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A novel two-dimensional parallel sequence spread spectrum (2D-PSSS) structure for the physical layer of wireless communication systems is introduced. The proposed 2D-PSSS system partitions a data block into two groups of bits, representing the two dimensions. The first dimension represents the selected code from a predefined set of Gold codes. While the second dimension determines a shift value applied to the chosen code. The shifted Gold code will represent the data block. By design, the 2D-PSSS system overcomes the challenge of inter-code interference encountered in conventional PSSS systems without introducing additional computational complexity. Moreover, the 2D-PSSS system offers reduced encoder computational complexity compared to PSSS systems, enhancing its suitability for a wide range of wireless communication applications. The performance of the 2D-PSSS system in terms of bit error rate has been evaluated in additive white Gaussian noise (AWGN) channel and under different fading channel conditions.