Iterated Space-Time Code Constructions From Cyclic Algebras

Abstract

We propose a full-rate iterated space-time code construction, to design codes of Q-rank 2n from cyclic algebra based codes of Q-rank n. We give a condition for determining whether the resulting codes satisfy the full diversity property, and study their maximum likelihood decoding complexity with respect to sphere decoding. Particular emphasis is given to the asymmetric MIDO (multiple input double output) codes. In the process, we derive an interesting way of obtaining division algebras, and study their center and maximal subfield.

Fast-decodable MIDO codes from non-associative algebras

“…Again, we use a cyclic division algebra D over a field F and some invertible element d ∈ D as main ingredients of the construction of the algebra. Our codes canonically generalize the iterated codes from [20] (for any invertible d ∈ D used in the construction) and look very similar to the ones in [21]. The case n = 2 yields the nonassociative algebras and related iterated codes also mentioned in [11].…”

“…For n = 2, this algebra is studied in [11]; it is implicitly used in the iterated codes constructed in [20].…”

“…The nonassociative algebras used in the construction can be viewed as generalizations of cyclic associative (or nonassociative) algebras. They generalize the nonassociative algebra behind the codes built in [20]. Their algebraic structure theory is similar to the classical one for associative cyclic algebras.…”

“…Their approach uses certain nonassociative algebras in the code construction, employing as main ingredients a cyclic division algebra D over a field F and some invertible element d ∈ D. The resulting codes coincide with the iterated codes from Markin and Oggier [20], if n = 2 and if the element d ∈ D used in the algebra (resp. code) construction lies in F .…”

“…Contribution and Organization. We propose an algebraic construction to build rate-n (for n transmit antennas) fully diverse STBCs which canonically generalize the iterated codes from [20] and cannot be obtained through the left regular representation of some associative division algebra. The nonassociative algebras used in the construction can be viewed as generalizations of cyclic associative (or nonassociative) algebras.…”