This paper contains bounds for the distortion in the spherical metric, that is to say, bounds for the constant of Hölder continuity of mappings f : (Rn, q) → (Rn, q) where q denotes the spherical metric. The mappings considered are K-quasiconformal (K ≥ 1) and satisfy some normalizations or restrictions. All bounds are explicit and asymptotically sharp as K → 1.

We consider a rate-distortion problem with side information at multiple decoders. Several upper and lower bounds have been proposed for this general problem or special cases of it. We provide an upper bound for general instances of this problem, which takes the form of a linear program, by utilizing random binning and simultaneous decoding techniques [1] and compare it with the existing bounds....

Given reasonably chosen fixed sets of reproduction letters and/or their probabilities, the authors define new rate-distortion functions which are coding bounds under these alphabet constraints. Calculations are made of these functions for the Gaussian and Laplacian sources and the squared-error distortion measure and find that performance near the rate-distortion bound is achievable using a rep...

We consider the problem of distributed lossy linear function computation in a tree network. We examine two cases: (i) data aggregation (only one sink node computes) and (ii) consensus (all nodes compute the same function). By quantifying the accumulation of information loss in distributed computing, we obtain fundamental limits on network computation rate as a function of incremental distortion...

Rate-distortion theory is considered for the Shannon cipher system (SCS). The admissible region of cryptogram rateR, key rate Rk, legitimate receiver’s distortion D, and wiretapper’s uncertainty h is determined for the SCS with a noisy channel. Furthermore, inner and outer bounds of the admissible region of R, Rk, D, and wiretapper’s attainable minimum distortion ~ D are derived for the SCS wit...

We present a global Ziv-Zakai-type lower bound on the mean square error for estimation of signal parameter vectors, where some components of the distortion function may be periodic. Periodic distortion functions arise naturally in the context of direction of arrival or phase estimation problems. The bound is applied to an image registration problem, and compared to the performance of the Maximu...

Waveform coding of audio signals at low bit rates generally results in coding errors. In high-quality applications these must remain inaudible. The bit rate required to code audio signals without audible errors depends on both the signal's power spectral density function and masking properties of the human ear. It is shown how rate distortion theory and psy-choacoustic models of hearing can be ...

Keywords: Analytic functions Starlike and convex functions Multivalent functions Hadamard product (or convolution) Coefficient bounds Distortion inequalities Neighborhood properties Non-homogeneous Cauchy–Euler differential equations a b s t r a c t In this paper, by making use of the familiar concept of neighborhoods of p-valently analytic functions, we prove coefficient bounds, distortion ine...

Abstract. The object of the present paper is to study certain subclasses J∗ p (a, b, σ) and Cp(a, b, σ) of analytic p-valent functions, and obtain coefficient bounds and distortion properties for functions belonging to these subclasses. Further results include distortion inequalities and radii of close-toconvexity, starlikeness and convexity for these classes of functions.

Transformed codebooks are obtained by a transformation of a given codebook to best match the statistical environment at hand. The procedure, though suboptimal, has recently been suggested for feedback of channel state information (CSI) in multiple antenna systems with correlated channels because of their simplicity and effectiveness. In this paper, we first consider the general distortion analy...