|On the Error Exponent of Approximate Sufficient Statistics for M-ary Hypothesis Testing
|Jiachun Pan, Yonglong Li, Vincent Y. F. Tan, National University of Singapore, Singapore; Yonina C. Eldar, Weizmann Institute of Science, Israel
|E.6: Hypothesis Testing II
|Detection and Estimation
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|We consider the problem of detecting one of M signals corrupted with white Gaussian noise. Conventionally, to minimize the probability of error, one uses matched filters to obtain a set of M sufficient statistics. In practice, M may be prohibitively large; this motivates the design and analysis of a reduced set of statistics which we term approximate sufficient statistics. By considering a sequence of sensing matrices that possesses suitable coherence and orthogonality properties, we bound the error exponent of the approximate sufficient statistics and compare it to that of the sufficient statistics. Additionally, we show that lower bound on the error exponent increases linearly for small compression rates.