Author | Wolfowitz, Jacob. author |
---|---|
Title | Coding Theorems of Information Theory [electronic resource] / by Jacob Wolfowitz |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1978 |
Edition | Third Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-66822-7 |
Descript | XII, 176 p. online resource |
1. Heuristic Introduction to the Discrete Memoryless Channel -- 2. Combinatorial Preliminaries -- 2.1. Generated sequences -- 2.2. Properties of the entropy function -- Remarks -- 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 -- Remarks -- 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 determined -- 4.7. Proof of Theorem 4.6.4 -- 4.8. The d.m.c. with feedback -- Remarks -- 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 -- Remarks -- 6. Channels with Arbitrarily Varying Channel Probability Functions -- 6.1. Introduction -- 6.2. Necessary and sufficient conditions for a positive rate of transmission -- 6.3. Remarks on the capacity of an arbitrarily varying channel -- 6.4. The capacity C of an arbitrarily varying channel when b = 2 -- 6.5. Certain results for the general arbitrarily varying channel -- Remarks -- 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 -- 7.8. Strong converses -- 7.9. The strong converse for the d.m.c. revisited -- Remarks -- 8. The Semi-Continuous Memoryless Channel -- 8.1. Introduction -- 8.2. A coding theorem and its strong converse -- 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 -- Remarks -- 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. Fundamentals of Rate Distortion Theory -- 11.1. Introduction -- 11.2. The approximation theorem -- 11.3. Converse of the approximation theorem -- 11.4. Summary of the previous results -- 11.5. The rate distortion function when side information is available -- Remarks -- 12. Source Coding -- 12.1. Separate coding to span the product of two spaces -- 12.2. Source coding with side information at the decoder -- 12.3. Encoding assisted by a common channel -- Remarks -- 13. Source Coding and Rate Distortion -- 13.1. The problem of Section 12.3 for rate distortion -- 13.2. The rate distortion function for source coding with side information at the decoder -- 14. Multiple Access Channels -- 14.1. Description of the problem -- 14.2. A coding theorem -- 14.3. Converse of the coding theorem -- 14.4. Miscellaneous remarks -- 15. Degraded Broadcast Channels -- 15.1. Formulation of the problem -- 15.2. A coding theorem -- 15.3. Beginning of the proof of the strong converse -- 15.4. Proof of the weak converse -- 15.5. Miscellaneous remarks -- References