On the Effect of Timing Errors in Run Length Codes

Many redundancy removal algorithms employ some sort of run length code. Blocks of timing words are coded with synchronization words inserted between blocks. The probability of incorrectly reconstructing a sample because of a channel error in the timing data is a monotonically nondecreasing function of time since the last synchronization word. In this paper we compute the "probability that the accumulated magnitude of timing errors equal zero" as a function of time since the last synchronization word for a zero-order predictor (ZOP). The result is valid for any data source that can be modeled by a first-order Markov chain and any digital channel that can be modeled by a channel transition matrix. An example is presented.