Performance of Block Codes Using the Eigenstructure of the Code Correlation Matrix and Soft-Decision Decoding of BPSK

Abstract

A method is presented for obtaining the error probability for block codes. The method is based on the eigenvalue- eigenvector properties of the code correlation matrix. It is found that under a unary transformation and for an additive white Gaussian noise environment, the performance evaluation of a block code becomes a one-dimensional problem in which only one eigenvalue and its corresponding eigenvector are needed in the computation. The obtained error rate results show remarkable agreement between simulations and analysis.