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Ring Compute-and-Forward Over Block-Fading Channels.
- Source :
- IEEE Transactions on Information Theory; Nov2019, Vol. 65 Issue 11, p6931-6949, 19p
- Publication Year :
- 2019
-
Abstract
- The compute-and-forward (C&F) protocol in quasi-static channels normally employs lattice codes based on the rational integers $\mathbb {Z}$ , the Gaussian integers $\mathbb {Z} [i]$ , or the Eisenstein integers $\mathbb {Z} [\omega ]$ , while its extension to more general channels often assumes channel state information at transmitters (CSIT). In this paper, we propose a novel scheme for C&F in block-fading channels without CSIT, which is referred to as ring C&F because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers. Owing to the multiplicative closure of the algebraic lattices employed, a relay is able to decode an algebraic–integer linear combination of lattice codewords. We analyze its achievable computation rates and show it outperforms conventional C&F based on the $\mathbb {Z}$ -lattices. By investigating the effect of the Diophantine approximation by algebraic conjugates, we prove that the degrees of freedom (DoFs) of the optimized computation rate are ${n}/{L}$ , where $n$ is the number of blocks and $L$ is the number of users. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 139229553
- Full Text :
- https://doi.org/10.1109/TIT.2019.2927453