Design of dirty paper coding using low-density parity-check lattices

Abstract

We consider a dirty paper channel where the interference is non-causally known at the transmitter, and propose a dirty paper coding scheme. The lattice strategy and sign-bit shaping are applied to the proposed scheme. For the lattice structure, we use low-density parity-check (LDPC) lattices. In Chapter \ref{chap:LDPC_lattice}, we study the construction method and decoding algorithms of LDPC lattices. Such lattices can be constructed by applying Construction $D`$ to a nested sequence of LDPC codes. We construct a class of regular LDPC lattices using the extended progressive edge growth algorithm. Due to a sparse parity check matrix of the LDPC lattice, the decoding complexity is manageable under the iterative message passing algorithm. We generalize the application of the sum-product algorithm and the max-product algorithm to the Tanner graph of LDPC lattices. We evaluate the performance of two iterative message passing algorithms. In the proposed dirty paper coding scheme, LDPC lattices are used to encode the unsigned bits, and sign-bit shaping is applied to the sign bit. We use a rate-$1/2$ convolutional code as a shaping code. The sign bits are determined to minimize the average signal power. In addition to the shaping code, a high-rate LDPC code is used to carry some information using the sign bit. The encoding and decoding of the proposed scheme are described, and simulation results are provided.