Investigation of error control properties of orthogonal codes

Abstract

In this paper we investigate the distance properties of orthogonal codes and evaluate its error control properties. We examine this by noting that an n-bit orthogonal code has n/2 1's and n/2 0's; i.e., there are n/2 positions where 1's and 0's differ. Therefore, the distance between two orthogonal codes is also n/2. By exploiting this distance property, we show that a code rate r=k/n, where n is the code length and k is the data length, is available out of orthogonal codes with error control capabilities. We then develop a method of coded modulation with bandwidth efficiency. The proposed technique offers a simpler solution to error control coding with bandwidth efficiency. Finally, the construction of an orthogonal coded modulation scheme is presented to illustrate the concept.