Coding Theorems of Information Theory

Coding Theorems of Information Theory by Jacob Wolfowitz.

The imminent exhaustion of the first printing of this monograph and the kind willingness of the publishers have presented me with the opportunity to correct a few minor misprints and to make a number of additions to the first edition. Some of these additions are in the form of remarks scattered thro...

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Bibliographic Details
Main Author: Wolfowitz, Jacob (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1964.
Edition:2nd ed. 1964.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics ; 31
Springer eBook Collection.
Subjects:
Coding theory.
Information theory.
Mathematics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1. Heuristic Introduction to the Discrete Memoryless Channel
  • 2. Combinatorial Preliminaries.
  • 2.1. Generated sequences
  • 2.2. Properties of the entropy function
  • 3. The Discrete Memoryless Channel
  • 3.1. Description of the channel
  • 3.2. A coding theorem
  • 3.3. The strong converse
  • 3.4. Strong converse for the binary symmetric channel
  • 3.5. The finite-state channel with state calculable by both sender and receiver
  • 3.6. The finite-state channel with state calculable only by the sender
  • 4. Compound Channels
  • 4.1. Introduction
  • 4.2. The canonical channel
  • 4.3. A coding theorem
  • 4.4. Strong converse
  • 4.5. Compound d.m.c. with c.p.f. known only to the receiver or only to the sender
  • 4.6. Channels where the c.p.f. for each letter is stochastically deter-mined
  • 4.7. Proof of Theorem 4.6 4
  • 4.8. The d.m.c. with feedback
  • 4.9. Strong converse for the d.m.c. with feedback
  • 5. The Discrete Finite-Memory Channel.
  • 5.1. The discrete channel
  • 5.2. The discrete finite-memory channel
  • 5.3. The coding theorem for the d.f.m.c
  • 5.4. Strong converse of the coding theorem for the d.f.m.c
  • 5.5. Rapidity of approach to C in the d.f.m.c
  • 5.6. Discussion of the d.f.m.c
  • 6. Discrete Channels with a Past History.
  • 6.1. Preliminary discussion
  • 6.2. Channels with a past history
  • 6.3. Applicability of the coding theorems of Section 7.2 to channels with a past history
  • 6.4. A channel with infinite duration of memory of previously transmitted letters
  • 6.5. A channel with infinite duration of memory of previously received letters
  • 6.6. Indecomposable channels
  • 6.7. The power of the memory
  • 7. General Discrete Channels
  • 7.1. Alternative description of the general discrete channel
  • 7.2. The method of maximal codes
  • 7.3. The method of random codes
  • 7.4. Weak converses
  • 7.5. Digression on the d.m.c
  • 7.6. Discussion of the foregoing
  • 7.7. Channels without a capacity
  • 8. The Semi-Continuous Memoryless Channel
  • 8.1. Introduction
  • 8.2. Strong converse of the coding theorem for the s.c.m.c
  • 8.3. Proof of Lemma 8.2.1
  • 8.4. The strong converse with (math) in the exponent
  • 9. Continuous Channels with Additive Gaussian Noise.
  • 9.1. A continuous memoryless channel with additive Gaussian noise
  • 9.2. Message sequences within a suitable sphere
  • 9.3. Message sequences on the periphery of the sphere or within a shell adjacent to the boundary
  • 9.4. Another proof of Theorems 9.2.1 and 9.2.2
  • 10. Mathematical Miscellanea
  • 10.1. Introduction
  • 10.2. The asymptotic equipartition property
  • 10.3. Admissibility of an ergodic input for a discrete finite-memory channel
  • 11. Group Codes. Sequential Decoding.
  • 11.1. Group Codes
  • 11.2. Canonical form of the matrix M
  • 11.3. Sliding parity check codes
  • 11.4. Sequential decoding
  • References
  • List of Channels Studied or Mentioned.

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