Non-Random Coding Error Exponent for Lattices

Yuval Domb; Meir Feder

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arXiv · 1201.6022

Non-Random Coding Error Exponent for Lattices

Yuval Domb·Meir Feder

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Abstract

An upper bound on the error probability of specific lattices, based on their distance-spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers. In many ways, the new bound greatly resembles the Shulman-Feder bound for linear codes. Based on the new bound, an error-exponent is derived for specific lattice sequences (of increasing dimension) over the AWGN channel. Measuring the sequence's gap to capacity, using the new exponent, is demonstrated.

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Yuval Domb, Meir Feder. 2013-01-01. Non-Random Coding Error Exponent for Lattices. https://arxiv.org/abs/1201.6022

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