We study the problem of computing a low-distortion embedding between two metric spaces. More precisely given an input metric space M we are interested in computing in polynomial time an embedding into a host space M ′ with minimum multiplicative distortion. This problem arises naturally in many applications, including geometric optimization, visualization, multi-dimensional scaling, network spa...

This paper presents an algorithm that jointly optimizes a lattice vector quantizer (LVQ) and an entropy coder in a subband coding at all ranges of bit rate. Estimation formulas for both entropy and distortion of lattice quantized subband images are derived. From these estimates, we then develop dynamic algorithm optimizing the LVQ and entropy coder together for a given entropy rate. Compared to...

We show that the cyclic lamplighter group C2 oCn embeds into Hilbert space with distortion O ( √ log n ) . This matches the lower bound proved by Lee, Naor and Peres in [14], answering a question posed in that paper. Thus the Euclidean distortion of C2 o Cn is Θ ( √ log n ) . Our embedding is constructed explicitly in terms of the irreducible representations of the group. Since the optimal Eucl...

Aggregating the preferences of individuals into a collective decision is core subject study social choice theory. In 2006, Procaccia and Rosenschein considered utilitarian setting, where agents have explicit numerical values for alternatives, yet they only report their linear orderings over them. To compare different aggregation mechanisms, introduced notion distortion, which quantifies ineffic...

This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit of the cumulant generating function of codeword lengths allowing positive excess distortion probability. It is shown that the achievability and converse bound...

This paper considers the joint problem of dirty-paper and Wyner-Ziv coding with partial host information at the receiver. The rate-distortion and the capacity expressions have been derived for the Gaussian case. It is shown that the availability of the partial host information to the receiver has positive effects to the compression performance and the overall capacity. Moreover, a practical cod...

The objective of this work is the characterization of the Wyner-Ziv rate-distortion function for memoryless continuous sources, when the correlation between the sources is modeled via an additive noise channel. Modeling the distribution of the correlation noise via a Gaussian mixture, with discrete or continuous mixing variable, provides a unified signal model able to describe a wide class of d...

A problem in the transmission of analog information across a noisy discrete channel is the choice of channel code rate that optimally allocates the available transmission rate between lossy source coding and block channel coding. We establish tight bounds on the channel code rate that minimizes the average distortion of a vector quantizer cascaded with a channel coder and a binary symmetric cha...