List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel
In this paper, we determine the capacity of the Gaussian arbitrarily-varying channel with a (possibly stochastic) encoder and a deterministic list-decoder under the average probability of error criterion. We assume that both the legitimate and the adversarial signals are restricted by their power co...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-06-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/21/6/575 |
| _version_ | 1817995691525406720 |
|---|---|
| author | Fatemeh Hosseinigoki Oliver Kosut |
| author_facet | Fatemeh Hosseinigoki Oliver Kosut |
| author_sort | Fatemeh Hosseinigoki |
| collection | DOAJ |
| description | In this paper, we determine the capacity of the Gaussian arbitrarily-varying channel with a (possibly stochastic) encoder and a deterministic list-decoder under the average probability of error criterion. We assume that both the legitimate and the adversarial signals are restricted by their power constraints. We also assume that there is no path between the adversary and the legitimate user but the adversary knows the legitimate user’s code. We show that for any list size <i>L</i>, the capacity is equivalent to the capacity of a point-to-point Gaussian channel with noise variance increased by the adversary power, if the adversary has less power than <i>L</i> times the transmitter power; otherwise, the capacity is zero. In the converse proof, we show that if the adversary has enough power, then the decoder can be confounded by the adversarial superposition of several codewords while satisfying its power constraint with positive probability. The achievability proof benefits from a novel variant of the Csiszár-Narayan method for the arbitrarily-varying channel. |
| first_indexed | 2024-04-14T02:09:59Z |
| format | Article |
| id | doaj.art-1aada6752fb24590a369746f755649d5 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T02:09:59Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-1aada6752fb24590a369746f755649d52022-12-22T02:18:27ZengMDPI AGEntropy1099-43002019-06-0121657510.3390/e21060575e21060575List-Decoding Capacity of the Gaussian Arbitrarily-Varying ChannelFatemeh Hosseinigoki0Oliver Kosut1School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USASchool of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USAIn this paper, we determine the capacity of the Gaussian arbitrarily-varying channel with a (possibly stochastic) encoder and a deterministic list-decoder under the average probability of error criterion. We assume that both the legitimate and the adversarial signals are restricted by their power constraints. We also assume that there is no path between the adversary and the legitimate user but the adversary knows the legitimate user’s code. We show that for any list size <i>L</i>, the capacity is equivalent to the capacity of a point-to-point Gaussian channel with noise variance increased by the adversary power, if the adversary has less power than <i>L</i> times the transmitter power; otherwise, the capacity is zero. In the converse proof, we show that if the adversary has enough power, then the decoder can be confounded by the adversarial superposition of several codewords while satisfying its power constraint with positive probability. The achievability proof benefits from a novel variant of the Csiszár-Narayan method for the arbitrarily-varying channel.https://www.mdpi.com/1099-4300/21/6/575gaussian arbitrarily-varying channellist-decodingstochastic encodercapacity |
| spellingShingle | Fatemeh Hosseinigoki Oliver Kosut List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel Entropy gaussian arbitrarily-varying channel list-decoding stochastic encoder capacity |
| title | List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel |
| title_full | List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel |
| title_fullStr | List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel |
| title_full_unstemmed | List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel |
| title_short | List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel |
| title_sort | list decoding capacity of the gaussian arbitrarily varying channel |
| topic | gaussian arbitrarily-varying channel list-decoding stochastic encoder capacity |
| url | https://www.mdpi.com/1099-4300/21/6/575 |
| work_keys_str_mv | AT fatemehhosseinigoki listdecodingcapacityofthegaussianarbitrarilyvaryingchannel AT oliverkosut listdecodingcapacityofthegaussianarbitrarilyvaryingchannel |