Interleaved Block Coding for Achieving Gaussian Random Access Channel Capacity

This paper studies the detection problem for the Gaussian random access channels, in which only a randomly chosen αK out of K senders wish to convey their messages to a receiver that has the side information of which sender is actively transmitting. A novel coding scheme, referred to as L-interleaved block coding, based on interleaving L single-user codes and successive cancellation decoding is proposed for the symmetric rate tuples in the capacity region of this channel. L-interleaved block coding with L sufficiently large is shown to achieve arbitrarily close to the symmetric capacity. Therefore, it replaces the efforts of finding capacity achieving codes for the Gaussian random access channels with selecting L off-the-shelf codes for Gaussian point-to-point channels for L sufficiently large. An example illustrates that this scheme with a small number of blocks (L = 16) achieves more than 0.95 of the symmetric capacity when two senders are active.