Optical Orthogonal Codes

In general an OOC family derived from {0,1} sequences is characterized by parameters ( $M, F, K, \lambda_a, \lambda_c$) [4,5]. Each code family consist of M distinct codewords C={C_i} of length Fand code weight K. The code weight K is equal to number of ones in the code words. The $\lambda_a$ and $\lambda_c$ are out of phase autocorrelation and crosscorrelation values respectively. The above implies that autocorrelation for a code family will obey the following equation

$$\begin{array}{l} \displaystyle \sum_{n=1}^F C_{jn}C_{j(n+m)} ... ... C_{jn} \in C, \hspace{0.05in} 1 \leq m \leq (F-1). \end{array}$$ (1)

Similarly, the crosscorrelation will follow the following equation

$$\begin{array}{l} \displaystyle \sum_{n=1}^{F} C_{in} C_{j(n+m... ...q C_{j} \in C, \hspace{0.05in} 1 \leq m \leq (F-1). \end{array}$$ (2)

The CDMA codes are generated by encoders. A passive CDMA encoder splits a short optical pulse and passes them through different delay lines before merging them together. In this manner a bit is converted to a code sequence. The encoding can also be done by directly modulating the optical source by code sequence. This is termed as active encoding. For decoding, the code sequence is split into multiple copies and passed through different delay lines in such a way that one pulse from each of the split path adds when the delayed signals are combined. This acts as correlator [6]