5 research outputs found
Active sequential hypothesis testing
Consider a decision maker who is responsible to dynamically collect
observations so as to enhance his information about an underlying phenomena of
interest in a speedy manner while accounting for the penalty of wrong
declaration. Due to the sequential nature of the problem, the decision maker
relies on his current information state to adaptively select the most
``informative'' sensing action among the available ones. In this paper, using
results in dynamic programming, lower bounds for the optimal total cost are
established. The lower bounds characterize the fundamental limits on the
maximum achievable information acquisition rate and the optimal reliability.
Moreover, upper bounds are obtained via an analysis of two heuristic policies
for dynamic selection of actions. It is shown that the first proposed heuristic
achieves asymptotic optimality, where the notion of asymptotic optimality, due
to Chernoff, implies that the relative difference between the total cost
achieved by the proposed policy and the optimal total cost approaches zero as
the penalty of wrong declaration (hence the number of collected samples)
increases. The second heuristic is shown to achieve asymptotic optimality only
in a limited setting such as the problem of a noisy dynamic search. However, by
considering the dependency on the number of hypotheses, under a technical
condition, this second heuristic is shown to achieve a nonzero information
acquisition rate, establishing a lower bound for the maximum achievable rate
and error exponent. In the case of a noisy dynamic search with size-independent
noise, the obtained nonzero rate and error exponent are shown to be maximum.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1144 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Extrinsic Jensen-Shannon Divergence: Applications to Variable-Length Coding
This paper considers the problem of variable-length coding over a discrete
memoryless channel (DMC) with noiseless feedback. The paper provides a
stochastic control view of the problem whose solution is analyzed via a newly
proposed symmetrized divergence, termed extrinsic Jensen-Shannon (EJS)
divergence. It is shown that strictly positive lower bounds on EJS divergence
provide non-asymptotic upper bounds on the expected code length. The paper
presents strictly positive lower bounds on EJS divergence, and hence
non-asymptotic upper bounds on the expected code length, for the following two
coding schemes: variable-length posterior matching and MaxEJS coding scheme
which is based on a greedy maximization of the EJS divergence.
As an asymptotic corollary of the main results, this paper also provides a
rate-reliability test. Variable-length coding schemes that satisfy the
condition(s) of the test for parameters and , are guaranteed to achieve
rate and error exponent . The results are specialized for posterior
matching and MaxEJS to obtain deterministic one-phase coding schemes achieving
capacity and optimal error exponent. For the special case of symmetric
binary-input channels, simpler deterministic schemes of optimal performance are
proposed and analyzed.Comment: 17 pages (two-column), 4 figures, to appear in IEEE Transactions on
Information Theor
Saddle Point in the Minimax Converse for Channel Coding
A minimax metaconverse has recently been proposed as a simultaneous generalization of a number of classical results and a tool for the nonasymptotic analysis. In this paper, it is shown that the order of optimizing the input and output distributions can be interchanged without affecting the bound. In the course of the proof, a number of auxiliary results of separate interest are obtained. In particular, it is shown that the optimization problem is convex and can be solved in many cases by the symmetry considerations. As a consequence, it is demonstrated that in the latter cases, the (multiletter) input distribution in information-spectrum (Verdú-Han) converse bound can be taken to be a (memoryless) product of single-letter ones. A tight converse for the binary erasure channel is rederived by computing the optimal (nonproduct) output distribution. For discrete memoryless channels, a conjecture of Poor and Verdú regarding the tightness of the information spectrum bound on the error exponents is resolved in the negative. Concept of the channel symmetry group is established and relations with the definitions of symmetry by Gallager and Dobrushin are investigated.National Science Foundation (U.S.) (Center for Science of Information, under Grant CCF-0939370