Cubic congruence codes used in optical two-dimensional codes to increase capacity of optical codes and analysis of its performance

Abstract

In this paper, we develop quadratic congruence codes (QCC) to cubic congruence codes (CCC), propose and analyze a new FUlTS two-dimensional (2-D) code by using the QCC and the CCC, named as the QCC/CCC 2-D codes. In contrast to the conventional QCC-based I-D and QCC-based FUlTS 2-D optical codes, our analysis indicates that the performance and the codes capacity of the CCC-based I-D and CCC-based FUlTS 2-D codes can be improved effectively at the same condition, respectively. These results show that the designed codes are feasible, these codes can support more users in optical code division multiple access (OCDMA).number of active users with BER performance increasing. To solve this problem, we firstly introduce the theory of cubic congruence codes (CCC) [8], develop the QCC to this CCC, and construct a new FH/TS-based 2-D DOC using the CCC and QCC, which is named as the QCC/CCC 2-D codes.The rest of this paper is organized as follows. Section II contains the basic principle and construction ofthe CCC. The QCC-and CCC-based FH/TS 2-D codes are proposed and designed. In Section III, the performance of the QCC/CCC-based FH/TS codes is analyzed and compared to the previous codes. Section IV concludes this work.