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Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks

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2 Author(s)
Goela, N. ; Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, Berkeley, CA, USA ; Gastpar, M.

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 nonconvex 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-Loève 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.

Published in:

Signal Processing, IEEE Transactions on  (Volume:60 ,  Issue: 6 )

Date of Publication:

June 2012

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