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UBC Theses and Dissertations

Achieving channel capacities with nested linear/lattice codes : a unified approach Qi, Renming


Random nested lattice codes have played an important role in network information theory. However, they are less accessible than conventional random codes because their achievability proofs are often involved, even for the case of the additive white Gaussian noise (AWGN) channel. In sharp contrast, their finite field counterparts, nested linear codes, enjoy much simpler achievability proofs. In this thesis, we make use of an intriguing connection between nested lattice codes and nested linear codes to handle their achievability proofs in a unified approach. As a by-product of this unified approach, we show it’s capable of proving that the algebraic lattice codes constructed using number field could achieve the AWGN channel capacity.

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