Lattice problem: Difference between revisions

Revision as of 15:08, 3 December 2023

Revision as of 19:21, 28 December 2023

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===Sphere decoding===

Algorithms for CVP, especially the Fincke and Pohst variant,<ref name=":0">{{cite journal |last1=Fincke |first1=U. |last2=Pohst |first2=M. |title=Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis |journal=Math. Comp. |volume=44 |issue=170 |pages=463–471 |year=1985 |doi=10.1090/S0025-5718-1985-0777278-8 |doi-access=free }}</ref> have been used for data detection in multiple-input multiple-output ([[MIMO]]) wireless communication systems (for coded and uncoded signals).<ref>{{cite book |last1=Biglieri |first1=E. |last2=Calderbank |first2=R. |author-link3=Anthony G. Constantinides |first3=Anthony G. |last3=Constantinides |last4=Goldsmith |first4=A. |last5=Paulraj |first5=A. |last6=Poor |first6=H. V. |title=MIMO Wireless Communications |publisher=Cambridge U. P. |___location=Cambridge |year=2007 }}</ref><ref name=":2">{{cite journal |last1=Agrell |first1=E. |last2=Eriksson |first2=T. |last3=Vardy |first3=A. |last4=Zeger |first4=K. |title=Closest Point Search in Lattices |journal=IEEE Trans. Inf. Theory |volume=48 |issue=8 |pages=2201–2214 |year=2002 |doi=10.1109/TIT.2002.800499 |url=httpshttp://researchpublications.lib.chalmers.se/enrecords/publicationfulltext/14990/local_14990.pdf }}</ref> In this context it is called ''sphere decoding'' due to the radius used internal to many CVP solutions.<ref>{{cite journal |first1=Ping |last1=Wang |first2=Tho |last2=Le-Ngoc |title=A List Sphere Decoding Algorithm with Improved Radius Setting Strategies |journal=Wireless Personal Communications |year=2011 |volume=61 |issue=1 |pages=189–200 |doi=10.1007/s11277-010-0018-4 |s2cid=30919872 }}</ref>

It has been applied in the field of the integer ambiguity resolution of carrier-phase GNSS (GPS).<ref>{{cite journal |last1=Hassibi |first1=A. |last2=Boyd |first2=S. |title=Integer Parameter Estimation in Linear Models with Applications to GPS |journal=IEEE Trans. Sig. Proc. |volume=46 |issue=11 |pages=2938–2952 |year=1998 |doi=10.1109/78.726808 |bibcode=1998ITSP...46.2938H |citeseerx=10.1.1.114.7246 }}</ref> It is called ''LAMBDA method'' in that field. In the same field, the general CVP problem is referred to as ''Integer Least Squares''.