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Block-Coded Modulation Using Two-Level Group Codes Over Generalized Quaternion Groups

Selvakumaran, TV and Rajan, Sundar B (1999) Block-Coded Modulation Using Two-Level Group Codes Over Generalized Quaternion Groups. In: IEEE Transactions on Information Theory, 45 (1). pp. 365-372.


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A length a group code over a group G is a subgroup of G(n) under component-wise group operation. Two-level group codes over the class of generalized quaternion groups, Q(2m) m greater than or equal to 3, are constructed using a binary code and a code over Z(2m-1), the ring of integers module 2(m-1), as component codes and a mapping f from Z(2) X Z(2m-1) to Q2m. A set of necessary and sufficient conditions on the component codes is derived which will give group codes over Q(2m). Given the generator matrices of the component codes, the computational effort involved in checking the necessary and sufficient conditions is discussed. Starting from a four- dimensional signal set matched to Q(2m), it is shown that the Euclidean space codes obtained from the group codes over Q(2m) have Euclidean distance profiles which are independent of the coset representative selection involved in f. A closed-form expression for the minimum Euclidean distance of the resulting group codes over Q(2m) is obtained in terms of the Euclidean distances of the component codes. Finally, it is shown that all four-dimensional signal sets matched to Q(2m) have the same Euclidean distance profile and hence the Euclidean space codes corresponding to each signal set for a given group code over Q(2m) are automorphic Euclidean distance equivalent.

Item Type: Journal Article
Publication: IEEE Transactions on Information Theory
Publisher: IEEE
Additional Information: ©1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: Coded modulation;group codes;multilevel construction
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 25 Aug 2008
Last Modified: 19 Sep 2010 04:15
URI: http://eprints.iisc.ac.in/id/eprint/1661

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