# A Novel 64 QAM-OFDM Optical Access System Based on Bit Reconstruction
## 2 Theory and Principle  
For the optical access system, the proposed 64 QAM-OFDM optical transmission scheme is shown in Figure 1. In this scheme, channel multiplexing PON based on OFDM technology is adopted, and each ONU occupies a different orthogonal subcarrier. We form a strong correlation signal by reconstructing the information bit and use QAM modulation. On the OLT side, the transmission data are modulated by using OFDM technology. The modulated data is multiplexed to different subcarriers and then broadcast to different ONUs. To enhance the reliability of the data transmission, this paper proposes a novel 64 QAM-OFDM signal generation method through reconstruction in the time domain. The generation of bit reconstruction-based 64 QAM-OFDM optical signals is shown in the \"Bit Reconstruction\" part of Figure 1.  
In our proposed theory, the original data information at the transmitter side is serially transformed into a serial data stream of the same number as the modulation order. According to the modulation order M of the proposed scheme, the original information is divided into data(1,2), data(3,4), data5 and data6, as shown in Figure 1. The bit reconstruction unit consists of two parts, the logical code circuit and the partition mapping unit. The serial raw data stream needs to be grouped two by two before entering the logical code circuit, i.e., data(1,2), data(3,4), data5 and data6, where data(1,2) and data(3,4), are used as the input into the logical code circuit for the relevant coding. The output, which is a two-stage symmetric signal concerning the zero level, will be obtained by adding two unequal binary branches via an adder. This information is combined with the information of data 5 and 6 (not entered into the logical code circuit, but are directly added into the partition mapping unit) to achieve bit reconstruction after the filling bit. We assume that the independent binary data are generated at the transmitter, whose symbol matrix \(P\) can be expressed as:  
\[P= \begin{bmatrix}P_{0,0}&\cdots&P_{0,k-1}\\ \vdots&\ddots&\vdots\\ P_{M-1,0}&\cdots&P_{M-1,k-1}\end{bmatrix}  \tag{1}\]  
Figure 1: Principle of 64 QAM-OFDM optical signal generation based on bit reconstruction. where \(\left\{P_{M,k}\right\}_{M=0}^{M=n}\) denotes the signal generated over \(k\) time intervals. Then the bit reconstruction matrix \(G\) is defined as:  
\[G= \begin{bmatrix}G_{0,0}&\cdots&G_{0,M-1}\\ \vdots&\ddots&\vdots\\ G_{M-1,0}&\cdots&G_{N-1,k-1}\end{bmatrix}  \tag{2}\]  
where \(\left\{G_{N-1,k-1}\right\}\), \(N\in M\) represents the data processing of the corresponding element of the symbol matrix \(P\) by the bit reconstruction matrix \(G\). The initialization matrix \(G\) is an all-in-one matrix. Noticed that the particularity of matrix \(G\) here, if the system modulation format is \(2^{M}-QAMM\), rows \(M-2\) and \(M-1\) of \(G\) are set to 0. Here \(G\) refers to the initialized bit reconstruction matrix \(G_{0}\). In the bit reconstruction section, we can see that the last two groups of the input bit streams after grouping do not enter the logic code circuit for relevant coding but directly enter the partition mapping stage. The last two rows of the initialized bit reconstruction \(G_{0}\) are set to 0, as shown in Equation (3), which keeps the ungrouped data streams in the signal matrix \(P\) (i.e., the data streams that do not enter the logic code circuit) from being controlled by the bit reconstruction matrix operation when the relevant operation is performed with the signal matrix \(P\). For our proposed method, the bit reconstruction matrix \(G_{0}\) is initialized as follows:  
\[G_{0}= \begin{bmatrix}1&\cdots&1\\ \vdots&\ddots&\vdots\\ 1&\cdots&1\\ 0&\cdots&0\end{bmatrix}  \tag{3}\]  
In particular, \"0\" is not an assignment element, but rather denoting not dealing with elements in the same position when compared to the symbol matrix \(P\).