A Kraft–Type Inequality for d–Delay Binary Search Codes

Abstract

Among the models of delayed search discussed in [1], [2], the simplest one can be formulated as the following two–player game. One player, say A, holds a secret number $m\in{\mathcal M}\triangleq\{1,2,\dots,M\}$ and another player, say Q, tries to learn the secret number by asking A at time i questions, like “Is m≥x _i ?”, where x _i is a number chosen by Q. The rule is that at time i + dA must answer Q ’s question at time i correctly and at time jQ can choose x _j according to all answers he has received.