We study the average distortion introduced by scalar, vector, and entropy coded quantization of compressive sensing (CS) measurements. The asymptotic behavior of the underlying quantization schemes is either quantified exactly or characterized via bounds. We adapt two benchmark CS reconstruction algorithms to accommodate quantization errors, and empirically demonstrate that these methods signif...

In this paper, we make use of the concept q−calculus in theory univalent functions, to obtain bounds for certain coefficient functional problems Janowski type starlike functions and find Fekete–Szegö functional. A similar results have been done function ℘−1. Further, newly defined class determine estimates, distortion bounds, radius problems, related partial sums.

Gersho’s bounds on the asymptotic performance of vector quantizers are valid for vector distortions which are powers of the Euclidean norm. Yamada, Tazaki and Gray generalized the results to distortion measures that are increasing functions of the norm of their argument. In both cases, the distortion is uniquely determined by the vector quantization error, i.e., the Euclidean difference between...

Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases T = R and T = Z. Extending the scope of time scale variant of Gronwall’s inequality we determine function bounds for the solutions of the integro dynamic equation.

We investigate the joint source–channel coding (JSCC) excess distortion exponent (the exponent of the probability of exceeding a prescribed distortion level) for some memoryless communication systems with continuous alphabets. We first establish upper and lower bounds for for systems consisting of a memoryless Gaussian source under the squared-error distortion fidelity criterion and a memoryles...

Any monotone Boolean circuit computing the n-dimensional Boolean convolution requires at least n2 and-gates. This matches the obvious upper bound. The previous best bound for this problem was Ω(n4/3), obtained by Norbert Blum in 1981. More generally, exact bounds are given for all semi-disjoint bilinear forms.