Grassmannian codes from multiple families of mutually unbiased bases

Olav Tirkkonen, Christopher Boyd, Roope Vehkalahti

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

4 Citations (Scopus)

Abstract

We explore the underlying algebraic structure of Mutually Unbiased Bases (MUBs), and their application to code design. Columns in MUBs have inner products with absolute values less or equal to 1/√N. MUBs provide a systematic way of generating optimal codebooks for various coding and precoding applications. A maximal set of MUBs (MaxMUBs) in N = 2m dimensions, with m Z, can produce codebooks of QPSK lines with good distance properties and alphabets which limit processing complexity. We expand the construction by identifying that in N = 2m dimensions there exists N(m-1)/2 families of MUB, each with N matrices. Inner products of columns of these matrices are less or equal to 1/√2. As an example, we construct Grassmannian line codes from the columns of these matrices. Then decoding or encoding these codebooks can be performed without multiplications, and with a number of additions that scales linearly with the number of codewords, irrespectively of the dimension.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherIEEE
Pages789-793
Number of pages5
ISBN (Electronic)9781509040964
DOIs
Publication statusPublished - 9 Aug 2017
MoE publication typeA4 Conference publication
EventIEEE International Symposium on Information Theory - Eurogress Aachen, Aachen, Germany
Duration: 25 Jun 201730 Jun 2017
https://isit2017.org/

Publication series

NameIEEE International Symposium on Information Theory
ISSN (Print)2157-8095
ISSN (Electronic)2157-8117

Conference

ConferenceIEEE International Symposium on Information Theory
Abbreviated titleISIT
Country/TerritoryGermany
CityAachen
Period25/06/201730/06/2017
Internet address

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