Dual-time-sharing high-order QAM symbol error correction network of mix-select cells connected with bit-transfer lines - some numerical experiments

Abstract

An error correction network that consists of multi-tone delta-sigma (DS) domain mix-select cells connected each other with bit-transfer lines is proposed. The network functions as a factor graph executing min-max belief propagation algorithm with adders (mixers) and min/max selectors operating on multi-tone DS modulated signals and outputting signals in the same form. The network is used repeatedly q/p times for error correction of all decomposed 2^p-QAM sub-symbols of received 2^q-QAM symbols, p<q. Then, the network is considered as a time-sharing processor for the error correction of 2^q-QAM symbols. Each cell of the network processes all elements of several 2^p-dimensional message vectors and passes them to other cells. The one message vector is modulated to one 2^p-tone DS modulated sequence and the one cell processes the 2^p elements of the vector in turn. Then, each cell is considered as a time-sharing processor of the message vector. The former time-sharing error correction and the latter time-sharing message processing are executed in slow and fast time-scales, respectively. Thus, the network is a dual-scale time-sharing system. The network has two advantages. First, the network can be adopted to adaptive QAM communication. Even if modulation order 2^q is changed to 2^q′, the same network operates q′/p times with nothing changed. Secondly, elements of a message vector decrease from 2^q to (q/p)2^p. From results of circuit simulation, it was found that the circulated DS modulation noise in the network did not impair the error correction ability when the bit-transfer lines were long enough.