Linked-Loop Codes for the Unsourced A- and B-Channels With Erasures

The A-channel is a noiseless multiple access channel in which users simultaneously transmit <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i>−ary symbols and the receiver observes the union of all input symbols. An A-channel is said to be unsourced if additionally, all users’ transmissions are encoded across time using a common codebook and decoding is performed without regard to the identities of the active users. Whereas the A-channel employs a traditional set union, the B-channel employs a multiset union so that the receiver observes the set of input symbols together with their respective multiplicities. In this paper, we consider the task of coding for the unsourced A- and B-channels in the presence of i.i.d. erasures and we propose a novel tail-biting code called the linked loop code (LLC) for these channels. The LLC is shown to outperform contemporary codes in part due to its resilience to lost sections. The performance of the LLC code is investigated theoretically and bounds on the error performance are provided.