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...

We consider the problem of multiple description scalar quantizers and describing the achievable rate-distortion tuples in that setting. We formulate it as a combinatorial optimization problem of arranging numbers in a matrix to minimize the maximum difference between the largest and the smallest number in any row or column. We develop a technique for deriving lower bounds on the distortion at g...

— New bounds on the rate distortion function of certain non-Gaussian sources, with a proportional-weighted mean-square error (MSE) distortion measure, are given. The growth, g, of the rate distortion function, as a result of changing from a non-weighted MSE distortion measure to a proportional-weighted distortion criterion is analyzed. It is shown that for a small distortion, d, the growth, g, ...

We obtain estimates for derivative and cross–ratio distortion for C (any η > 0) unimodal maps with non–flat critical points. We do not require any ‘Schwarzian–like’ condition. For two intervals J ⊂ T , the cross–ratio is defined as the value B(T, J) := |T ||J | |L||R| where L, R are the left and right connected components of T \J respectively. For an interval map g such that gT : T → R is a dif...

The explicit form of the rate-distortion function has rarely been obtained, except for few cases where the Shannon lower bound coincides with the rate-distortion function for the entire range of the positive rate. From an information geometrical point of view, the evaluation of the rate-distortion function is achieved by a projection to the mixture family defined by the distortion measure. In t...

Digital signals are complex-valued functions on Zn. Signal sets with certain properties are required in various communication systems. Traditional signal sets consider only the time distortion during transmission. Recently, signal sets against both the time and phase distortion have been studied, and are called time-phase signal sets. Several constructions of time-phase signal sets are availabl...