Codes, Systems, and Graphical Models

Front Cover
Brian Marcus, Joachim Rosenthal
Springer Science & Business Media, Mar 1, 2001 - Computers - 513 pages
Coding theory, system theory, and symbolic dynamics have much in common. Among the central themes in each of these subjects are the construction of state space representations, understanding of fundamental structural properties of sequence spaces, construction of input/output systems, and understanding the special role played by algebraic structure. A major new theme in this area of research is that of codes and systems based on graphical models. This volume contains survey and research articles from leading researchers at the interface of these subjects.
 

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Contents

AN INTRODUCTION TO THE ANALYSIS OF ITERATIVE CODING SYSTEMS
1
CONNECTIONS BETWEEN LINEAR SYSTEMS AND CONVOLUTIONAL CODES
39
MULTIDIMENSIONAL SYMBOLIC DYNAMICAL SYSTEMS
67
LINEARCONGRUENCE CONSTRUCTIONS OF LOWDENSITY PARITYCHECK CODES
83
ON THE EFFECTIVE WEIGHTS OF PSEUDOCODEWORDS FOR CODES DEFINED ON GRAPHS WITH CYCLES
101
EVALUATION OF GALLAGER CODES FOR SHORT BLOCK LENGTH AND HIGH RATE APPLICATIONS
113
MILDLY NONLINEAR CODES
135
CAPACITYACHIEVING SEQUENCES
153
RECURSIVE CONSTRUCTION OF GROBNER BASES FOR THE SOLUTION OF POLYNOMIAL CONGRUENCES
299
ON ITERATIVE DECODING OF CYCLE CODES OF GRAPHS
311
SOME BASIC RESULTS
327
SYMBOLIC DYNAMICS AND CONVOLUTIONAL CODES
347
LINEAR CODES AND THEIR DUALS OVER ARTINIAN RINGS
361
UNIT MEMORY CONVOLUTIONAL CODES WITH MAXIMUM DISTANCE
381
BASIC PROPERTIES OF MULTIDIMENSIONAL CONVOLUTIONAL CODES
397
LENGTH DISTRIBUTIONS AND REGULAR SEQUENCES
415

A GENERALIZATION OF TRELLIS AND FACTOR GRAPH
167
BSC THRESHOLDS FOR CODE ENSEMBLES BASED ON TYPICAL PAIRS DECODING
195
PROPERTIES OF THE TAILBITING BCJR DECODER
211
ITERATIVE DECODING OF TAILBITING TRELLISES AND CONNECTIONS WITH SYMBOLIC DYNAMICS
239
ALGORITHMS FOR DECODING AND INTERPOLATION
265
AN ALGEBRAIC DESCRIPTION OF ITERATIVE DECODING SCHEMES
283
HANDELMANS THEOREM ON POLYNOMIALS WITH POSITIVE MULTIPLES
439
TOPOLOGICAL DYNAMICS OF CELLULAR AUTOMATA
447
A SPANNING TREE INVARIANT FOR MARKOV SHIFTS
487
LIST OF WORKSHOP PARTICIPANTS
499
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