Robust Rateless Spatially Coupled Repeat-Accumulate-Repeat Multi-User Codes on IDMA Systems

In this paper, we design a kind of robust rateless multi-user code, which is called spatially coupled repeat-accumulate-repeat (SC-RA-R) code, for the interleave-division multiple-access (IDMA) system. The code is constructed by serially concatenating a fixed outer spatially coupled repeat-accumulate (SC-RA) code with an adjustable inner irregular repetition code. It achieves rateless property by simply adjusting the parameters of the inner repetition code. The IDMA system with the proposed SC-RA-R multi-user codes can adapt to varying channel qualities and varying number of users via rateless property while keeping encoder and decoder implementation unchanged. Analytical extrinsic information transfer (EXIT) functions are derived to determine belief propagation (BP) decoding thresholds of SC-RA-R codes on the IDMA system. The optimization expression is also given under the constraint that repeat parameters are monotonically non-decreasing with the sum rate decreasing. The numerical results show that the maximum achievable sum rates of the SC-RA-R codes can be close to the Shannon bound for arbitrary channel qualities. Besides, our proposed SC-RA-R codes have better BP thresholds and bit-error-rate (BER) performances than the conventional optimal parallel-concatenate codes (PCC) and the optimal partially repeated spatially coupled low-density parity-check (PR-SC-LDPC) codes on IDMA systems.