Communication Under Strong Asynchronism

Abstract

We consider asynchronous communication over point-to-point discrete memoryless channels without feedback. The transmitter starts sending one block codeword at an instant that is uniformly distributed within a certain time period, which represents the level of asynchronism. The receiver, by means of a sequential decoder, must isolate the message without knowing when the codeword transmission starts but being cognizant of the asynchronism level. We are interested in how quickly can the receiver isolate the sent message, particularly in the regime where the asynchronism level is exponentially larger than the codeword length, which we refer to as 'strong asynchronism. ' This model of sparse communication might represent the situation of a sensor that remains idle most of the time and, only occasionally, transmits information to a remote base station which needs to quickly take action. Because of the limited amount of energy the sensor possesses, assuming the same cost per transmitted symbol, it is of interest to consider minimum size codewords given the asynchronism level.The first result is an asymptotic characterization of the largest asynchronism level, in terms of the codeword length, for which reliable communication can be achieved: vanishing error probability can be guaranteed as the codeword length N tends to infinity while the asynchronism level grows as e N α if and only if α does not exceed the synchronization threshold, a constant that admits a simple closed form expression, and is at least as large as the capacity of the synchronized channel.The second result is the characterization of a set of achievable strictly positive rates in the regime where the asynchronism level is exponential in the codeword length, and where the rate is defined with respect to the expected (random) delay between the time information starts being emitted until the time the receiver makes a decision. Interestingly, this achievability result is obtained by a coding strategy whose decoder not only operates in an asynchronously, but has an almost universal decision rule, in the sense that it is almost independent of the channel statistics.As an application of the first result we consider antipodal signaling over a Gaussian additive channel and derive a simple necessary condition between blocklength, asynchronism level, and SNR for achieving reliable communication.

On asynchronous capacity and dispersion

“…With such modifications, one defines the capacityC(A) in exactly the same manner as C(A); the key results of [1], [2] provide upper and lower bounds onC(A) (but notC ǫ (A)). The definition (6) was chosen, perhaps, to model the situation when one wants to assess the minimal number of channel uses (per data bit) that the channel remains under the scrutiny of the decoder, whereas our definition…”

“…Recently, motivated in part by the sensor networks in which nodes exchange data very infrequently (thus, making constant channel-tracking impractical), Tchamkerten et al [1] formulated the problem in an elegant way and later demonstrated [2] that there are indeed significant advantages in going beyond the conventional synchronization approach.…”

“…Mathematically, the formulation of [1] is a generalization of the change point detection problem [3], close in spirit to the so called "detection and isolation" problem introduced in [4], except that in the latter the set of distributions that the original one can switch to is pre-specified whereas [1] allows for an optimal codebook design. Such formulation is quite different from the classical modeling of asyncronism in point-to-point channels as random insertion-deletion [5], [6] or randomly shifting back-to-back codewords [7].…”

“…In this paper we consider a variation of the setup of [1], [2]. In particular, we define the rate as the number of data bits k divided by the time n the codeword occupies the channel (as opposed to [1] that defines the rate as the ratio of k and the time it takes the decoder to react to transmission).…”

“…In particular, we define the rate as the number of data bits k divided by the time n the codeword occupies the channel (as opposed to [1] that defines the rate as the ratio of k and the time it takes the decoder to react to transmission). The definition of rate as in this paper has also been considered in the context of asynchronous communication in [12] and [13].…”