Cross-correlation and system performance of modified prime codes for all-optical CDMA applications

Prime codes are a family of optical address codes that are suitable for opt ical fibre code-division multiple access (CDMA) systems using all-optical p rocessing. However, the code weight omega of a prime code is always fixed t o the maximum number of users N. This means that, once N becomes large (e.g . in a system with many users), the resulting cost and optical power losses of all-optical CDMA encoder/decoder can be high. In turn, this may prevent the use of integrated optics from implementing such encoders and decoders. To effectively solve these problems, we present the modified prime (MPR) c odes for all-optical CDMA systems. It is shown that MPR codes can maintain the fixed omega for a given bit error rate (e.g. 10(-9)) but for any N. We also prove that MPR codes preserve the same cross-correlation constraint as original prime codes. Moreover, the proposed code-design procedure can be extended to construct special MPR codes, such as variable-length MPR codes and nonconstant-weight MPR codes.