A Kraft-Type Inequality for d-Delay Binary Search Codes
نویسندگان
چکیده
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 ∈ M {1, 2, . . . ,M} and another player, say Q, tries to learn the secret number by asking A at time i questions, like “Is m ≥ xi?”, where xi is a number chosen by Q. The rule is that at time i+ d A must answer Q’s question at time i correctly and at time j Q can choose xj according to all answers he has received. How many questions has Q at least to ask to get the secret number. Let
منابع مشابه
Permutation codes, source coding and a generalisation of Bollobás-Lubell-Yamamoto-Meshalkin and Kraft inequalities
We develop a general framework to prove Krafttype inequalities for prefix-free permutation codes for source coding with various notions of permutation code and prefix. We also show that the McMillan-type converse theorem in most of these cases does not hold, and give a general form of a counterexample. Our approach is more general and works for other structures besides permutation codes. The cl...
متن کاملMinimax Trees in Linear Time
A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves’ depths, it minimizes the maximum of any leaf’s weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffman-like, O(n log n)-time algorithm for building them. Drmota and Szpankowski (2002) gave another O(n log n)-time algorithm, which checks the Kraft Inequali...
متن کاملGeneralized Kraft Inequality and Arithmetic Coding
Algorithms for encoding and decoding finite strings over a finite alphabet are described. The coding operations are arithmetic involving rational numbers li as parameters such that Zi2"i 5 2". This coding technique requires no blocking, and the per-symbol length of the encoded string approaches the associated entropy within E . The coding speed is comparable to that of conventional coding metho...
متن کاملCodes and sofic constraints
We study the notion of a code in a sofic subshift. We first give a generalization of the Kraft-McMillan inequality to this case. We then prove that the polynomial of the alphabet in an irreducible sofic shift divides the polynomial of any finite code which is complete for this sofic shift. This settles a conjecture from Reutenauer.
متن کاملNew Lower Bounds on the Cost of Binary Search Trees
In this paper we provide new lower bounds on the cost C of binary search trees. The bounds are expressed in terms of the entropy H of the probability distribution, the number of elements and the probability that a search is successful. Most of our lower bounds are derived by means of a new technique which exploits the relation between trees and codes. Our lower bounds compare favorably with kno...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 21 شماره
صفحات -
تاریخ انتشار 2005