On the reliability exponent of the additive exponential noise channel

We study the reliability exponent of the additive exponential noise channel (AENC) in the absence as well as in the presence of noiseless feedback. For rates above the critical rate, the fixed-transmission-time reliability exponent of the AENC is completely determined, while below the critical rate an expurgated exponent is obtained. Using a fixed-block-length code ensemble (with block length denoting the number of recorded departures), we obtain a lower bound on the random-transmission-time reliability exponent of the AENC. Finally, with a variable-block-length code ensemble, a lower bound on the random-transmission-time zero-error capacity of the AENC with noiseless feedback is obtained.