The capacity of channels with feedback
In this paper, we introduce a general framework for treating channels with memory and feedback. First, we prove a general feedback channel coding theorem based on Massey's concept of directed information. Second, we present coding results for Markov channels. This requires determining appropria...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Institute of Electrical and Electronics Engineers
2010
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/53579 https://orcid.org/0000-0002-8619-1295 |
| _version_ | 1811083250288820224 |
|---|---|
| author | Mitter, Sanjoy K. Tatikonda, Sekhar |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Mitter, Sanjoy K. Tatikonda, Sekhar |
| author_sort | Mitter, Sanjoy K. |
| collection | MIT |
| description | In this paper, we introduce a general framework for treating channels with memory and feedback. First, we prove a general feedback channel coding theorem based on Massey's concept of directed information. Second, we present coding results for Markov channels. This requires determining appropriate sufficient statistics at the encoder and decoder. We give a recursive characterization of these sufficient statistics. Third, a dynamic programming framework for computing the capacity of Markov channels is presented. Fourth, it is shown that the average cost optimality equation (ACOE) can be viewed as an implicit single-letter characterization of the capacity. Fifth, scenarios with simple sufficient statistics are described. Sixth, error exponents for channels with feedback are presented. |
| first_indexed | 2024-09-23T12:29:37Z |
| format | Article |
| id | mit-1721.1/53579 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:29:37Z |
| publishDate | 2010 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/535792022-10-01T09:21:04Z The capacity of channels with feedback Mitter, Sanjoy K. Tatikonda, Sekhar Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Mitter, Sanjoy Mitter, Sanjoy K. sufficient statistics feedback dynamic programming directed information Markov channels Capacity In this paper, we introduce a general framework for treating channels with memory and feedback. First, we prove a general feedback channel coding theorem based on Massey's concept of directed information. Second, we present coding results for Markov channels. This requires determining appropriate sufficient statistics at the encoder and decoder. We give a recursive characterization of these sufficient statistics. Third, a dynamic programming framework for computing the capacity of Markov channels is presented. Fourth, it is shown that the average cost optimality equation (ACOE) can be viewed as an implicit single-letter characterization of the capacity. Fifth, scenarios with simple sufficient statistics are described. Sixth, error exponents for channels with feedback are presented. National Science Foundation (Awards CCF-0430922, CCF-0325774, and ECCS-0801549) 2010-04-08T14:15:24Z 2010-04-08T14:15:24Z 2008-12 2007-01 Article http://purl.org/eprint/type/JournalArticle 0018-9448 http://hdl.handle.net/1721.1/53579 Tatikonda, S., and S. Mitter. “The Capacity of Channels With Feedback.” Information Theory, IEEE Transactions on 55.1 (2009): 323-349. © 2009 IEEE https://orcid.org/0000-0002-8619-1295 en_US http://dx.doi.org/10.1109/TIT.2008.2008147 IEEE Transactions on Information Theory Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers IEEE |
| spellingShingle | sufficient statistics feedback dynamic programming directed information Markov channels Capacity Mitter, Sanjoy K. Tatikonda, Sekhar The capacity of channels with feedback |
| title | The capacity of channels with feedback |
| title_full | The capacity of channels with feedback |
| title_fullStr | The capacity of channels with feedback |
| title_full_unstemmed | The capacity of channels with feedback |
| title_short | The capacity of channels with feedback |
| title_sort | capacity of channels with feedback |
| topic | sufficient statistics feedback dynamic programming directed information Markov channels Capacity |
| url | http://hdl.handle.net/1721.1/53579 https://orcid.org/0000-0002-8619-1295 |
| work_keys_str_mv | AT mittersanjoyk thecapacityofchannelswithfeedback AT tatikondasekhar thecapacityofchannelswithfeedback AT mittersanjoyk capacityofchannelswithfeedback AT tatikondasekhar capacityofchannelswithfeedback |