| 研究実績の概要 |
A novel lattice construction embeds an arbitrary binary block code, such as a CRC, in the lattice. This provides a “self-certifying property” which allows retrying decoding without requesting retransmission. For the point-to-point channel, an analytic expression predicts that approximately 0.5 dB gain is possible; a practical code achieved 0.1 dB gain. For multiuser cooperative communications using the compute-forward paradigm, a more substantial 1.0 dB of gain was achieved. This shows that lattice codes can significantly increase the throughput of wireless networks. Lattices based on low-density parity check codes using quasi-cyclic constructions are shown to operate at lower probability of decoding error than existing modulation methods due to lower transmit power; they are also highly practical, making them a promising candidate for future wireless communication systems. Memory approximate message passing is shown to reduce the complexity of parameter estimation in linear systems using memory to avoid the complexity of MMSE estimation, making it a promising candidate for decoding high-dimensional lattices. Such systems naturally induce L-banded matrices, and interesting algebraic properties of such matrices were shown.
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