2 research outputs found
On optimal quantization rules for some problems in sequential decentralized detection
We consider the design of systems for sequential decentralized detection, a
problem that entails several interdependent choices: the choice of a stopping
rule (specifying the sample size), a global decision function (a choice between
two competing hypotheses), and a set of quantization rules (the local decisions
on the basis of which the global decision is made). This paper addresses an
open problem of whether in the Bayesian formulation of sequential decentralized
detection, optimal local decision functions can be found within the class of
stationary rules. We develop an asymptotic approximation to the optimal cost of
stationary quantization rules and exploit this approximation to show that
stationary quantizers are not optimal in a broad class of settings. We also
consider the class of blockwise stationary quantizers, and show that
asymptotically optimal quantizers are likelihood-based threshold rules.Comment: Published as IEEE Transactions on Information Theory, Vol. 54(7),
3285-3295, 200
Asymptotic Optimality Theory For Decentralized Sequential Multihypothesis Testing Problems
The Bayesian formulation of sequentially testing hypotheses is
studied in the context of a decentralized sensor network system. In such a
system, local sensors observe raw observations and send quantized sensor
messages to a fusion center which makes a final decision when stopping taking
observations. Asymptotically optimal decentralized sequential tests are
developed from a class of "two-stage" tests that allows the sensor network
system to make a preliminary decision in the first stage and then optimize each
local sensor quantizer accordingly in the second stage. It is shown that the
optimal local quantizer at each local sensor in the second stage can be defined
as a maximin quantizer which turns out to be a randomization of at most
unambiguous likelihood quantizers (ULQ). We first present in detail our results
for the system with a single sensor and binary sensor messages, and then extend
to more general cases involving any finite alphabet sensor messages, multiple
sensors, or composite hypotheses.Comment: 14 pages, 1 figure, submitted to IEEE Trans. Inf. Theor