Analysis of Digital Communications Systems Using Binary Error Correcting Codes

A set of equations is derived which permits the calculation of the figure of merit for a communications channel in which a binary error correcting code is used in conjunction with correlation decoding at the receiver. The figure of merit is expressed in terms of the required probability of error and the parameters of the code. These equations are then used to determine the figure of merit for a number of systems using error correcting codes. In particular, a comparison is made between those systems which use orthogonal codes, and a class of systems using codes for which the ratio of bandwidth to information rate is equal to two.