Finite Field Spreading for Multiple-Access Channel

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.