Lattice network coding over Euclidean Domains
We propose a novel approach to design and analyse lattice-based network coding. The underlying alphabets are carved from (quadratic imaginary) Euclidean domains with a known Euclidean division algorithm, due to their inherent algorithmical ability to capture analog network coding computations. These...
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/97292 http://hdl.handle.net/10220/24384 http://ieeexplore.ieee.org.ezlibproxy1.ntu.edu.sg/xpl/login.jsp?tp=&arnumber=6952389&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6952389 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | We propose a novel approach to design and analyse lattice-based network coding. The underlying alphabets are carved from (quadratic imaginary) Euclidean domains with a known Euclidean division algorithm, due to their inherent algorithmical ability to capture analog network coding computations. These alphabets are used to embed linear p-ary codes of length n, p a prime, into n-dimensional Euclidean ambient spaces, via a variation of the so-called Construction A of lattices from linear codes. A study case over one such Euclidean domain is presented and the nominal coding gain of lattices obtained from p-ary Hamming codes is computed for any prime p such that p ≡ 1 (mod 4). |
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