explicitly found from the spectral-domain
characterization.Comment: Accepted for publications in the IEEE Transactions on Information
Theory. Title have been shortened, abstract clarified, and paper
significantly restructure
Zero-Delay Multiple Descriptions of Stationary Scalar Gauss-Markov Sources
In this paper, we introduce the zero-delay multiple-description problem, where an encoder constructs two descriptions and the decoders receive a subset of these descriptions. The encoder and decoders are causal and operate under the restriction of zero delay, which implies that at each time instance, the encoder must generate codewords that can be decoded by the decoders using only the current and past codewords. For the case of discrete-time stationary scalar Gauss—Markov sources and quadratic distortion constraints, we present information-theoretic lower bounds on the average sum-rate in terms of the directed and mutual information rate between the source and the decoder reproductions. Furthermore, we show that the optimum test channel is in this case Gaussian, and it can be realized by a feedback coding scheme that utilizes prediction and correlated Gaussian noises. Operational achievable results are considered in the high-rate scenario using a simple differential pulse code modulation scheme with staggered quantizers. Using this scheme, we achieve operational rates within 0.415 bits / sample / description of the theoretical lower bounds for varying description rates
n-Channel Asymmetric Entropy-Constrained Multiple-Description Lattice Vector Quantization
This paper is about the design and analysis of an index-assignment (IA) based
multiple-description coding scheme for the n-channel asymmetric case. We use
entropy constrained lattice vector quantization and restrict attention to
simple reconstruction functions, which are given by the inverse IA function
when all descriptions are received or otherwise by a weighted average of the
received descriptions. We consider smooth sources with finite differential
entropy rate and MSE fidelity criterion. As in previous designs, our
construction is based on nested lattices which are combined through a single IA
function. The results are exact under high-resolution conditions and
asymptotically as the nesting ratios of the lattices approach infinity. For any
n, the design is asymptotically optimal within the class of IA-based schemes.
Moreover, in the case of two descriptions and finite lattice vector dimensions
greater than one, the performance is strictly better than that of existing
designs. In the case of three descriptions, we show that in the limit of large
lattice vector dimensions, points on the inner bound of Pradhan et al. can be
achieved. Furthermore, for three descriptions and finite lattice vector
dimensions, we show that the IA-based approach yields, in the symmetric case, a
smaller rate loss than the recently proposed source-splitting approach.Comment: 49 pages, 4 figures. Accepted for publication in IEEE Transactions on
Information Theory, 201
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