|M.Sc Student||Ovadia Yakir|
|Subject||On the Reliability Exponent of The Exponential Telephone|
|Department||Department of Electrical Engineering||Supervisor||Dr. Shraga Bross|
A lower bound on the reliability exponent of the memory-less exponential server timing-channel with noiseless feedback is provided. The lower bound depends on whether fixed or random transmission-time, as well as on whether fixed block-length or variable block-length, codes are considered (with block-length denoting the number of recorded departures). In all cases, the encoder makes use of feedback to avoid queuing and to control completely the idling times of the server. Feedback, however, is not used to choose the waiting times. Nevertheless, it is shown that Arikan's random coding lower bound on the reliability exponent, obtained for the one-way exponential server timing channel, is still achievable with fixed transmission-time variable block-length codes , while at low rates a tighter estimate using expurgation is provided . The performance analysis of the various codes is based on Gallager's random and expurgated exponents. Still a specific decoding scheme is suggested, analyzing it gives rise to some results which coincide with those obtained via Gallager's expressions .
On the other hand we show that Arikan's one-way sphere-packing bound for fixed transmission-time codes applies as well to fixed transmission-time codes for the case at hand, even if feedback is used to choose the waiting times .
With the family of random transmission-time variable block-length codes, a lower bound on the zero error capacity is established .
It is observed that, as expected, the families of random transmission-time codes have , in general, better achievable exponents than the fixed transmission-time codes . Moreover, for the families of codes investigated herein, the exponents achievable with variable block-length codes are better than those achievable with fixed block-length ones.