# A Novel CDMA-Based Secret Message Multiplexing Scheme by Image Data Hiding +
## 2 CDMA Multiplexing  
Code Division Multiple Access (CDMA) [33; 34; 35; 36; 37; 38] is a channel access method employing spread spectrum technology. Being a multiplexing scheme in essence, CDMA is also known as Code Division Multiplexing (CDM). Multiplexing is the sharing of a communication channel or bandwidth. It is the process in which multiple signals coming from multiple sources are combined and transmitted over a shared communication link. The receiver recovers the separate signals by a process called demultiplexing. Compared to CDM, the term CDMA is mentioned more often to emphasize the asynchronous and random nature of multiuser connections. The spread spectrum technique has been developed for a long time. It was formerly used in military communications to achieve anti-jamming. In spread spectrum communication, the bandwidth occupied by a single transmitted signal is much higher than in systems using conventional modulation methods. This bandwidth spread is accomplished by means of a spreading code, which is independent of the data. A very popular approach is to multiply the data signal with a fast-spreading signal, which is also named the spreading code. This technique is known as Direct-Sequence (DS) Spread Spectrum. Figure 1a displays the waveforms of binary data signal, spreading signal, and the transmitted signals in a Direct-Sequence Spread Spectrum (DSSS) system. As seen in Figure 1a, the binary antipodal spreading signal comprises eight chips with values 1, 1, 1, 1, \(-\)1, \(-\)1, \(-\)1 in sequence. The chip rate is 8 times that of the bit rate, which means the bandwidth of the transmitted signals will be 8 times larger than that of the data signal. In the case that multiple users share the same radio spectrum but use different codes to discriminate respective transmitted signals, we called it Code Division Multiple Access (CDMA). At present, Direct-Sequence CDMA (DS-CDMA) has been widely applied to mobile communications. In the following, we will focus on DS-CDMA technology. The spreading codes for CDMA could be classified into two categories, orthogonal codes and pseudorandom (PN) codes. For PN codes, such as Maximum Length sequences and Gold codes, there is a low correlation between the codes, while orthogonal codes, such as Hadamard codes, have a cross-correlation equal to zero. Here, an illustrative example of DS-CDMA communication system is shown in Figure 1b where the 8-bit Hadamard codes are used as spreading codes and two users are displayed. In the transmitter, the binary data signal of each user is multiplied by a specific spreading code, and they are superimposed together to form the DS-CDMA signal. In the receiver, the received signal is again multiplied by a spreading code and integrated over one data bit interval. Note that this operation is equivalent to taking the inner product. A CDMA receiver can retrieve the original data signal only by multiplying the received signal with the same code as the one used during transmission. A more detailed example is demonstrated. Suppose the number of concurrent users in the system is four, and the four users' data are \(A= \begin{bmatrix}1&0&1\end{bmatrix} \), \(B= \begin{bmatrix}1&1&0\end{bmatrix} \), \(C= \begin{bmatrix}0&0&1\end{bmatrix} \), \(D= \begin{bmatrix}0&1&1\end{bmatrix} \), each with three bits. Every user will be assigned a four-bit Hadamard code as the spreading code. In the transmitter side, the steps for CDMA multiplexing are listed below. Figure 1: Diagrammatic illustration of the Spread Spectrum and CDMA techniques. (**a**) Signal waveforms in a Direct-Sequence Spread Spectrum (DSSS) system. (**b**) Block diagram of a DS-CDMA communication system. Step 1. Process the bit value conversion with \(1\to 1\) and \(0\to-1\) on users' data. The resultant antipodal bits are \(A^{\prime}= \begin{bmatrix}1&-1&1\end{bmatrix} \), \(B^{\prime}= \begin{bmatrix}1&1&-1\end{bmatrix} \), \(C^{\prime}= \begin{bmatrix}-1&-1&1\end{bmatrix} \), and \(D^{\prime}= \begin{bmatrix}-1&1&1\end{bmatrix} \). Step 2.