Errorless codes for over-loaded synchronous CDMA systems and evaluation of channel capacity bounds

In this paper we introduce a new class of codes for over-loaded synchronous wireless and optical CDMA systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of an overloaded CDMA are derived that can predict the existence of such overloaded codes. Although a high percentage of the overloading factor degrades the system performance in noisy channels, simulation results show that this degradation is not significant.