Distributed Hypothesis Testing over Noisy Broadcast Channels
This paper studies binary hypothesis testing with a single sensor that communicates with two decision centers over a memoryless broadcast channel. The main focus lies on the tradeoff between the two type-II error exponents achievable at the two decision centers. In our proposed scheme, we can partia...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Information |
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| Online Access: | https://www.mdpi.com/2078-2489/12/7/268 |
| _version_ | 1827600961581875200 |
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| author | Sadaf Salehkalaibar Michèle Wigger |
| author_facet | Sadaf Salehkalaibar Michèle Wigger |
| author_sort | Sadaf Salehkalaibar |
| collection | DOAJ |
| description | This paper studies binary hypothesis testing with a single sensor that communicates with two decision centers over a memoryless broadcast channel. The main focus lies on the tradeoff between the two type-II error exponents achievable at the two decision centers. In our proposed scheme, we can partially mitigate this tradeoff when the transmitter has a probability larger than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> to distinguish the alternate hypotheses at the decision centers, i.e., the hypotheses under which the decision centers wish to maximize their error exponents. In the cases where these hypotheses cannot be distinguished at the transmitter (because both decision centers have the same alternative hypothesis or because the transmitter’s observations have the same marginal distribution under both hypotheses), our scheme shows an important tradeoff between the two exponents. The results in this paper thus reinforce the previous conclusions drawn for a setup where communication is over a common noiseless link. Compared to such a noiseless scenario, here, however, we observe that even when the transmitter can distinguish the two hypotheses, a small exponent tradeoff can persist, simply because the noise in the channel prevents the transmitter to perfectly describe its guess of the hypothesis to the two decision centers. |
| first_indexed | 2024-03-09T04:46:28Z |
| format | Article |
| id | doaj.art-fb65bcbbbbb74c3689209d4ba694b5f3 |
| institution | Directory Open Access Journal |
| issn | 2078-2489 |
| language | English |
| last_indexed | 2024-03-09T04:46:28Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Information |
| spelling | doaj.art-fb65bcbbbbb74c3689209d4ba694b5f32023-12-03T13:15:57ZengMDPI AGInformation2078-24892021-06-0112726810.3390/info12070268Distributed Hypothesis Testing over Noisy Broadcast ChannelsSadaf Salehkalaibar0Michèle Wigger1Department of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran 1433957131, IranLTCI, Telecom Paris, IP Paris, 91120 Paris, FranceThis paper studies binary hypothesis testing with a single sensor that communicates with two decision centers over a memoryless broadcast channel. The main focus lies on the tradeoff between the two type-II error exponents achievable at the two decision centers. In our proposed scheme, we can partially mitigate this tradeoff when the transmitter has a probability larger than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> to distinguish the alternate hypotheses at the decision centers, i.e., the hypotheses under which the decision centers wish to maximize their error exponents. In the cases where these hypotheses cannot be distinguished at the transmitter (because both decision centers have the same alternative hypothesis or because the transmitter’s observations have the same marginal distribution under both hypotheses), our scheme shows an important tradeoff between the two exponents. The results in this paper thus reinforce the previous conclusions drawn for a setup where communication is over a common noiseless link. Compared to such a noiseless scenario, here, however, we observe that even when the transmitter can distinguish the two hypotheses, a small exponent tradeoff can persist, simply because the noise in the channel prevents the transmitter to perfectly describe its guess of the hypothesis to the two decision centers.https://www.mdpi.com/2078-2489/12/7/268hypothesis testingbroadcast channelerror exponents |
| spellingShingle | Sadaf Salehkalaibar Michèle Wigger Distributed Hypothesis Testing over Noisy Broadcast Channels Information hypothesis testing broadcast channel error exponents |
| title | Distributed Hypothesis Testing over Noisy Broadcast Channels |
| title_full | Distributed Hypothesis Testing over Noisy Broadcast Channels |
| title_fullStr | Distributed Hypothesis Testing over Noisy Broadcast Channels |
| title_full_unstemmed | Distributed Hypothesis Testing over Noisy Broadcast Channels |
| title_short | Distributed Hypothesis Testing over Noisy Broadcast Channels |
| title_sort | distributed hypothesis testing over noisy broadcast channels |
| topic | hypothesis testing broadcast channel error exponents |
| url | https://www.mdpi.com/2078-2489/12/7/268 |
| work_keys_str_mv | AT sadafsalehkalaibar distributedhypothesistestingovernoisybroadcastchannels AT michelewigger distributedhypothesistestingovernoisybroadcastchannels |