Abstract
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.
Highlights
Sensor networks are important parts of the future Internet of Things (IoT)
We propose coding and testing schemes for general hypothesis testing over three basic noisy networks: discrete memoryless channel (DMC), multiple-access channel (MAC), and broadcast channels (BC)
For DMCs, we propose a scheme that combines the SHA hypothesis testing scheme in a separate source-channel coding architecture with Borade’s Unequal Error Protection (UEP) [14], [15] coding that specially protects the source-coding message 0
Summary
Sensor networks are important parts of the future Internet of Things (IoT). In these networks, data collected at sensors is transmitted over a wireless medium to remote decision centers, which use this information to decide on one of multiple hypotheses. This problem statement has first been considered for the setup with a single sensor and a single decision center when communication is over a noiseless link of given capacity [1], [2] For this canonical problem, the optimal error exponent has been identified in the special cases of testing against independence [1] and testing against conditional independence. The error exponent region corresponding to this scheme, is built on four competing error exponents at each receiver; two of them coincide with the exponents in the noiseless setup [13]; one of them with Borade’s missed-detection exponent; the fourth corresponds to the event that a decision center wrongly decodes the sensor’s tentative decision in favour of the other hypothesis In this case, the error exponents region achieved by our scheme exhibit only a wek tradeoff between the two exponents. We conclude this introduction with a summary of the main contributions of the paper and remarks on notation
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