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Group synchronization systems with digital feedback are studied, which are particularly applicable for PCM systems. Group synchronization is used to determine the time origin of a sequence of binary signals by finding a specified deterministic pattern from a randomly modulated binary sequence. A statistical analysis is made on the recovery process of synchronization, which is a discrete-time random process with finite-state transitions. A new system with faster recovery characteristics is presented, and an optimal framing pattern is shown. Considerations on the minimization of the recovery time and on the improvement of the stability of synchronism are also made. Experimental results obtained by a recovery process simulator are shown together with the theoretical results.