On the reliability exponent of the exponential timing channel

We determine the reliability exponent E(R) of the Anantharam-Verdu (see ibid., vol.42, p.4-18, Jan.1996) exponential server timing channel with service rate /spl mu/ for all rates R between a critical rate R/sub c/ = (/spl mu//4) log 2 and the channel capacity C = e/sup -1//spl mu/. For rates between 0 and R/sub c/, we provide a random-coding lower bound E/sub r/(R) and a sphere-packing upper bound E/sub sp/(R) on E(R). We also determine that the cutoff rate R/sub 0/ for this channel equals /spl mu//4, thus answering a question posed by Sundaresan and Verdu (see ibid., vol.46, p.705-9, Mar. 2000). An interesting aspect of our results is that the lower bound E/sub r/ (R) for the reliability exponent of the timing channel coincides with Wyner's reliability exponent for the photon-counting channel with no dark current and with peak power constraint it. Whether the reliability exponents of the two channels are actually equal everywhere remains open. This shows that the exponential server timing channel is at least as reliable as this type of a photon-counting channel for all rates.