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 μ for all rates R between a critical rate R_c = (μ/4) log 2 and the channel capacity C = e^-1μ. For rates between 0 and R_c, we provide a random-coding lower bound E_r(R) and a sphere-packing upper bound E_sp(R) on E(R). We also determine that the cutoff rate R₀ for this channel equals μ/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_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