Set partitioning of Gaussian integer constellations and its application to two‐dimensional interleaving

Freudenberger, Jürgen; Spinner, Jens; Shavgulidze, Sergo

doi:10.1049/iet-com.2013.0640

Cited by 3 publications

(1 citation statement)

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“…These techniques can be used to construct multilevel codes similar to ordinary coded modulation schemes [19]- [21]. Moreover, set partitioning can be applied to the design of twodimensional interleavers [22]. We generalize the methods from [4] to Lipschitz integers.…”

Section: Introductionmentioning

confidence: 99%

New Four-Dimensional Signal Constellations From Lipschitz Integers for Transmission Over the Gaussian Channel

Freudenberger

Shavgulidze

2015

IEEE Trans. Commun.

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Codes over quotient rings of Lipschitz integers have recently attracted some attention. This work investigates the performance of Lipschitz integer constellations for transmission over the AWGN channel by means of the constellation figure of merit. A construction of sets of Lipschitz integers that leads to a better constellation figure of merit compared to ordinary Lipschitz integer constellations is presented. In particular, it is demonstrated that the concept of set partitioning can be applied to quotient rings of Lipschitz integers where the number of elements is not a prime number. It is shown that it is always possible to partition such quotient rings into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is strictly larger than in the original set. The resulting signal constellations have a better performance for transmission over an additive white Gaussian noise channel compared to Gaussian integer constellations and to ordinary Lipschitz integer constellations. In addition, we present multilevel code constructions for the new signal constellations.

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