Search with Noisy and Delayed Responses

It is well–known that search problems with a stochastic response matrix acting independently for the questions can be equivalently formulated as transmission problems for a discrete memoryless channel (DMC) with feedback. This is explained in Chapter 3 of the book Search Problems by R. Ahlswede and I. Wegener (Wiley 1987, translation of Suchprobleme, Teubner 1979). There also Ahlswede’s coding scheme for the DMC and also for the arbitrarily varying channel (AVC) achieving the capacities are described. The latter can be viewed as a robust model for search. In this paper we analyse this robust model with a time delay for the noiseless feedback. In the terminology of search this means that the answers are given with delay. We determine the (asymptotically) optimal performances, that is, find the capacities, for the cases where the delay is constant and linear in the blocklength. Finally we also give the corresponding results for the DMC with zero–error probability.