Optimal Allocation of Redundancy Between Packet-Level Erasure Coding and Physical-Layer Channel Coding in Fading Channels

For a block-fading channel, this paper optimizes the allocation of redundancy between packet-level erasure coding (which provides additional packets to compensate for packet loss) and physical layer channel coding (which lowers the probability of packet loss). After some manipulation, standard optimization techniques determine the trade-off between the amount of packet-level erasure coding and physical-layer channel coding that minimizes the transmit power required to provide reliable communication. Our results indicate that the optimal combination of packet-level erasure coding and physical-layer coding provides a significant benefit over pure physical-layer coding when no form of channel diversity is present within a packet transmission. However, the benefit of including packet-level erasure coding diminishes as more diversity becomes available within a packet transmission. Even with no diversity within a packet transmission, this paper shows that as the total redundancy becomes large the optimal redundancy for packet-level erasure coding reaches a limit while the optimal redundancy for physical-layer coding continues to increase. Hence providing limitless redundancy at the packet-level with rateless codes such as fountain codes is not the best use of limitless redundancy for block-fading channels.