Extended Reed-Solomon Codes for Optical CDMA

In this paper, the extended Reed-Solomon codes are modified to construct a new family of 2-D codes for asynchronous optical code-division multiple access (O-CDMA). In addition of having expanded and asymptotically optimal cardinality, these 2-D asynchronous optical codes can be partitioned into multiple tree structures of code subsets, in which code cardinality is a function of the (periodic) cross-correlation value assigned to the subset. The performance of these 2-D optical codes is analyzed and compared with that of the multilevel prime codes. Our results show that the unique partition property of the new optical codes supports a trade-off between code cardinality and performance for meeting different system requirements, such as user capacity and throughput. In addition, the multiple tree structures of the new codes potentially support applications that require rapid switching of many codewords, such as in O-CDMA-network gateway or in strategic environments where code obscurity is essential.