Frame sync acquisition for biorthogonally coded data

Abstract

The paper analyzes the optimum frame-synchronization problem for biorthogonally coded data received over the additive white Gaussian noise (AWGN) channel and decoded prior to sync acquisition. In deriving the optimum frame-sync algorithm, the discussion is restricted to the case in which each frame contains F complete code words, including a frame-sync prefix of P complete code words. The k-bit source words and k-bit decoded words are regarded as super symbols from an alphabet of binary k-tuples. The biorthogonal encoder, the AWGN channel, and the decoder are lumped into a super symbol channel whose characteristics determine the form of the optimum frame-sync decision rule. A union-bound approach is used to provide a quantitative measure of the probability of false synchronization for the algorithm derived.