Low overhead XOR algorithms for the Broadcast Erasure Channel with Feedback

In this paper low overhead coding algorithms are presented for a network of one transmitter and arbitrary number of users, with multiple unicast traffic, in a broadcast erasure channel. The packets arrive stochastically at the transmitter and feedback is returned to it in ACK/NACK messages. In order to exploit the overhearing benefits of broadcast channel, packets that are not received by their destinations are stored in virtual queues at the transmitter and combined, through XOR addition, with other packets, according to coding rules that ensure instant decodability. In the earlier work of the authors, in [1], an algorithm was proposed for N users, that specified packet combinations and packet movements among the virtual queues of this coding scheme. This algorithm was proved to perform optimally for the case of 4 users and i.i.d. erasure events, but required great packet overhead which grew prohibitively as N increased. In this work low overhead alternatives to the earlier proposed algorithm in [1]] are examined and their performance is studied. Specifically, an algorithm named PQS is proposed, that maintains XOR-only and instantaneous decoding characteristics but also reduces overhead and complexity significantly. Algorithm PQS performs close to the optimal in many cases, while it offers the ability to adjust trade-off between overhead and performance.