Transmission scheme and code design for broadcast networks

Abstract

In this thesis, we proposed transmission schemes for broadcast channels and analyzed their corresponding achievable rate regions.

We introduced a class of broadcast channels called noisy Blackwell channel, which generalize the Blackwell channel to include noises and to more than two receivers. Noisy Blackwell channel can be applied to model the random I/O code over multi-level cell flash memories to improve the random I/O performance. We applied Marton’s coding scheme for noisy Blackwell channels. We appropriately chose the joint probability distribution of auxiliary random variables and the mapping from the auxiliary random variables to the channel input in Marton’s coding scheme such that the sum-rate inner bound closely achieves the sum-rate capacity. Based on the Marton’s coding scheme, we designed practical codes for noisy Blackwell channels using the channel polarization. To our best knowledge, polar code extensions to more than 2 receiver broadcast channels with simulation results are first proposed. The proposed polar code for the noisy Blackwell channel works well both theoretically and practically even for a large number of receivers.

To increase the transmission rates and improve the reliability of communications, we introduced a relay node to the broadcast channel. The relay recovers a part of the message for each receiver or fully decodes the message for each receiver according to the channel conditions. Then, the relay re-encode these messages into a codeword and sends it to all receivers. Since the broadcast relay channel can be seen as a two-hop broadcast channel, where the first hop is the channel from the transmitter to the receivers and the second hop is the channel from the relay to the receivers, we applied Marton’s coding scheme at both the transmitter and the relay. Our scheme outperforms some decode-forward based schemes in the literature and is optimal in some cases.