Secrecy and Error Exponents of k-Transmitter Multiple Access Wire-tap Channel

Abstract

This paper strengthens the known secrecy results for a k-transmitter multiple access channel (MAC) with an external eavesdropper from weak to strong without any rate loss on the achievable region. More specifically, the results are derived under a strong secrecy metric defined by the information leakage to the eavesdropper, instead of the weaker secrecy criteria defined by the information leakage rate or the (average) variation distance. To this end, different approaches are taken to analyze the information leakage and the decoding error probability. Interestingly, both the secrecy and error exponents could be characterized by the (conditional) Rényi mutual information in a concise form. Thus, the region is guaranteed with both information leakage and decoding error probability decreasing exponentially in the code length. Our technique for strong secrecy analysis reflects the resolvability for the k-transmitter MAC; while our error exponent could be regarded as a generalization of Gallager’s error exponent.