On the suboptimality of linear codes for binary distributed hypothesis testing
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911377673682944 |
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| author | Girish, Adway Cung, Robinson D. H. Telatar, Emre |
| author_facet | Girish, Adway Cung, Robinson D. H. Telatar, Emre |
| contents | We study a binary distributed hypothesis testing problem where two agents observe correlated binary vectors and communicate compressed information at the same rate to a central decision maker. In particular, we study linear compression schemes and show that simple truncation is the best linear scheme in two cases: (1) testing opposite signs of the same magnitude of correlation, and (2) testing for or against independence. We conjecture, supported by numerical evidence, that truncation is the best linear code for testing any correlations of opposite signs. Further, for testing against independence, we also compute classical random coding exponents and show that truncation, and consequently any linear code, is strictly suboptimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10526 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the suboptimality of linear codes for binary distributed hypothesis testing Girish, Adway Cung, Robinson D. H. Telatar, Emre Information Theory Statistics Theory We study a binary distributed hypothesis testing problem where two agents observe correlated binary vectors and communicate compressed information at the same rate to a central decision maker. In particular, we study linear compression schemes and show that simple truncation is the best linear scheme in two cases: (1) testing opposite signs of the same magnitude of correlation, and (2) testing for or against independence. We conjecture, supported by numerical evidence, that truncation is the best linear code for testing any correlations of opposite signs. Further, for testing against independence, we also compute classical random coding exponents and show that truncation, and consequently any linear code, is strictly suboptimal. |
| title | On the suboptimality of linear codes for binary distributed hypothesis testing |
| topic | Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2601.10526 |