On Minimizing the Average Packet Decoding Delay in Wireless Network Coded Broadcast

TL;DR

This paper addresses minimizing average packet decoding delay in wireless broadcast using network coding, proving NP-hardness, proposing approximation algorithms, and demonstrating their effectiveness through experiments.

Contribution

It introduces a new methodology for designing approximation algorithms that outperform RLNC for minimizing decoding delay in wireless broadcast.

Findings

NP-hardness of the problem established

Approximation algorithms with ratio 2 proposed

Experimental results show improved performance

Abstract

We consider a setting in which a sender wishes to broadcast a block of K data packets to a set of wireless receivers, where each of the receivers has a subset of the data packets already available to it (e.g., from prior transmissions) and wants the rest of the packets. Our goal is to find a linear network coding scheme that yields the minimum average packet decoding delay (APDD), i.e., the average time it takes for a receiver to decode a data packet. Our contributions can be summarized as follows. First, we prove that this problem is NP-hard by presenting a reduction from the hypergraph coloring problem. Next, we show that %\alexn{an MDS-based solution or} a random linear network coding (RLNC) provides an approximate solution to this problem with approximation ratio $2$ with high probability. Next, we present a methodology for designing specialized approximation algorithms for this problem that outperform RLNC solutions while maintaining the same throughput. In a special case of practical interest with a small number of wanted packets our solution can achieve an approximation ratio (4-2/K)/3. Finally, we conduct an experimental study that demonstrates the advantages of the presented methodology.