Codes for data synchronization with timing

This paper investigates the design and analysis of data synchronization codes whose decoders have the property that, in addition to reestablishing correct decoding after encoded data is lost or afflicted with errors, they produce the original time index of each decoded data symbol modulo some integer T. The motivation for such data synchronization with timing is that in many situations where data must be encoded, it is not sufficient for the decoder to present a sequence of correct data symbols. Instead, the user also needs to know the position in the original source sequence of the symbols being presented. With this goal in mind, periodic prefix-synchronized (PPS) codes are introduced and analyzed on the basis of their synchronization delay D, rate R, and timing span T. Introduced are two specific PPS designs called natural marker and cascaded codes. A principal result is that when coding binary data with rate R, the largest possible timing span attainable with PPS codes grows exponentially with delay D, with exponent D(1-R). Thus, a large timing span can be attained with little redundancy and moderate values of delay.