theta (logN) architectures for RNS arithmetic decoding

Decoding in residue-number-system (RNS)-based architectures can be a bottleneck. A high-speed, flexible modulo decoder is an essential computational element to maintain the advantages of RNS. A fast and flexible modulo decoder, based on the Chinese remainder theorem (CRT), is presented. It decodes a set of residues into its equivalent representation in either unsigned magnitude or two's-complement binary number system. Two different architectures are analyzed: the first one uses carry-save adders, and the other uses modified structure carry-save adders. Both architectures are modular and are based on simple cells, which leads to efficient VLSI implementation. The decoder has a time complexity of theta (log N).<>