ISSN 0032-9460, Problems of Information Transmission, 2011, Vol. 47, No. 4, pp. 305–326.
Pleiades Publishing, Inc., 2011.
Original Russian Text
A.A. Kreshchuk, A.A. Davydov, V.V. Zyablov, 2011, published in Problemy Peredachi Informatsii, 2011, Vol. 47,
No. 4, pp. 3–26.
Codes for MIMO Transmission
Based on Orthogonal Sequences
A. A. Kreshchuk, A. A. Davydov, and V. V. Zyablov
Kharkevich Institute for Information Transmission Problems,
Russian Academy of Sciences, Moscow
email@example.com firstname.lastname@example.org email@example.com
Received March 24, 2011; in ﬁnal form, July 4, 2011
Abstract—We consider MIMO communication systems with Rayleigh fading. We propose a
new coded modulation based on orthogonal sequences and state a new decodability condition.
We introduce concepts and constructions of permutation free (PF) and permutation and repe-
tition free (PRF) codes. We also propose a construction of PRF codes with sign manipulation,
whose code rate can exceed 1. For better analysis and construction of these codes we introduce
a one-to-one mapping that transforms signal matrices to vectors over a ﬁnite ﬁeld. We propose
construction algorithms for PF and PRF codes. We build PF and PRF codes with large car-
dinality, which in several case achieve the maximum cardinality. Simulation of the constructed
codes and estimation of their performance was done in Simulink environment. Results show
high error-correcting capability, which often reaches that of STBC codes with full transmit
In this paper we propose a new coded modulation for MIMO (multiple-input, multiple-output)
communication systems. Such systems use multiple receiving and transmitting antennas, each pair
having independent path gains. Simultaneous use of multiple antennas increases the transmission
rate and decreases the error probability. This kind of communication systems is also called spatial
diversity systems. For further information on the diversity, see . It is not suﬃcient to use only
spatial diversity to reach high throughput. Coded modulation constructions utilizing both spatial
and time diversity are called space-time codes. One of the ﬁrst attempts to build an eﬃcient
full-rate space-time code was made in . The technique proposed in  allowed to halve the
number of receiving antennas by using two transmitting antennas without any loss of error-correction
capability. In  this technique was generalized to any number of transmitting antennas, but the
code rate dropped to 0.5. For a detailed review of state-of-the-art space-time codes, see [4–6].
Modern coded modulations for MIMO communication systems have small code lengths. That
is why they require using an external code, which limits their applicability. The coded modulation
considered in this paper was announced in . It allows us to build codes of any length with
proportionally increasing squared Euclidean code distance. This distance metric is equal to the
energy distance between signals.
Now we describe the channel model. We consider a wireless communication system with N
transmitting and N
receiving antennas. Data are transmitted in blocks of length L through all the
transmitting antennas simultaneously. Symbol interference is assumed to be negligible. During the
transmission of one block, the channel is stationary. The channel can be described by the following