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/sup -1//spl mu/ nats/sec. More recently, Sundaresan and Verdu (2000) considered sequential decoding for this channel and found that its cutoff rate R/sub 0/ is at least e/sup -1//spl mu//2. We show that R/sub 0/=/spl mu//4. We also determine the reliability exponent E(R) of the ETC for all rates between a "critical" rate R/sub c/=(/spl mu//4) ln 2 and the channel capacity C=e/sup -1//spl mu/. We show that, for R/spl ges/R/sub c/, E(R) coincides with the reliability exponent for the ideal photon channel (IPC).