Joint estimation of data and timing in the presence of inter-symbol interference

A channel with inter-symbol interference and random perturbations to timing is approximated using a finite-state Markov model. The inter-symbol interference is approximated by a finite-impulse response and the timing perturbations are approximated by a first-order random walk. A Viterbi algorithm is then applied to find the maximum-likelihood sequence of states on this model. The resulting state sequence defines the data sequence and timing trajectory which jointly maximize a likelihood function on the observed signal. This approach provides a means of detecting data with rapidly fluctuating timing perturbations at low signal-to-noise ratio. This is particularly relevant to data storage applications where mechanical fluctuations are translated into timing perturbations. Codes can be incorporated into the detector. The coding gain improves the reliability of both data detection and timing recovery. Codes which can be represented using a reasonably small state machine, such as trellis codes and high rate block parity codes, can be incorporated directly into the finite state model. For iterative decoders a BCJR algorithm can also be applied to this state machine to yield a posteriori probabilities on the data bits.