Parallel Algorithms for Message Decomposition

Shang-Hua Teng, Bin Wang

Abstract: We consider the deterministic and random parallel complexity (time and processor) of message decoding: an essential problem in communication systems and translation systems. We present an optimal parallel algorithm to decompose prefix-coded messages and uniquely decipherable-coded messages in O(nP)<math><mtext>O(</mtext><mtext>n</mtext><mtext>P</mtext><mtext>)</mtext></math> time, using O(P) processors (for all P: 1 ⩽ P ⩽ n/log n) deterministically as well as randomly on the weakest version of parallel random access machines in which concurrent read and concurrent write to a cell in the common memory are not allowed. This is done by reducing decoding to parallel finite-state automata simulation and the prefix sums. We also present an optimal parallel simulation algorithm for finite-state automata using new parallel algorithm design techniques: parallel tree contraction. As a consequence, from the complexity point of view as well as from the data compression point of view, uniquely decipherable coding is better than prefix coding.