5,003 research outputs found
Rate-Distortion for Ranking with Incomplete Information
We study the rate-distortion relationship in the set
of permutations endowed with the Kendall t-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 t-metric we provide bounds for small, medium, and large distortion regimes, while for the Chebyshev metric we present bounds that are valid for all distortions and are especially accurate for small
distortions. In addition, for the Chebyshev metric, we provide a construction for covering codes
A Rate-Distortion Approach to Index Coding
We approach index coding as a special case of rate-distortion with multiple
receivers, each with some side information about the source. Specifically,
using techniques developed for the rate-distortion problem, we provide two
upper bounds and one lower bound on the optimal index coding rate. The upper
bounds involve specific choices of the auxiliary random variables in the best
existing scheme for the rate-distortion problem. The lower bound is based on a
new lower bound for the general rate-distortion problem. The bounds are shown
to coincide for a number of (groupcast) index coding instances, including all
instances for which the number of decoders does not exceed three.Comment: Substantially extended version. Submitted to IEEE Transactions on
Information Theor
Frame Permutation Quantization
Frame permutation quantization (FPQ) is a new vector quantization technique
using finite frames. In FPQ, a vector is encoded using a permutation source
code to quantize its frame expansion. This means that the encoding is a partial
ordering of the frame expansion coefficients. Compared to ordinary permutation
source coding, FPQ produces a greater number of possible quantization rates and
a higher maximum rate. Various representations for the partitions induced by
FPQ are presented, and reconstruction algorithms based on linear programming,
quadratic programming, and recursive orthogonal projection are derived.
Implementations of the linear and quadratic programming algorithms for uniform
and Gaussian sources show performance improvements over entropy-constrained
scalar quantization for certain combinations of vector dimension and coding
rate. Monte Carlo evaluation of the recursive algorithm shows that mean-squared
error (MSE) decays as 1/M^4 for an M-element frame, which is consistent with
previous results on optimal decay of MSE. Reconstruction using the canonical
dual frame is also studied, and several results relate properties of the
analysis frame to whether linear reconstruction techniques provide consistent
reconstructions.Comment: 29 pages, 5 figures; detailed added to proof of Theorem 4.3 and a few
minor correction
- …