A. Orlitsky. Average-case interactive communication. IEEE Trans. Info. Thy., 38:1534--1547, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the problems: Do restrictions on the size or structure of the key space help Alice and Bob to agree while exchanging substantially fewer than n bits We treat questions of secrecy and channel noise as secondary, regarding them as factors that can make communication expensive. Orlitsky and others [24, 21, 22, 23, 20] have studied communication complexity in settings where Alice observes a random variable X, Bob observes a random variable Y (often dependent on X) and the object is for them to exchange single outcomes each has seen. For example, Y may select two teams i and j from a league S = f1; ....

A. Orlitsky. Average-case interactive communication. IEEE Trans. Info. Thy., 38:1534--1547, 1992.

....two person communication problems using a pointer jumping model are considered, where each host has a list of pointers to the other s list and the task is to follow a pointer chain until the k th pointer. Finally, a large body of relevant work on interactive communication problems is detailed in [3, 4, 12, 15] and the many citations therein. These results mostly focus on theoretical bounds for exchange of information about two related random variables. The work most closely related to ours is that of Orlitsky [16] who considers from an information theoretic perspective the reconciliation of binary ....

Orlitsky, A. Average-case interactive communication. In IEEE Transactions on Information Theory (July 1992), vol. 38, pp. 1534--1547.

....the problems: Do restrictions on the size or structure of the key space help Alice and Bob to agree while exchanging substantially fewer than n bits We treat questions of secrecy and channel noise as secondary, regarding them as factors that can make communication expensive. Orlitsky and others [24, 21, 22, 23, 20] have studied communication complexity in settings where Alice observes a random variable X, Bob observes a random variable Y (often dependent on X) and the object is for them to exchange single outcomes each has seen. For example, Y may select two teams i and j from a league S = f 1; ....

A. Orlitsky. Average-case interactive communication. IEEE Trans. Info. Thy., 38:1534--1547, 1992.

....by the client. We rst show that for any 0 h n, there is a class of distributions D h with entropy h, such that when a distribution D h is chosen uniformly at random from D h , the expected number of bits that must be exchanged is at least n. This result follows from techniques developed in [20]. There are, on the other hand, speci c distributions D 0 where the optimum expected number of bits exchanged is o(n) but for which our protocols require n) bits to be exchanged. Thus, a natural question to ask is: does there exist a protocol where the client and the server exchange close to ....

....by the client plus the number of black box queries is at least n. 1. 4 Previous and related work The question of sending a string x from a client to a server, where the server has some information about x unknown to the client, has a long history in the area known as interactive communication [14, 17, 18, 19, 20, 21, 22, 25]. Here, it is typically assumed that a pair (x; y) is drawn from a joint probability distribution D p over pairs (x; y) where D p is known to both the client and the server in advance. The string x is given to the client, the string y is given to the server, and the task is 5 to communicate the ....

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A. Orlitsky. Average-case interactive communication. IEEE Trans. on Information Theory, 38(4):1534-1547, 1992.

....by the client. We first show that for any 0 h n, there is a class of distributions D h with entropy h, such that when a distribution D h is chosen uniformly at random from D h , the expected number of bits that must be exchanged is at least n. This result follows from techniques developed in [18]. There are, on the other hand, specific distributions D 0 where the optimum expected number of bits exchanged is o(n) but for which our protocols require Omega Gamma n) bits to be exchanged. Thus, a natural question to ask is: does there exist a protocol where the client and the server ....

....sent by the client plus the number of black box queries is at least n. 1. 4 Previous and related work The question of sending a string x from a client to a server, where the server has some information about x unknown to the client, has a long history in the area known as interactive communication [12, 15, 16, 17, 18, 19, 20, 22]. Here, it is typically assumed that a pair (x; y) is drawn from a joint probability distribution D p over pairs (x; y) where D p is known to both the client and the server in advance. The string x is given to the client, the string y is given to the server, and the task is to communicate the ....

[Article contains additional citation context not shown here]

A. Orlitsky. Average-case interactive communication. IEEE Trans. on Information Theory, 38(4):1534--1547, 1992.

....with Yao s idea of exchanging messages in several rounds. Cum grano salis it can be said, that this can be traced back to [1] See also the discussion in [26] It is very interesting to see what has happened in the last decade in this direction, called interactive data communication (see [21] [25] and [27] 29] mainly in several contributions of Alon Orlitsky ( 22] 25] IV. We recall first in our terminology the model studied. Given are the (abstract) correlated source (V; W;S) and two communicators P V , an informant, and PW , a recipient. P V knows output v 2 V and PW knows ....

.... be said, that this can be traced back to [1] See also the discussion in [26] It is very interesting to see what has happened in the last decade in this direction, called interactive data communication (see [21] 25] and [27] 29] mainly in several contributions of Alon Orlitsky ( 22] [25]) IV. We recall first in our terminology the model studied. Given are the (abstract) correlated source (V; W;S) and two communicators P V , an informant, and PW , a recipient. P V knows output v 2 V and PW knows output w 2 W . Both communicators want the recipient PW to learn v without error, ....

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A. Orlitsky, "Average--case interactive communication", IEEE Trans. Inform. Theory, vol. IT--38, pp. 1534--1547, 1992.

....the problems: Do restrictions on the size or structure of the key space help Alice and Bob to agree while exchanging substantially fewer than n bits We treat questions of secrecy and channel noise as secondary, regarding them as factors that can make communication expensive. Orlitsky and others [OG90, Orl90, Orl91b, Orl91a, Orl92, NOS93] have studied communication complexity in settings where Alice observes a random variable X , Bob observes a random variable Y (often dependent on X) and the object is for them to exchange single outcomes each has seen. For example, Y may select two teams i and j from a league S = f 1; ....

A. Orlitsky. Average-case interactive communication. IEEE Trans. Info. Thy., 38:1534--1547, 1992.

....2 bits. We first demonstrate that for any 0 h n, there is a class of distributions D h with entropy h, such that when a distribution D h is chosen uniformly at random from D h , the expected number of bits that need to be exchanged is at least n. This result follows from techniques developed in [17]. There are, on the other hand, specific distributions D 0 where the optimum expected number of bits exchanged is o(n) but for which our protocols require Omega Gamma n) bits to be exchanged. Thus, a natural question to ask is: does there exist a protocol where the client and the server ....

....sent by the client plus the number of black box queries is at least n. 1. 4 Previous and related work The question of sending a string x from a client to a server, where the server has some information about x unknown to the client, has a long history in the area known as interactive communication [11, 14, 16, 15, 17, 18, 19, 21]. Here, it is typically assumed that a pair (x; y) is drawn from a joint probability distribution D p over pairs (x; y) where D p is known to both the client and the server in advance. The string x is given to the client, the string y is given to the server, and the task is to communicate the ....

[Article contains additional citation context not shown here]

A. Orlitsky. Average-case interactive communication. IEEE Trans. on Information Theory, 38(4):1534-- 1547, 1992.

....(X; Y ) is implicit in the notation and will be implied by the context. of messages exchanged. Clearly, C 1 C 2 C 3 Delta Delta Delta C1 : The following example and results, taken from [3] relate these complexity measures. For others aspects of interactive communication, see [4, 5, 6]. Example 1 A league has t teams. P Y knows two teams that played in a game, and PX knows the team that won the game. They communicate in order for P Y to learn the winning team. If only one message is allowed, necessarily from PX to P Y , it must be based solely on the winner (for that is all PX ....

.... 2 Z, let S Y ( def = fy : y) g be the set of Y values with ambiguity . Clearly, for all feasible 5 , 1 jS Y ( j X y2SY ( 1 X x: x;y)2S OE (x; y) log : The next theorem says that this average lower bound can be almost met. Its proof resembles that of Theorem 3 in [6], hence omitted. Theorem 2 Let (X; Y ) be a random pair. There is a four message protocol OE such that for all feasible , 1 jS Y ( j X y2SY ( 1 X x: x;y)2S OE (x; y) log 4 log log : 2 Two, progressively stronger, statements are false in general. 1. For every (balanced) X; ....

A. Orlitsky. Average-case interactive communication. IEEE Transactions on Information Theory, 38(4):1534--1547, July 1992.

....2 we make a small step towards a resolution of this problem. We show that asymptotically four messages require at most three times the minimum number of bits: for all random pairs C 4 3 C1 o( C1 ) We remark that for average case complexity four messages are asymptotically optimum [8]. 1.3 Balanced pairs: two messages may require twice the minimum number of bits Let (X; Y ) be a random pair. Its support set is the set S of possible inputs. The support set is of interest as it determines the m message complexity Cm for all m. P Y s ambiguity when he has the value y is ....

....remains: Is there an m such that m messages are asymptotically optimum, namely, for all random pairs Cm C1 o( C1 ) 8) Note that for average case complexity four messages are asymptotically optimum. Let Cm be the m message average case complexity. Then for all random pairs [8], C 4 C1 3 log C1 13:5 : It seems that an essential element in proving (8) is a lower bound on C1 that improves on Result 1 (Section 2) 5.2 Balanced pairs We have proved that there exists a balanced pair for which two messages require twice the minimum number of bits. It ....

A. Orlitsky. Average-case interactive communication. IEEE Transactions on Information Theory, 38(4):1534--1547, July 1992.

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