(Professor Kannan Ramchandran)

(DARPA) F30602-00-2-0538 and (NSF) CCR-0219722

We study the problem of rate-constrained robust estimation of
noisy sensor measurements in an unreliable sensor network. Noisy
measurements of physical process *X* (e.g., temperature)
made by individual sensors need to be communicated to a central
observer over unreliable channels. Limited power resources of the
sensors place a strong limit on the resolution with which the noisy
sensor readings can be transmitted. Both the sensors and the
communication links can break down. However, the central observer is
guaranteed to reliably receive readings from a minimum of *k* out
of *n* sensors. The goal of the central observer is to estimate
the observed physical process from the received transmissions where a
specified distortion metric provides an objective measure of
estimation quality. In this work, we derive an information-theoretic
achievable rate-distortion region for this problem when the sensor
measurement noise statistics are symmetric with respect to the
sensors.

In the special case of a Gaussian sensor network, i.e., when the
source is i.i.d. Gaussian, the sensor noise processes are additive
i.i.d. Gaussian, and the distortion metric is mean squared error, we
have the following remarkable result. When any *k* out of
*n* unreliable sensor transmissions are received, the
central decoder's estimation quality can be as good as the best
reconstruction quality that can be achieved by deploying only
*k* reliable sensors and the central decoding unit is able to
receive transmissions from all *k* sensors. Furthermore,
when more than *k* out of the *n* sensor transmissions are
received, the estimation quality strictly improves.

Figure 1: An unreliable sensor network. A noisy version of source *X* is
observed at each of the *n* sensors. The noisy observations
Y_{1},...,Y_{n} are encoded and the encoded
indices I_{1},...,I_{n} are transmitted. The
network delivers some m >= k indices. The decoder
obtains the best possible reconstruction of *X* from the received
indices.

Figure 2: Random code construction. *n* independent random codebooks of
block length *l* are constructed, each containing
2^{lR'} codewords. Each codebook is randomly
partitioned into 2^{lR} bins each with approximately
2^{l(R'-R)} codewords.

Figure 3: Structure of sensor encoders that can achieve rate-distortion
performance. The encoder of each sensor consists of a rate *R'*
quantizer, for block length *l,* followed by a rate *R*
random binning function.

Figure 4: Structure of the central observer decoder that can achieve
rate-distortion performance. The central observer first decodes the
received indices to intermediate representations of length *l*,
and then forms the best estimate of the source. Here, m >= k.

^{1}Postdoctoral Researcher

^{2}Postdoctoral Researcher

^{3}Professor, University of Michigan, Ann Arbor

Edit this abstract