We design polar codes for empirical coordination and strong coordination in two-node networks. Our constructions hinge on the fact that polar codes enable explicit low complexity schemes for soft covering. We leverage this property to propose explicit and low-complexity coding schemes that achieve the capacity regions of both empirical coordination and strong coordination for sequences of actio...

We study concepts of decidability (recursivity) for subsets of Euclidean spaces R k within the framework of approximate computability (type two theory of ef-fectivity). A new notion of approximate decidability is proposed and discussed in some detail. It is an eeective variant of F. Hausdorr's concept of resolvable sets and modiies and generalizes notions of recursivity known from computable an...

Generalized t-designs, which form a common generalization of objects such as tdesigns, resolvable designs and orthogonal arrays, were defined by Cameron [P.J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835–4842]. In this paper, we define a related class of combinatorial designs which simultaneously generalize packing designs and packing arrays. We describe the sometimes...

We study the minimum random bit rate required to simulate a random system (channel), where the simulator operates with a given external input. As measures of simulation accuracy we use both the variational distance and the d distance between joint input-output distributions. We find the asymptotic number of random bits per input sample required for accurate simulation, as a function of the dist...

We determine, for both countable and uncountable collections of functions, informationtheoretic conditions on a penalty pen(f) such that the optimizer f̂ of the penalized log likelihood criterion log 1/likelihood(f) + pen(f) has statistical risk not more than the index of resolvability corresponding to the accuracy of the optimizer of the expected value of the criterion. If F is the linear span ...

This work establishes the exact exponent for the soft-covering phenomenon of a memoryless channel under the total variation metric. The exponent, established herein, is a strict improvement (in both directions) on bounds found in the literature. This complements the recent literature establishing the exact exponent under the relative entropy metric; however, the proof techniques have significan...

We develop a new approach to image denoising based on complexity regularization. This technique presents a flexible alternative to the more conventional l, l, and Besov regularization methods. Different complexity measures are considered, in particular those induced by state– of–the–art image coders. We focus on a Gaussian denoising problem and derive a connection between complexity–regularized...

In the present study, influence of three zone asymmetric apodizer on the resolution of composite image of two object points with given intensity ratio ‘c’ has been investigated. The proposed pupil function and its transmittance is formulated and studied. Fourier analytical properties of three zone aperture systems are studied by applying the modified sparrow criterion. The results are discussed...

Let R be an arbitrary commutative ring and R〈X〉 = R〈X1, ..., Xn〉 the free algebra of n generators over R. Note that Bergman’s diamond lemma characterizes the resolvability of ambiguities of monic relations of the form Wσ − fσ with fσ a linear combination of monomials ≺ Wσ, where ≺ is a semigroup partial ordering on 〈X〉; and that in the algorithmic language of Gröbner basis theory over a ground ...

Zariski defined equisingularity on an n-dimensional hypersurface V via stratification by “dimensionality type,” an integer associated to a point by means of a generic local projection to affine n-space. A possibly more intuitive concept of equisingularity can be based on stratification by simultaneous resolvability of singularities. The two approaches are known to be equivalent for families of ...