K-user nonbinary parallel concatenated code for Gaussian multiple-access channel

A K-user nonbinary parallel concatenated code (PCC) is proposed for a Gaussian MAC with symbol synchronization, equal-power, and equal-rate users. In a K-user q-ary PCC over finite field GF(q), each user employs a parallel concatenated code, with a rate-(1/r) q-ary repetition component code and M rate-1 q-ary accumulation component codes. Employing q-ary repetition code is to overcome the multi-user interference and also provide coding gain. The K-user q-ary PCC is not only rate compatible, but also with very low encoding and decoding complexities due to employing such simple component codes. An EXIT chart analysis is given to estimate the decoding threshold of the K-user q-ary PCC. Numerical results show that the decoding threshold of K-user q-ary PCC improves as the field order q increases. The 10-user 64-ary PCC improves the decoding threshold by 1.88 dB over the binary case. The decoding threshold of 15-user 64-ary PCC at sum rate 3/4 is only 0.75 dB away from the Shannon bound. Bit-error-rate simulations are provided to verify the analysis.