Binary Orthogonal Code Generation for Multi-User Communication Using n-Bit Gray and Inverse Gray Codes
K. K. Usha, K. Jaya Sankar · 2012
This paper presents a technique for the generation of Binary Orthogonal Codes using Gray and Inverse Gray codes. Orthogonal codes and Pseudo random Noise codes are used as spreading sequences in multi-user communications. The Spreading codes are also referred to as spreading sequences. Walsh Codes, Gold Codes, Maximal Length sequences, Barker Codes and Kasami codes are commonly used orthogonal codes. In this paper orthogonal codes obtained using Gray code and its inverse are presented. An n-bit Cyclic Gray Code is a circular list of all 2 n bit strings such that successive code words differ in only one bit position. An 'n' bit Inverse Gray Code , is defined exactly opposite to Gray code, it is a circular list of all 2 n bit strings of length 'n' each, such that successive code words differ in (n-1) bit positions. Algorithms discussed in this paper for the generation of Gray and Inverse Gray codes result in n! combinations. The method explained in this paper enables us to generate six and eight length Binary Orthogonal Codes and also Codes of lengths of their even multiples. The auto and cross correlation properties of these codes along with 8, 16-length Walsh Codes are also presented in the current work.