Application of error-correcting codes to the DCPSK system

The relation between differential coding and the error-correcting code is discussed. A detailed investigation is first made of the method of Nakamura and Iijima (1978) in which a block code to be applied inside the differential coding is applied outside that coding. It is shown that in block code a paired error-correcting code can be constructed by a linear transformation from the random error-correcting code. The theory is applied to the convolution code and the code suited to the DCPSK system is sought on a computer. A code is constructed which can correct the error attributable to slip of the reference phase in synchronous detection and to random error in the channel.