AbsrructAn analysis of the rate-distortion performance of differential pulse code modulation (DPCM) schemes operating on discrete-tbue autoregressive processes is presented. The approach uses an iterative algorithm for the design of the predictive quantizer subject to an entropy constraint on the output sequence. At each stage the iterative algorithm optimizes the quantizer structure, given the...

We consider the transmission of a real i.i.d. Gaussian source over a quasi-static MIMO fading channel. The relevant performance criterion is end-toend average quadratic distortion D versus channel SNR, for given spectral efficiency η, defined as the ratio of the source bandwidth over the channel bandwidth. In the limit of high-resolution (vanishing distortion) for high-SNR, we define the distor...

We study the combinatorics of fully commutative elements in Coxeter groups of type H n for any n > 2. Using the results, we construct certain canonical bases for non-simply-laced generalized Temperley–Lieb algebras and show how to relate them to morphisms in the category of decorated tangles.

We address the attainability of the Hashin-Shtrikman bounds for multiphase composite materials. We demonstrate that the Hashin-Shtrikman bounds are not always attainable and give new restrictions on the attainable Hashin-Shtrikman bounds in terms of the conductivities and volume fractions of the constituent phases. New optimal microstructures are also constructed to attain the Hashin-Shtrikman ...

We simplify and improve upon recent lower bounds on the minimum distortion of embedding certain finite metric spaces into L1. In particular, we show that for every n ≥ 1, there is an n-point metric space of negative type that requires a distortion of Ω(log log n) for such an embedding, implying the same lower bound on the integrality gap of a well-known semidefinite programming relaxation for s...

Recent work has suggested that low-density generator matrix (LDGM) codes are likely to be effective for lossy source coding problems. We derive rigorous upper bounds on the effective rate-distortion function of LDGM codes for the binary symmetric source, showing that they quickly approach the rate-distortion function as the degree increases. We also compare and contrast the standard LDGM constr...

Achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers. It is known that for the cascade of asymptotically good channel codes and asymptotically good vector quantizers the end-to-end distortion decays to zero exponentially fast as a function of the overall transmission rate, and is achieved by choosing ...

We introduce and study a class l dom 1 () of l 1-embeddable metrics corresponding to a given metric. This class is deened as the set of all convex combinations of-dominated line metrics. Such metrics were implicitly used before in several constuctions of low-distortion embeddings into l p-spaces, such as Bourgain's embedding of an arbitrary metric on n points with O(log n) distortion. Our main ...

We consider the problem of source compression under three different scenarios in the one-shot (nonasymptotic) regime. To be specific, we prove one-shot achievability and converse bounds on the coding rates for distributed source coding, source coding with coded side information available at the decoder and source coding under maximum distortion criterion. The one-shot bounds obtained are in ter...

Data processing lower bounds on the expected distortion are derived in the finite–alphabet semi–deterministic setting, where the source produces a deterministic, individual sequence, but the channel model is probabilistic, and the decoder is subjected to various kinds of limitations, e.g., decoders implementable by finite–state machines, with or without counters, and with or without a restricti...