The impact of causality on information-theoretic source and channel coding problems by Harikrishna R. Palaiyanur Doctor of Philosophy in Engineering — Electrical Engineering and Computer Sciences University of California, Berkeley Professor Anant Sahai, Chair This thesis studies several problems in information theory where the notion of causality comes into play. Causality in information theory...

An improved upper bound on the error probability (first error event) of time-invariant convolutional codes, and the resulting error exponent, is derived in this paper. The improved error bound depends on both the delay of the code and its width (the number of symbols that enter the delay line in parallel) . Determining the error exponent of time-invariant convolutional codes is an open problem....

Multifractional Processes with Random Exponent (MPRE) are obtained by replacing the Hurst parameter of Fractional Brownian Motion (FBM) with a stochastic process. This process need not be independent of the white noise generating the FBM. MPREs can be conveniently represented as random wavelet series. We will use this type of representation to study their Hölder regularity and their self-simila...

Error exponent bounds for a noise free optical channel using a direct detection receiver are computed for the cases of Pulse Position Modulation (PPM) and for the basic channel with binary output and average intensity constraint. Some consequences are derived regarding the behavior of the interleaving scheme suggested by Massey, the optimality of the PPM format and the significance of the Ro pa...

THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. Achievable error exponent regions of a twoway additive white Gaussian noise (AWGN) channel, where two terminals exchange a fixed number of messages M , are derived. In particular, error exponent regions for M = 2 messages under expected power and M = 3 messages under almost sure power constraints are considered. For M = 2 messages the use of a...

Recently it was shown that a lattice code with lattice decoding can achieve the capacity of the additive white Gaussian noise (AWGN) channel. This was achieved by using a minimum mean-square error (MMSE) scaling and dithering to transform the AWGN channel into a modulo-lattice additive noise (mod-Λ) channel. Further, Liu et. al. have shown that lattice decoding can achieve the error exponent of...

The Hurst exponent (H) is a statistical measure used to classify time series. H=0.5 indicates a random series while H>0.5 indicates a trend reinforcing series. The larger the H value is, the stronger trend. In this paper we investigate the use of the Hurst exponent to classify series of financial data representing different periods of time. Experiments with backpropagation Neural Networks show ...

We measure the persistence exponent in a phase separating two-dimensional spin system with non-conserved dynamics quenched in a region with four coexisting stripe phases. The system is an Ising model with nearest neighbor, next-to-the-nearest neighbor and plaquette interactions. Due the particular nature of the ground states, the order parameter is defined in terms of blocks of spins. Our estim...

We prove that certain categories arising from atoms in a Grothendieck topos are themselves Grothendieck toposes. We also investigate enrichments of these categories over the base topos; there are in fact often two distinct enrichments.

where As3 is the Laplace-Beltrami operator on B' . Let 0* C (0, 7r) be the radius o r B ' , i.e., the geodesic distance of the North pole to OBq The values 0 < 0* < 7r/2 correspond to a spherical cap contained in the Northern hemisphere, 0* -7r/2 corresponds to B ~ being the Northern hemisphere and the values rr/2 < 0* < ~c correspond to a spherical cap which covers the Northern hemisphere. Fin...