Algorithmic Information Theory: Mathematics of Digital Information Processing / Edition 1

by Peter Seibt

Overview

Shall we be destined to the days of eternity, on holy-days,as well as working days, to be shewing the RELICKS OF LEARNING, as monks do the relicks of their saints – without working one – one single miracle with them? Laurence Sterne, Tristram Shandy This book deals with information processing; so it is far from being a book on information theory (which would be built on description and estimation). The reader will be shown the horse, but not the saddle. At any rate, at the very beginning, there was a series of lectures on “Information theory, through the looking-glass of an algebraist”, and, as years went on, a steady process of teaching and learning made the material evolve into the present form. There still remains an algebraic main theme: algorithms intertwining polynomial algebra and matrix algebra, in the shelter of signal theory. A solid knowledge of elementary arithmetic and Linear Algebra will be the key to a thorough understanding of all the algorithms working in the various bit-stream landscapes we shall encounter. This priority of algebra will be the thesis that we shall defend. More concretely: We shall treat, in five chapters of increasing difficulty, five sensibly different subjects in Discrete Mathem- ics. The firsttwochaptersondatacompaction(losslessdatacompression) and cryptography are on an undergraduate level – the most difficult mathematical prerequisite will be a sound understanding of quotient rings, especially of- nite fields (mostly in characteristic 2).

Product Details

ISBN-13:	9783642069789
Publisher:	Springer Berlin Heidelberg
Publication date:	11/29/2010
Series:	Signals and Communication Technology
Edition description:	Softcover reprint of hardcover 1st ed. 2006
Pages:	443
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Data Compaction.- Cryptography.- Information Theory and Signal Theory: Sampling and Reconstruction.- Error Control Codes.- Data Reduction: Lossy Compression.

Editorial Reviews

From the reviews:

"This book, consisting of five chapters, deals with information processing. … The format of chapters … is very good. … It is very readable and provides a valuable source about information processing. This is a good book on the subject … . it is a welcome addition." (Arjun K. Gupta, Zentralblatt MATH, Vol. 1136 (14), 2008)

From the Publisher