Codes over matrix rings for space-time coded modulations
Date of Issue2011
School of Physical and Mathematical Sciences
Singapore National Research Foundation
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 non-commutative 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.
DRNTU::Engineering::Electrical and electronic engineering::Wireless communication systems
IEEE transactions on information theory
© 2011 IEEE. This is the author created version of a work that has been peer reviewed and accepted for publication by IEEE. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: http://dx.doi.org/10.1109/ISIT.2009.5205614 .