Encoding method of a rational number M-ary signal

As the M-ary signaling scheme is mapping of N bits information to M signal elements, M has to be generally represented as 2 to Nth power (2^N), which results in degrading the degree of freedom of a system design. In this paper, we introduce an encoding method of the M-ary signal with an arbitrary rational number by grouping two different M-ary signals. It enables us to choose M freely to satisfy a desired error probability and increases the channel efficiency up to two times. We show that the signal error probability of the suggested method is lower than that of the conventional method for the AWGN channel in numerical result.