On the reliability exponent of the exponential timing channel

Anantharam. and Verdu (1996) introduced the exponential server timing channel (ETC) and determined that its capacity equals e^-1μ nats/sec. More recently, Sundaresan and Verdu (2000) considered sequential decoding for this channel and found that its cutoff rate R₀ is at least e^-1μ/2. We show that R₀=μ/4. We also determine the reliability exponent E(R) of the ETC for all rates between a "critical" rate R_c=(μ/4) ln 2 and the channel capacity C=e^-1μ. We show that, for R≥R_c, E(R) coincides with the reliability exponent for the ideal photon channel (IPC).