Distributed Hypothesis Testing Based on Unequal-Error Protection Codes

Coding and testing schemes for binary hypothesis testing over noisy networks are proposed and their corresponding type-II error exponents are derived. When communication is over a discrete memoryless channel (DMC), our scheme combines Shimokawa-Han-Amari's hypothesis testing scheme with Borade-Nakiboglu-Zheng's unequal error protection (UEP) for channel coding where source and channel codewords are simultaneously decoded. The resulting exponent is optimal for the newly introduced class of generalized testing against conditional independence. When communication is over a multi-access channel (MAC), our scheme combines hybrid coding with UEP. The resulting error exponent over the MAC is optimal in the case of generalized testing against conditional independence with independent observations at the two sensors when the MAC decomposes into two individual DMCs. In this case, separate source-channel coding is sufficient and no UEP is required. This same conclusion holds also under arbitrarily correlated sensor observations when testing is against independence.