On the Zero-Rate Error Exponent of the Exponential-Server Timing Channel

We prove that the zero-rate error exponent of the exponential-server timing channel is at least μ/2, where 1/μ is the mean service time. This proves that at low data rates, the timing channel is strictly more reliable than the related Poisson channel with peak intensity μ and zero dark current. This answers a question recently posed by Arikan, who proved that the timing channel’s reliability function is at least as large as the Poisson channel’s at all rates, and that the two reliability functions coincide at high rates. Our proofs provide insight into the construction of good codes for the timing channel by revealing a useful distance metric between codewords.