Low ML Decoding Complexity STBCs via Codes over GF(4)

In this paper, we give a new framework for constructing low ML decoding complexity Space-Time Block Codes (STBCs) using codes over the finite field ${\mathbb{F}}_4$. Almost all known low ML decoding complexity STBCs can be obtained via this approach. New full-diversity STBCs with low ML decoding complexity and cubic shaping property are constructed, via codes over ${\mathbb{F}}_4$, for number of transmit antennas \mbox{$N=2^m$}, \mbox{$m \geq 1}, and rates \mbox{R>1} complex symbols per channel use. When \mbox{R=N$}, the new STBCs are information-lossless as well. The new class of STBCs have the least known ML decoding complexity among all the codes available in the literature for a large set of \mbox{$(N,R)$} pairs.