The paper addresses the problem of constructing an asynchronous multiple access system for a multi-user Q-frequency channel with additive white Gaussian noise (AWGN). We propose a coding scheme for the channel which allows a large number of users to work simultaneously in the system. The scheme combines the ideas of Frequency Shift Keying (FSK) and Frequency Hopping Spread Spectrum (FHSS). The major component of the scheme is a non-binary low-density parity-check (LDPC) code. The efficiency of the resulting multiple-access system is shown by simulations.