On the algebraic structure of the Silver code: A 2 × 2 perfect space-time block code

Camilla Hollanti*, J. Lahtonen, K. Ranto, R. Vehkalahti, E. Viterbo

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

32 Citations (Scopus)


Recently, a family of full-rate, full-diversity spacetime block codes (STBCs) for 2 × 2 multiple-input multipleoutput (MIMO) channels was proposed in [1], [2], [3], [4] using a combination of Clifford algebra and Alamouti structures, namely twisted space-time transmit diversity code. This family was recently rediscovered by Paredes et al., and they pointed out that such STBCs enable reduced-complexity maximum-likelihood (ML) decoding. Independently, the same STBCs were found in [8], and named multi-strata space-time codes. In this paper we show how this code can be constructed algebraically from a particular cyclic division algebra (CDA). This formulation enables to prove that the code has the nonvanishing determinant (NVD) property and hence achieves the diversity-multiplexing tradeoff (DMT) optimality. The fact that the normalized minimum determinant is 1/√7 places this code in the second position with respect to the Golden code, which exhibits a minimum determinant of 1/√5, and motivates the name Silver code.

Original languageEnglish
Title of host publication2008 IEEE Information Theory Workshop, ITW
Number of pages4
ISBN (Electronic)978-1-4244-2270-8
ISBN (Print)978-1-4244-2269-2
Publication statusPublished - 2008
MoE publication typeA4 Article in a conference publication
EventIEEE Information Theory Workshop - Porto, Portugal
Duration: 5 May 20088 May 2008


WorkshopIEEE Information Theory Workshop
Abbreviated titleITW




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