As a generalization of the binary spreading scheme in conventional direct-sequence code-division multiple-access (DS-CDMA) and interleave-division multiple-access (IDMA), a finite field spreading scheme is proposed for a synchronous multiple-access channel (MAC) with Gaussian noise and equal-power users. For each user, each information symbol over a finite field is spread into a length-L field vector by L-field multiplications. At the receiver, an iterative multi-user decoding algorithm on a factor graph is developed to recover each user's information symbol. To estimate the bit error rate performance of an uncoded finite field spreading system, an extrinsic information transfer analysis of the finite field despreading is given. This analysis shows that in addition to overcoming multi-user interference, the finite field spreading scheme can also provide an additional coding gain to overcome Gaussian noise compared with the conventional spreading scheme. This coding gain increases with the field order. The finite field spreading serially concatenated with a nonbinary low-density parity-check (LDPC) code, with field order 64, approaches the MAC capacity within 0.26 dB at a sum rate of 0.25.

As a generalization of the binary coding-spreading scheme, nonbinary coding-spreading scheme is proposed for a synchronous binary-input multiple-access channel (MAC) with Gaussian noise, equal-power, and equal-rate users. In this scheme, each user employs the same nonbinary low-density parity-check code serially concatenated with a nonbinary low-rate mapping, referred to as nonbinary spreading. A user-specific interleaving is employed to make the transmitted data of each user random-like. It is shown that the iterative multi-user decoding threshold of nonbinary coding-spreading scheme is less than 0.5 dB away from the MAC capacity at many sum rates.