Distributed Hypothesis Testing Over Discrete Memoryless Channels
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A distributed binary hypothesis testing problem is studied in which multiple helpers transmit their observations to a remote detector over orthogonal discrete memoryless channels. The detector uses the received samples from the helpers along with its own observations to test for the joint distribution of the data. Single-letter inner and outer bounds for the type 2 error exponent (T2EE) is established for the special case of testing against conditional independence (TACI). Specializing this result for the one-helper problem, a single-letter characterization of the optimal T2EE is obtained. For the general hypothesis testing problem, a lower bound on the T2EE is established by using a separation based scheme that performs independent channel coding and hypothesis testing. It is shown that this separation based scheme recovers the optimal T2EE previously obtained when specialized for the case of TACI. Finally, a joint hypothesis testing and channel coding scheme based on hybrid coding is proposed and the T2EE achievable under this scheme is analyzed. In general, this scheme is expected to achieve a better performance compared to the separation based scheme.
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