Lattices which are good for (almost) everything

By Uri Erez, Simon Litsyn, Ram Zamir. Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674), 2003

402 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/81bd7f3a0c449e52033b588701bc3ea1b576339b

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Citations in the corpus

Joint Physical Layer Coding and Network Coding for Bidirectional Relaying (2008, methodology): “The main idea in [12], [14] is to use the coarse lattice as a shaping region and the lattice points from the fine lattice contained within the basic Voronoi region of the coarse lattice as the codewords.”
Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels (2004, methodology): “From a union bound argument similar to what was used in [28] to prove the simultaneous goodness of lattices, we can see that there exist lattices in the ensembles such that their ambiguity probability is upper-bounded by the second term in (83) and their packing efficiency is lowerbounded by (88).”
Capacity of the Gaussian Two-way Relay Channel to within 1/2 Bit (2009, background): “ Λ n 2 ⊆ Λ n C exists that satisﬁes the following properties. a) Λn 1 and Λn 2 are simultaneously Rogers-good and Poltyrev-good whileΛn C is Poltyrev-good (for the notion of goodness of lattices, see [20]). b) For any ǫ > 0, Pi − ǫ ≤ σ2(Λn i ) ≤ Pi, i ∈ {1,2}, for sufﬁciently large n, where σ2(·)”
Compute-and-Forward: Harnessing Interference Through Structured Codes (2009, methodology): “In [69] and [71], some useful properties of nested lattices derived from Construction A are established.”
A unified framework for tree search decoding: rediscovering the sequential decoder (2005, background): “While the outstanding performance of appropriate preprocessing and lattice decoding can be motivated via rigorous information-theoretic arguments [20], [21], [28], here we are more concerned with the algorithmic aspects of the decoder and we shall give some heuristic motivation based on “signal-proc”
Capacity of the Gaussian Two-Way Relay Channel to Within ${1\over 2}$ Bit (2009, background): “For a comprehensive review, we refer readers to [12], [22], [23], and the references therein.”