# 2010 Research Summary

## Linear Compressive Networks

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Naveen Goela and Michael Gastpar

NDSEG Fellowship

The linear compressive network (LCN)[1] is introduced to analyze compression and estimation of correlated sources distributed in a network. The LCN is a directed, acyclic graph (DAG) of source nodes, linear relay nodes, and decoding leaf nodes. Source nodes (sensors) and relays compress high-dimensional input signals by applying a linear transform, and transmit low-dimensional subspace projections to decoders over a multi-hop network. The communication channels between source, relay, and decoding nodes are modeled as vector channels with additive white Gaussian noise. All decoding nodes estimate linear functions of the original network sources by minimizing a mean squared error (MSE) cost function. One important design problem is to select linear transforms for all network nodes to minimize end-to-end MSE distortion at the decoders. An iterative optimization using quadratic programs (QPs) with general linear and quadratic constraints is constructed to solve the problem. A key part of our analysis are lower bounds on decoding distortion for linear transforms based on cut-set properties of graphs, and side information relaxations. The design of linear, dimensionality-reducing transforms for DAG networks generalizes the Karhunen-Loeve transform, and is related to network coding over finite fields.

- [1]
- N. Goela and M. Gastpar, Linear Compressive Networks. IEEE Int. Symp. on Info. Theory, Seoul, S. Korea, July, 2009.