Look-ahead computation: Improving iteration bound in linear recursions

The maximum achievable sampling rate of recursive algorithms is inherently bounded due to the computational latency associated with the loop computation. This recursion or feedback in the algorithms destroys the opportunity to pipeline any recursive loop. In this paper, we introduce a technique of look-ahead computation applicable to any linear recursive algorithm (LRA) to achieve equivalent realizations with reduced iteration period and higher sampling rate. The concurrency created by the use of look-ahead computation can be used to obtain pipelined and/or block implementations. We illustrate the applicability of the look-ahead computation technique to obtain high speed VLSI realizations of linear time-invariant, and time-varying systems. A generalized look-ahead computation technique theorem for arbitrary interleaving is also presented. Finally, it is shown that the iteration period in certain synchronous data flow graphs can also be reduced by the use of look-ahead computation.