The CR capacity of a two-teminal model is defined as the maximum rate of common randomness that the terminals can generate using resources specified by the given model. We determine CR capacity for several models, including those whose statistics depend on unknown parameters. The CR capacity is shown to be achievable robustly, by common randomness of nearly uniform distribution no matter what the unknown parameters are. Our CR capacity results are relevant for the problem of identification capacity, and also yield a new result on the regular (transmission) capacity of arbitrarily varying channels with feedback. Key words: common randomness, identification capacity, correlated sources, arbitrarily varying channel, feedback, randomization. I. Csisz'ar was partially supported by the Hungarian National Foundation for Scientific Research, Grant T16386. 1 Introduction Suppose two terminals, called Terminal X and Terminal Y, have resources such as access to side information and communica...

The method of types is one of the key technical tools in Shannon Theory, and this tool is valuable also in other fields. In this paper, some key applications will be presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method, and a wide selection of further applications will be surveyed. These range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems. While the method of types is suitable primarily for discrete memoryless models, its extensions to certain models with memory will also be discussed. Index Terms---Arbitrarily varying channels, choice of decoder, counting approach, error exponents, extended type concepts, hypothesis testing, large deviations, multiuser problems, universal coding. I.

Abstract—To transmit information by timing arrivals to a singleserver queue, we consider using the exponential server channel’s maximum-likelihood decoder. For any server with service times that are stationary and ergodic with mean I seconds, we show that the rate I nats per second (capacity of the exponential server timing channel) is achievable using this decoder. We show that a similar result holds for the timing channel with feedback. We also show that if the server jams communication by adding an arbitrary amount of time to the nominal service time, then the rate I I P @ I C PA nats per second is achievable with random codes, where the nominal service times are stationary and ergodic with mean I I seconds, and the arithmetic mean of the delays added by the server does not exceed I P seconds. This is a model of an arbitrarily varying channel where the current delay and the current input can affect future outputs. We also show the counterpart of these results for single-server discrete-time queues. Index Terms—Arbitrarily varying channel, channels with feedback, mismatched decoder, point-process channel, robust decoding, single-server queue, timing channels. I.

We study the following problem: two agents Alice and Bob are connected to each other by independent discrete memoryless channels. They wish to generate common randomness, i.e., agree on a common random variable, by communicating interactively over the two channels. Assuming that Alice and Bob are allowed access to independent external random sources at rates (in bits per step of communication) of HA and HB , respectively, we show that they can generate common randomness at a rate of maxfmin[HA + H(W j Q);I(P;V)] + min[HB + H(V j P );I(Q;W)]g bits per step, by exploiting the noise on the two channels. Here, V is the channel from Alice to Bob, and W is the channel from Bob to Alice. The maximum is over all probability distributions P and Q on the input alphabets of V and W , respectively. We also prove a strong converse which establishes the above rate as the highest attainable in this situation.

In this paper, we generalize our previous results on generating common randomness at two terminals to a situation where any finite number of agents, interconnected by an arbitrary network of independent, point-to-point, discrete memoryless channels, wish to generate common randomness by interactive communication over the network. Our main result is an exact characterization of the common randomness capacity of such a network, i.e., the maximum number of bits of randomness that all the agents can agree on per step of communication. As a by-product, we also obtain a purely combinatorial result, viz., a characterization of (the incidence vectors of) the spanning arborescences rooted at a specified vertex in a digraph, and having exactly one edge exiting the root, as precisely the extreme points of a certain unbounded convex polyhedron, described by a system of linear inequalities.

Abstract—We consider the problem of communicating over a channel for which no mathematical model is specified. We present achievable rates as a function of the channel input and output sequences known a-posteriori for discrete and continuous channels. Furthermore we present a rate-adaptive scheme employing feedback which achieves these rates asymptotically without prior knowledge of the channel behavior. I.

Consider a fthire number of agents interconnected by an arbitrary network of independent, point-to-point, discrete memoryless channels. The agents wish to generate common randomness by interactive communication over the network. Our main result is an exact characterization of the common randomness capacity of such a network, i.e. the maximum number of bits of randomness that all the agents can agree on, per step of communication. As a by-product, we also ob- tain a description by linear inequalities of the blocking-type polyhedron whose extreme points are precisely the incidence vectors of all arborescences in a digraph, with a prescribed root of out-degree 1.

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Abstract. Error-correcting codes tackle the fundamental problem of recovering from errors during data communication and storage. A basic issue in coding theory concerns the modeling of the channel noise. Shannon’s theory models the channel as a stochastic process with a known probability law. Hamming suggested a combinatorial approach where the channel causes worst-case errors subject only to a limit on the number of errors. These two approaches share a lot of common tools, however in terms of quantitative results, the classical results for worst-case errors were much weaker. We survey recent progress on list decoding, highlighting its power and generality as an avenue to construct codes resilient to worst-case errors with information rates similar to what is possible against probabilistic errors. In particular, we discuss recent explicit constructions of list-decodable codes with information-theoretically optimal redundancy that is arbitrarily close to the fraction of symbols that can be corrupted by worst-case errors.

universal capacity of channels with given rate-distortion in the absence of common randomness