Lattice network codes based on Eisenstein integers

Sun, Qifu, Yuan, Jinhong, Huang, Tao, and Shum, Kenneth (2013) Lattice network codes based on Eisenstein integers. IEEE Transactions on Communications, 61 (7). pp. 2713-2725.

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In this paper, we investigate lattice network codes (LNCs) constructed from Eisenstein integer based lattices. Quantization and encoding algorithms over Eisenstein integers are first introduced. Then, a union bound estimation (UBE) of the decoding error probability is derived when the shaping region of the LNC is a product of regular hexagons. Next, the Gaussian reduction algorithm is generalized to be applicable to complex lattices over Eisenstein integers such that an optimal coefficient vector can be found in the two-transmitter single-relay system. Based on the UBE, design criteria for optimal LNCs with minimum decoding error probability are formulated and applied to construct both Gaussian integer and Eisenstein integer based good LNCs from rate-1/2 feed-forward convolutional codes by Complex Construction A. The constructed codes provide up to 7.65 dB nominal coding gains over Rayleigh fading channels. Furthermore, we introduce the construction of LNCs from linear codes by Complex Construction B. The nominal coding gains and error performance of the LNCs thus constructed are explicitly analyzed. Examples show that the LNCs constructed by Complex Construction B provide a better tradeoff between code rate and nominal coding gain.

Item ID: 59885
Item Type: Article (Research - C1)
ISSN: 1558-0857
Keywords: Compute-and-forward, lattice network codes, decoding error probability, Gaussian reduction for complex lattices, complex Construction B
Copyright Information: © 2013 IEEE
Date Deposited: 07 Dec 2021 00:02
FoR Codes: 10 TECHNOLOGY > 1005 Communications Technologies > 100510 Wireless Communications @ 50%
10 TECHNOLOGY > 1005 Communications Technologies > 100504 Data Communications @ 50%
SEO Codes: 89 INFORMATION AND COMMUNICATION SERVICES > 8901 Communication Networks and Services > 890199 Communication Networks and Services not elsewhere classified @ 100%
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