Capacity of 1-to-K Broadcast Packet Erasure Channels with Channel Output Feedback

TL;DR

This paper characterizes the capacity regions of 1-to-K broadcast packet erasure channels with feedback, providing exact solutions for specific cases and bounds for general scenarios, relevant for network coding and ARQ systems.

Contribution

It derives the capacity region for 1-to-3 broadcast PECs and for symmetric and spatially independent PECs with fairness, plus bounds for general PECs.

Findings

Capacity region for 1-to-3 broadcast PECs is established.

Capacity region for symmetric and spatially independent PECs with fairness is characterized.

Outer and inner bounds for general PECs are provided and often tight.

Abstract

This paper focuses on the 1-to-K broadcast packet erasure channel (PEC), which is a generalization of the broadcast binary erasure channel from the binary symbol to that of arbitrary finite fields GF(q) with sufficiently large q. We consider the setting in which the source node has instant feedback of the channel outputs of the K receivers after each transmission. Such a setting directly models network coded packet transmission in the downlink direction with integrated feedback mechanisms (such as Automatic Repeat reQuest (ARQ)). The main results of this paper are: (i) The capacity region for general 1-to-3 broadcast PECs, and (ii) The capacity region for two classes of 1-to-K broadcast PECs: the symmetric PECs, and the spatially independent PECs with one-sided fairness constraints. This paper also develops (iii) A pair of outer and inner bounds of the capacity region for arbitrary 1-to-K broadcast PECs, which can be evaluated by any linear programming solver. For most practical scenarios, the outer and inner bounds meet and thus jointly characterize the capacity.