A Two-Dimensional Extension of the Mueller & Müller Timing Error Detector

A timing error detector (TED) forms an integral part of feedback symbol timing recovery systems in digital communications. We present here a two-dimensional (2-D) extension of a TED originally developed by Mueller and Müller for multi-level pulse amplitude modulation (PAM) over one-dimensional (1-D) channels. Our detector extracts bidimensional timing information (i.e., bidimensional sampling information) from the output of a noisy channel with bidimensional transfer function and subject to sampling errors. Applications for such a scenario include synchronization in multi-level 2-D bar code systems and synchronization in spatial domain image data-hiding. To our knowledge, our proposal is the first one of its kind for this type of scenario. We provide accurate theoretical expressions of the performance of the proposed scheme, and we verify its applicability by studying a particular case with a minimal set of parameters. The 2-D TED thus obtained is used as the engine of a 2-D phase locked loop (PLL) for timing recovery in that scenario, in which we also show the performance gain obtained by the bidimensional approach with respect to the application of standard 1-D TED

PLL-based synchronization of dither-modulation data hiding

A new approach to synchronization recovery for signals watermarked using the Dither Modulation data hiding scheme is presented. The strategy followed involves the use of a digital phase-locked loop to track the offsets applied by an attacker to the sampling grid of the watermarked signal. The main element in this synchronization loop is the timing error detector which is responsible for generating an error signal, used to update the estimates of the applied offsets. It is shown how a timing error detector which has been used in digital communications may be easily adapted to extract timing information from DM watermarked signals. The performance of the proposed synchronizer is evaluated using the probability of decoding error under different models for the sampling grid offsets. 1