Frame Sync Acquisition for Biorthogonally Coded Data

Abstract

The optimum procedure for locating a sync word periodically inserted in uncoded binary data received over a binary symmetric channel is based on the Hamming or bit distance metric. This paper addresses the corresponding frame sync problem for biorthogonally coded data transmitted over the additive white Gaussian noise channel. For conceptual convenience, the k-bit words from the decoder output are treated as "super symbols" from an alphabet of dimension 2ᵏ. It is argued that the optimum sync word search over the decoded data stream is based on a super symbol distance rule matched to the properties of the biorthogonally coded transmissions over the noisy channel. An optimum frame sync acquisition algorithm based on this distance rule is formulated, and its performance is investigated. As an example, the performance of this optimum frame sync algorithm is contrasted analytically with that of a Hamming distance algorithm operating on decoded (32, 6) biorthogonal data, a case of interest to some recent unmanned American space missions.