28,085 research outputs found
Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks
A model, called the linear transform network (LTN), is proposed to analyze
the compression and estimation of correlated signals transmitted over directed
acyclic graphs (DAGs). An LTN is a DAG network with multiple source and
receiver nodes. Source nodes transmit subspace projections of random correlated
signals by applying reduced-dimension linear transforms. The subspace
projections are linearly processed by multiple relays and routed to intended
receivers. Each receiver applies a linear estimator to approximate a subset of
the sources with minimum mean squared error (MSE) distortion. The model is
extended to include noisy networks with power constraints on transmitters. A
key task is to compute all local compression matrices and linear estimators in
the network to minimize end-to-end distortion. The non-convex problem is solved
iteratively within an optimization framework using constrained quadratic
programs (QPs). The proposed algorithm recovers as special cases the regular
and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the
distortion region of multi-source, multi-receiver networks are given for linear
coding based on convex relaxations. Cut-set lower bounds are also given for any
coding strategy based on information theory. The distortion region and
compression-estimation tradeoffs are illustrated for different communication
demands (e.g. multiple unicast), and graph structures.Comment: 33 pages, 7 figures, To appear in IEEE Transactions on Signal
Processin
Networked Slepian-Wolf: theory, algorithms, and scaling laws
Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the data-gathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by Slepian-Wolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed
Analog Multiple Descriptions: A Zero-Delay Source-Channel Coding Approach
This paper extends the well-known source coding problem of multiple
descriptions, in its general and basic setting, to analog source-channel coding
scenarios. Encoding-decoding functions that optimally map between the (possibly
continuous valued) source and the channel spaces are numerically derived. The
main technical tool is a non-convex optimization method, namely, deterministic
annealing, which has recently been successfully used in other mapping
optimization problems. The obtained functions exhibit several interesting
structural properties, map multiple source intervals to the same interval in
the channel space, and consistently outperform the known competing mapping
techniques.Comment: Submitted to ICASSP 201
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