Lattice coding for downlink multiuser transmission

Abstract

In this thesis, we mainly investigate the lattice coding problem of downlink communications where the base station broadcasts messages to multiple users. The capacity limit of such a system setting is already well-known while the design of practical coding and modulation schemes to approach this limit has not been fully studied and investigated in the literature. This thesis attempts to address this problem by providing a systematic design on lattice coding and modulation schemes for downlink multiuser communications. The research work of this thesis contains three topics. The first topic is designing a class of multi-dimensional lattice codes to approach the capacity of the classical point-to-point communication channel before we address the multiuser systems later. A novel encoding structure of our lattice codes is introduced and this approach is proved to allow our designed codes exhibit symmetry and permutation-invariance properties. By exploring these two properties, the degree distributions and the decoding thresholds of our codes are optimized by using one-dimensional extrinsic information transfer charts, which were mainly used for designing binary linear codes previously. The second topic is about designing practical lattice coding schemes for downlink non-orthogonal multiple access (NOMA) without successive interference cancellation (SIC) at the receiver. In particular, we develop three different lattice based schemes for three cases: NOMA over slow fading channels with full channel state information at the transmitter (CSIT), NOMA over slow fading with statistical CSIT and NOMA over block fading with statistical CSIT. For the proposed three schemes in these three scenarios, we analyze the individual achievable rate, individual outage rate and the minimum product distance of the superimposed constellation, respectively. The last topic is designing a class of product codes with high code rate and low error floor for ultra-reliable digital systems such as fibre-optic communications and data-storage systems. The unique encoding structure allows the decoder to easily detect and correct more error patterns that contribute to the error floor. Moreover, an efficient post processing technique is proposed to enhance the decoding performance by further lowering the error floor. Theoretical analysis of the error pattern occurrence and the decoding performance is provided.