Parallel algorithms for multi-indexed recurrence relations with applications to DPCM image compression

Summary form only given. DPCM decoding is essentially the computation of a 2-indexed scalar recurrence relation; the two indices are: the row and column positions of the pixels. Although several logarithmic-time parallel algorithms for solving 1-indexed recurrence relations have been designed, no work has been reported on multi-indexed recurrence relations. Considering the importance of fast DPCM decoding of imagery, parallel algorithms for solving multi-indexed recurrence relations merit serious study. We designed novel parallel algorithms for solving 2-indexed recurrence relations, and identified the parallel architectures best suited for them. We developed three approaches: index sequencing, index decoupling, and dimension shifting. To solve a 2-indexed relation in DPCM decoding of an n×n image, index sequencing breaks down the relation into a sequence of n 1-indexed scalar recurrence relations that must be solved one after another. Each relation is then solved by a parallel O(nlogn) time algorithm on an n-processor hypercube or partitionable bus. Thus, the n equations take O(nlogn) time on n processors. Index decoupling, applicable in a common case of DPCM, breaks the 2-indexed relation into n independent 1-indexed recurrence relations, which are then solved simultaneously in O(logn) parallel time, using n² processors configured as a hypercube or a mesh of partitionable buses