The synchronization of short packets

The energy associated with synchronization becomes very significant when the total number of bits in a message is short. Short packets, i.e., small codes, also prevent a communications system from operating anywhere near channel capacity, even if perfect, zero energy synchronization were available. Since the power associated with synchronization is best measured as a fraction of the power required to send the information, the author begins by presenting a numerical evaluation of the sphere packing bound for the Gaussian channel. This bound places a lower limit on the energy per information bit as a function of the required error rate and block length. The author then goes on to present a maximum likelihood algorithm for estimating the parameters of a polynomially drifting sine wave in the presence of Gaussian noise