A New Capacity-Approaching Scheme for General 1-to-K Broadcast Packet Erasure Channels With ACK/NACK

Abstract

The capacity region of 1-to- K broadcast packet erasure channels with ACK/NACK is well known for some scenarios, e.g., $ {K}\leq 3$ , etc. However, existing achievability schemes either require knowing the target rate $\vec {{R}}$ in advance, and/or have a complicated description of the achievable rate region that is difficult to prove whether it matches the capacity or not. This work proposes a new network coding scheme with the following features: (i) its achievable rate region is identical to the capacity region for all the scenarios in which the capacity is known; (ii) its achievable rate region is much more tractable and has been used to derive new capacity rate vectors; (iii) it employs sequential encoding that naturally handles dynamic packet arrivals; (iv) it automatically adapts to unknown packet arrival rates $\vec {{R}}$ ; (v) it is based on $\mathsf {GF}({q})$ with ${q}\geq {K}$ . In addition to analytically characterizing the achievable rate region of the proposed scheme, numerical simulation has been used to verify its queue length and delay performance.