Paper Info
Title
Codes Over Matrix Rings for Space-Time Coded Modulations
Abstract
It is known that, for transmission over quasi-static MIMO fading channels with n transmit antennas, diversity can be obtained by using an inner fully diverse space-time block code while coding gain, derived from the determinant criterion, comes from an appropriate outer code. When the inner code has a cyclic algebra structure over a number field, as for perfect space-time codes, an outer code can be designed via coset coding, more precisely, by taking the quotient of the algebra by a two-sided ideal which leads to matrices over finite alphabets for the outer code. In this paper, we show that the determinant criterion induces various metrics on the outer code, such as the Hamming and Bachoc distances. When n = 2, partitioning the 2×2 Golden code by using an ideal above the prime 2 leads to consider codes over either M2(F2) or M2(F2 [i]), both being noncommutative alphabets. By identifying them as algebras over a finite field or a finite ring respectively, we establish an unexpected connection with classical error-correcting codes over F4 and F4 [i]. Matrix rings of higher dimension, suitable for 3×3 and 4×4 perfect codes, give rise to more complex examples.
Year
DOI
Venue
2012
10.1109/TIT.2011.2173732
Clinical Orthopaedics and Related Research
Keywords
DocType
Volume
perfect space-time code,inner code,perfect code,classical error-correcting code,determinant criterion,space-time coded modulations,appropriate outer code,diverse space-time block code,finite alphabet,golden code,matrix rings,outer code,error correction code,fading,finite field,modulation,antenna diversity,coding gain,space time code,encoding,fading channel,galois fields,vector space,channel coding,hamming distance,number fields,vectors,space time block code,determinants
Journal
58
Issue
ISSN
Citations 
2
0018-9448
6
PageRank 
References 
Authors
0.99
10
3
Name
Order
Citations
PageRank
Frédérique E. Oggier1123.16
Patrick Solé263689.68
J. -C. Belfiore348878.63