  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 a binary over-loaded CDMA are derived that can predict the
existence of such over-loaded codes. We also propose a simplified maximum
likelihood method for decoding these types of over-loaded codes. Although a
high percentage of the over-loading factor degrades the system performance in
noisy channels, simulation results show that this degradation is not
significant. More importantly, for moderate values of Eb/N0 (in the range of
6-10 dB) or higher, the proposed codes perform much better than the binary
Welch bound equality sequences.
