261 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
Multi-hop Diffusion LMS for Energy-constrained Distributed Estimation
We propose a multi-hop diffusion strategy for a sensor network to perform
distributed least mean-squares (LMS) estimation under local and network-wide
energy constraints. At each iteration of the strategy, each node can combine
intermediate parameter estimates from nodes other than its physical neighbors
via a multi-hop relay path. We propose a rule to select combination weights for
the multi-hop neighbors, which can balance between the transient and the
steady-state network mean-square deviations (MSDs). We study two classes of
networks: simple networks with a unique transmission path from one node to
another, and arbitrary networks utilizing diffusion consultations over at most
two hops. We propose a method to optimize each node's information neighborhood
subject to local energy budgets and a network-wide energy budget for each
diffusion iteration. This optimization requires the network topology, and the
noise and data variance profiles of each node, and is performed offline before
the diffusion process. In addition, we develop a fully distributed and adaptive
algorithm that approximately optimizes the information neighborhood of each
node with only local energy budget constraints in the case where diffusion
consultations are performed over at most a predefined number of hops. Numerical
results suggest that our proposed multi-hop diffusion strategy achieves the
same steady-state MSD as the existing one-hop adapt-then-combine diffusion
algorithm but with a lower energy budget.Comment: 14 pages, 12 figures. Submitted for publicatio
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