Rate-distortion bounds for scalable coding, and conditions under which they coincide with nonscalable bounds, have been extensively studied. These bounds have been derived for the general tree-structured refinement scheme, where reproduction at each layer is an arbitrarily complex function of all encoding indexes up to that layer. However, inmost practical applications (e.g., speech coding) “ad...

We study the rate-distortion relationship in the set of permutations endowed with the Kendall τ-metric and the Chebyshev metric. Our study is motivated by the application of permutation rate-distortion to the average-case and worst-case analysis of algorithms for ranking with incomplete information and approximate sorting algorithms. For the Kendall τ-metric we provide bounds for small, medium,...

We follow a method introduced by Ziv and Zakai for finding ‘informational’ lower bounds on delay constrained joint source-channel coding. Their method uses the data processing theorem for generalized measures of information. We introduce the use of Rényi’s information of order α in their framework, and use high-resolution approximations to find its rate distortion function for a source that pos...

Wavelet or subband coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate-distortion bounds for wavelet approximation of piecewise smooth functions, in particular the piecewise polynomial case. We contrast these results with rate-distortion bounds achievable using a...

In this paper, we briefly review the connection between subband coding, wavelet approximation and general cornpression problems. Wavelet or subband coding is successful in compression applications partly because of the good approximation properties of wavelets. First, we revisit some rate-distortion bounds for wavelet approximation of piecewise smooth functions. We contrast these results with r...

Wavelet or subband coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate-distortion bounds for wavelet approximation of piecewise smooth functions, in particular the piecewise polynomial case. We contrast these results with rate-distortion bounds achievable using a...

Sharp bounds for japþ2 lapþ1j and jap+3j are derived for certain p-valent analytic functions. These are applied to obtain Fekete-Szegö like inequalities for several classes of functions defined by convolution. 2006 Elsevier Inc. All rights reserved.