Performance Characterization and Transmission Schemes for Instantly Decodable Network Coding in Wireless Broadcast

TL;DR

This paper analyzes the performance limits of instantly decodable network coding (IDNC) in wireless broadcast, deriving bounds and designing schemes to optimize transmission efficiency and decoding delay under packet erasures.

Contribution

It characterizes fundamental performance limits of strict IDNC, derives closed-form expressions, proves NP-hardness of delay minimization, and designs optimal and heuristic transmission schemes.

Findings

Closed-form expression for minimum number of transmissions

NP-hardness of decoding delay minimization

G-IDNC can outperform S-IDNC in ideal conditions

Abstract

We consider broadcasting a block of packets to multiple wireless receivers under random packet erasures using instantly decodable network coding (IDNC). The sender first broadcasts each packet uncoded once, then generates coded packets according to receivers' feedback about their missing packets. We focus on strict IDNC (S-IDNC), where each coded packet includes at most one missing packet of every receiver. But we will also compare it with general IDNC (G-IDNC), where this condition is relaxed. We characterize two fundamental performance limits of S-IDNC: 1) the number of transmissions to complete the broadcast, and 2) the average delay for a receiver to decode a packet. We derive a closed-form expression for the expected minimum number of transmissions in terms of the number of packets and receivers and the erasure probability. We prove that it is NP-hard to minimize the decoding delay of S-IDNC. We also derive achievable upper bounds on the above two performance limits. We show that G-IDNC can outperform S-IDNC %in terms of the number of transmissions without packet erasures, but not necessarily with packet erasures. Next, we design optimal and heuristic S-IDNC transmission schemes and coding algorithms with full/intermittent receiver feedback. We present simulation results to corroborate the developed theory and compare with existing schemes.