Stable XOR-based Policies for the Broadcast Erasure Channel with Feedback
Sophia Athanasiadou, Marios Gatzianas, Leonidas Georgiadis and, Leandros Tassiulas

TL;DR
This paper introduces a simple XOR-based network coding scheme for the broadcast erasure channel with feedback, achieving optimal stability and capacity for certain network sizes and erasure conditions.
Contribution
It proposes a novel binary XOR coding scheme with queue management that guarantees instantaneous decodability and proves its optimality for specific cases.
Findings
Achieves stability region matching the capacity for N=4 with i.i.d. erasures.
Uses only XOR operations for coding, simplifying implementation.
Provides a stabilizing policy based on the proposed coding scheme.
Abstract
In this paper we describe a network coding scheme for the Broadcast Erasure Channel with multiple unicast stochastic flows, in the case of a single source transmitting packets to users, where per-slot feedback is fed back to the transmitter in the form of ACK/NACK messages. This scheme performs only binary (XOR) operations and involves a network of queues, along with special rules for coding and moving packets among the queues, that ensure instantaneous decodability. The system under consideration belongs to a class of networks whose stability properties have been analyzed in earlier work, which is used to provide a stabilizing policy employing the currently proposed coding scheme. Finally, we show the optimality of the proposed policy for and i.i.d. erasure events, in the sense that the policy's stability region matches a derived outer bound (which coincides with the system's…
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