In this article we present Pickands theorem and his double sum method. We follow Piterbarg’s proof of this theorem. Since his proof relies on general lemmas we present a complete proof of Pickands theorem using Borell inequality and Slepian lemma. The original Pickands proof is rather complicated and is mixed with upcrossing probabilities for stationary Gaussian processes. We give a lower bound...

Landau, Pollak, Slepian, and Tracy, Widom discovered that certain integral operators with so called Bessel and Airy kernels possess commuting differential operators and found important applications of this phenomenon in time-band limiting and random matrix theory. In this paper we announce that very large classes of integral operators derived from bispectral algebras of rank 1 and 2 (parametriz...

This paper gives a brief but comprehensive review of the Multitaper spectrum estimation method that uses the data tapers or windows in digital signal processing. Instead of using a single kind of window functions, here a cluster of window functions are mentioned, which is known as Slepian tapers. This taper family minimize leakage also, and computing them requires solving eigenvalue problems th...

We investigate the simplest Slepian-Wolf source network, consisting of an information source correlated with a second source used as a side-information for the decoder but not the encoder. The information source and side-information source are modeled as binary random sequences } { }, { i i Y Y X X = = , respectively, for which the pairs ) , ( i i Y X are independentidentically distributed (i.i...

In this paper, we analyze the asymptotics of the normalized remaining uncertainty of a source when a compressed or hashed version of it and correlated side-information is observed. For this system, commonly known as Slepian-Wolf source coding, we establish the optimal (minimum) rate of compression of the source to ensure that the remaining uncertainties vanish. We also study the exponential rat...

This paper discusses the Slepian-Wolf problem of distributed near-lossless compression of correlated sources. We introduce practical new tools for communicating at all rates in the achievable region. The technique employs a simple ‘sourcesplitting’ strategy that does not require common sources of randomness at the encoders and decoders. This approach allows for pipelined encoding and decoding s...

Distributed source coding schemes are typically based on the use of channels codes as source codes. In this paper we propose a new paradigm, named “distributed arithmetic coding”, which extends arithmetic codes to the distributed case employing sequential decoding aided by the side information. In particular, we introduce a distributed binary arithmetic coder for the Slepian-Wolf coding problem...