A new class ofM-ary communication systems has been put forward as a means of reducing the effects of impulsive noise. In the paper the performance of binary systems drawn from the new general class ofM-ary systems is examined both analytically and by computer simulation. A new technique based on the use of the Euler transformation of slowly convergent alternating series is developed as an aid in the analytical evaluation of system performance. The analytical and simulation results, which are in very good agreement, show that in the prsesence of impulsive noise the new class of communications systems can exhibit a performance superior to that of a conventional system.