Resolving Markov chains onto Bernoulli shifts (2009)
The Erwin, Schrödinger International Boltzmanngasse, Brian Marcus, Selim Tuncel, Brian Marcus, Selim Tuncel
It is well known from Ornstein’s isomorphism theory [FO, O] that entropy is a complete invariant of measure-theoretic isomorphism for mixing Markov chains. In that result the isomorphism is a...
Han, Guangyue, Marcus, Brian, Peres, Yuval
In this note, we show that small complex perturbations of positive matrices are contractions, with respect to a complex version of the Hilbert metric, on the standard complex simplex. We show that...
Citations From References: 1 (2009)
From Reviews, Roy L. Adler, Alan G. Konheim, M. Harry Mcandrew, Topological Entropy, ...
This is an attractive overview of the role played by “entropy ” in the study of dynamical systems since its discovery by Kolmogorov at the end of the 1950s. Several features make it a...
A method for computing lower bounds on capacities of 2-dimensional constraints having a symmetric presentation in either the horizontal or the vertical direction is presented. The method is a...
Asymptotics of Entropy Rate in Special Families of Hidden Markov Chains (2008)
We derive an asymptotic formula for entropy rate of a hidden Markov chain around a "weak Black Hole". We also discuss applications of the asymptotic formula to the asymptotic behaviors of certain...
Chapter 1 Variable Length Codes and Finite Automata (2008)
Marie-pierre Béal, Jean Berstel, Brian Marcus, Dominique Perrin, Christophe Reutenauer, ...
1.2 Definitions and notation...................... 3 1.3 Optimal prefix codes........................ 6 1.4 Prefix codes for integers...................... 19 1.5 Encoders and...
1 nondeterministic graph (2008)
Panu Chaichanavong, Brian Marcus
• Constrained systems and finite-state encoders • Block-decodable encoder and its relatives • Sets of principal states • Complexity of determining the optimal rate
Asymptotics of Input-Constrained Binary Symmetric Channel Capacity (2008)
We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set....
1995 Plenary Lecture Symbolic Dynamics and Coding Applications (2007)
This article is a summary of the plenary lecture that I gave at the 1995
Variable Length Codes and Finite Automata (2007)
Marie-pierre Béal, Jean Berstel, Brian Marcus, Dominique Perrin, Christophe Reutenauer
The aim of this chapter is to present, in appropriate perspective, some selected new progress in the theory of variable length codes. The emphasis will be on practical aspects. The chapter is of a...
Derivatives of Entropy Rate in Special Families of Hidden Markov Chains (2007)
Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Zuk, et. al. [16, 17] showed how, in principle, one can explicitly compute the...
Asymptotics of Noisy Constrained Channel Capacity (2007)
In this paper, we generalize a result in [17] and derive an asymptotic formula for the entropy rate of a hidden Markov chain, observed when a Markov chain passes through a binary symmetric channel....
Derivatives of Entropy Rate in Special Families of Hidden Markov Chains (2006)
Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how, in principle, one can explicitly compute the...
Analyticity of Entropy Rate of Hidden Markov Chains (2005)
We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine...
Tradeoff Function f for Finite-Type Constraints (2004)
Lei Poo, Panu Chaichanavong, Brian Marcus
• Given an insertion rate, find the maximum possible code rate. • Given an insertion rate, find a set of unconstrained positions that (nearly) achieve the maximum code rate. Outline:
Lei Poo, Panu Chaichanavong, Brian Marcus, Example [van Wijngaarden
Constrained Code: transforms data into constrained sequences that are suitable for the channel Error-Correcting Code (ECC): transforms data into sequences with large distance
Art of Constructing Low-complexity Encoders/Decoders for Constrained Block Codes (2001)
Dharmendra Modha, Brian Marcus
A rate p : q block encoder is a dataword-to-codeword assignment from 2 p p-bit datawords to 2 p q-bit codewords, and the corresponding block decoder is the inverse of the encoder. When designing...
Coding tradeoffs for high-density holographic data storage (1999)
Geoffrey W. Burr, Brian Marcus
We present an initial experimental evaluation of coding and signal processing tradeoffs in high–density holographic data storage. Block–based and low–pass modulation codes, predistortion of...
Optimizing the holographic digital data storage channel (1998)
Geoffrey W. Burr, Jonathan Ashley, Brian Marcus, C. Michael Jefferson, John A. Hoffnagle, Hans Coufal
Holographic storage has the potential to become a digital data storage technology with fast readout and high density. Computer users have come to expect, however, that data retrieved from their...
Resolving Markov chains onto Bernoulli shifts (1998)
The Erwin, Schrodinger International Boltzmanngasse, Brian Marcus, Brian Marcus, Selim Tuncel, Selim Tuncel
this paper, we will completely answer the following questions for an arbitrary Markov chain and a Bernoulli shift. (1) Does the Markov chain eventually factor onto the Bernoulli shift by...
Modulation coding for pixel–matched holographic data storage (1997)
Geoffrey W. Burr, Jonathan Ashley, Hans Coufal, Robert K. Grygier, John A. Hoffnagle, C. Michael Jefferson, ...
We describe a digital holographic storage system for the study of noise sources and the evaluation of modulation and error-correction codes. A precision zoom lens and Fourier transform optics provide...
The Efficiency of Information in Investment (1996)
Elza Erkip, Elza Erkip, Thomas M. Cover, John T. Gill, Brian Marcus
We investigate how the description of a correlated information V improves the investment in the stock market X. The objective is to maximize the growth rate of wealth in repeated investments. We find...
Symbolic Dynamics and Connections to Coding Theory, Automata Theory and System Theory (1995)
this article, we give an introduction to symbolic dynamics and then discuss some common themes in coding theory, automata theory and system theory. Although these subjects have grown up somewhat...