Coding for a class of unknown channels

An information-theoretic and game-theoretic study of timing channels

“…Our choices were guided by the theory of arbitrarily varying channels (AVC), initiated by Blackwell, Breiman, and Thomasian [8], as well as by our desire to have . See [12] and [23] for recent surveys of the theory of AVCs, and [34] for a study of the related error exponents. Three aspects of the jammed timing channel do not fit the original formulation of AVCs: i) the jammed timing channel has constraints, namely, an arrival rate constraint on the coder and, in the case of average-delay constraints, a delay constraint on the jammer, ii) the jammed timing channel has memory, and iii) the jammer can causally observe the particular input waveform used.…”

“…Therefore, we have that Fix an output and let be independent uniform random variables on . We have that (34) where is the indicator function taking value if is true and otherwise, with Equation (34) follows because . Let represent a vector of independent, exponential random variables with common mean .…”

Maximin performance of binary-input channels with uncertain noise distributions

“…Consider the decision hypothesis test for the standard binary-input additive-noise channel: (1) where is a random variable representing additive channel noise. Fix a random variable with symmetric probability density function (pdf) exhibiting second moment and consider a class of pdf's constrained in power and divergence with respect to Within this class, we wish to find a pdf which maximizes the ML probability of detection error criterion (2) corresponding to (1), where the random variable with pdf represents worst case power-and divergence-constrained noise.…”

“…For instance, worst case transition probabilities for a finite-input-alphabet, finite-output-alphabet channel are considered in [1], while assumed knowledge of the noise moments is used to generate a maximum-entropy distribution in [2]. Most often, a peak or average power constraint is imposed on the noise or interference and a worst case distribution is sought, either for guaranteed performance quantification [3]- [13] or in the context of a zerosum game formulation between communicator and jammer [14], [15].…”

“…Worst case amplitudeand power-constrained interference for an additive Gaussian channel with intersymbol interference is considered in [11]. Worst case power-constrained noise in "very noisy" channels is considered in [12] as an extension to [1]. A full solution for this problem is developed in [13] for maximum-likelihood detection, where the least favorable noise distributions for binary-input additive-noise channels with fixed signal-to-noise ratio (SNR) are found for several performance measures.…”