Coding Schemes for the Uncoordinated Unsourced Multiple Access Gaussian Channel

Krishna Narayanan (Texas A&M)

Abstract:
In the uncoordinated unsourced multiple access channel model introduced by Polyanksiy, a set of nodes each wish to communicate a short packet to a central receiver. In a twist from the standard multiple access channel, the receiver seeks to learn the set of transmitted messages without regard to which transmitter is associated with which message. Polyanksiy provided an achievability result for this communication problem and Ordentlich and Polyanksiy devised the first practical coding scheme. In this talk, we propose a new coding scheme for this problem that substantially improves the state of the art. Our proposed paradigm is composed of four main ingredients: (i) the transmission period is partitioned into sub-blocks, thereby instituting a slotted framework; (ii) The message (data) is split into two parts and one part chooses an interleaver for a low density parity check (LDPC) type code. This part of the message is encoded using spreading sequences or codewords that are designed to be decoded by a compressed sensing type decoder; (iii) The other part of the message is encoded using a low density parity check (LDPC) type code and decoded using a joint message passing decoding algorithm designed for the $T$-user binary input real adder channel; (iv) users repeat their codeword in multiple sub-blocks, with the transmission pattern being a deterministic function of message content and independent of the identity of the user. When decoded using a successive interference canceller type decoder, this coding scheme provides excellent performance. We will also point out connections between the unsourced multiple access channel problem and unsolved problems in compressed sensing and lattice coding.