Sequential frame synchronization over binary symmetrical channel for unequally distributed data symbols

Frame synchronization is a critical task in digital communications receivers as it enables the accurate decoding and recovery of transmitted information. Information transmitted over a wireless channel is represented as bit stream. The bit stream is typically organized into groups of bits which can be of the same or variable length, known as frames, with frames being demarcated prior to transmission by a known bit sequence. The task of the frame synchronizer in the receiver is then to correctly determine frame boundaries, given that the received bit stream is a possibly corrupted version of the transmitted bit stream due to the error-prone nature of the wireless channel. Bearing in mind that the problem of frame synchronization has been studied extensively for wireless communications, where frames have a known, constant length, this thesis examines and seeks to make a contribution to the problem of frame synchronization where frames are of variable, unknown lengths. This is a common occurrence in the transmission of multimedia information and in packet or burst mode communications. Furthermore, a uniform distribution of data symbols is commonly assumed in frame synchronization works as this simplifies analysis. In many practical situations however, this assumption may not hold true. An example is in bit streams generated in video sequences encoded through discrete cosine transform (DCT) and also in more recent video coding standards (H.264). In this work, we therefore propose a novel, optimal frame synchronization metric for transmission over a binary symmetric channel (BSC) with a known, unequal source data symbol distribution, and where frames are of unknown, varying lengths. We thus extend prior studies carried out for the additive White Gaussian noise (AWGN) channel. We also provide a performance evaluation for the derived metric, using simulations and by exact mathematical analysis. In addition, we provide an exact analysis for the performance evaluation of the commonly used hard correlation (HC) metric, in the case where data symbols have a known, unequal distribution, which hitherto has not been made available in literature. We thus compare the performance of our proposed metric with that of the HC metric. Finally, the results of our study are applied to the investigation of cross-layer frame synchronization in the transmission of H.264 video over a Worldwide Interoperability for Microwave Access (WiMAX) system. We thus demonstrate priori knowledge of the source data distribution can be exploited to enhance frame synchronization performance, for the cases where hard decision decoding is desirable