Embedded Alamouti space-time codes for high rate and low decoding complexity

Abstract

-We introduce a new family of space-time codes called embedded Alamouti space-time (EAST) codes which offer high rate, a nonvanishing determinant and low decoding complexity. The family is parameterized by both the number of transmit antennas, which can range from two to eight, and by the rate, which can range from one to half the number of transmit antennas. The EAST codes combine a modified version of the perfect spacetime codes with an Alamouti embedding. For rates higher than one, the resulting space-time codes are simultaneously lower in decoding complexity and better performing than all known previous constructions in terms of the error probability achieved on a quasistatic Rayleigh fading channel with a given dimension.Index Terms -transmit diversity, space-time coding. I. INTRODUCTIONRecent work in space-time code design has shifted away from increasing the diversity order [1,2] or transmission rate [3] alone to increasing both simultaneously [4][5][6][7][8][9]. The continuous tradeoff between the achievable diversity and multiplexing gains as a function of the signal-to-noise ratio (SNR) was characterized in [10]. The threaded algebraic space-time (TAST) codes of [4] achieve the extremal points of the diversity-multiplexing tradeoff for any number of antennas and arbitrary rates. The perfect space-time codes of [7] achieve the entire frontier of the diversity-multiplexing tradeoff. Perfect space-time codes were originally proposed for only two, three, four and six antennas in [7] and later generalized for any number of antennas in [8].One approach to constructing a high-rate code is to start with a maximal-rate TAST or perfect space-time code and then puncture one or more of its layers. For example, TAST and perfect space-time codes of rate R  {1, 2, 3, 4} are easily obtained by puncturing 4 -R layers of a rate-4 code. Unfortunately, the resulting codes often have a high decoding complexity and worse BER performance than space-time codes that were designed for a particular rate and a particular number of antennas.No previously reported space-time code achieve an arbitrary rate for arbitrary number of antennas while maintaining low decoding complexity. In this paper we partially fill this gap by proposing a framework for the construction and decoding of high rate space-time block codes. In particular, we make three contributions. First, we show that the complex rotation matrices of the perfect spacetime code of [7] can be replaced by equivalent real-valued matrices without affecting the diversity or coding gain; the real matrices lead to lower-complexity decoding. Second, we use the equivalent real generator matrices to construct the embedded Alamouti space-time (EAST) codes, which is a family of codes for any number of antennas up to eight, and for any rate up to half the number of antennas. When compared to previously reported codes with the same number of antennas and the same rate larger than one, the EAST codes are simultaneously lower in complexity and lower in error probability. Lastly, ...

Fast-Group-Decodable STBCs via Codes over GF(4): Further Results

“…Only rates greater than 1 are considered. Comparison is done with EAST (Embedded Alamouti Space-Time) codes from [15], 2-group ML decodable codes from [6] and [7], FD code from [17], FD code from [18] and the FGD code from [3]. The codes constructed in [1] have the same ML decoding complexity as the new codes in Section IV-A.…”

“…The 2 antenna code of [8] is information-lossless and has nonvanishing determinant property. In [15], FD codes for number of antennas N = 2, 4, 6, 8 and rates R = 1, . .…”

Achieving low-complexity maximum-likelihood detection for the 3D MIMO code

“…Recently a lot of efforts have been made in the STBC design to obtain both high code rate and low decoding complexity [5][6][7][8][9][10][11]. The decoding complexity reduction is commonly achieved by exploiting the orthogonality embedded in the STBC codeword.…”

Fast-group-decodable STBCs via codes over GF(4)

“…Only rates higher than 1 are considered. Comparison is done with EAST (Embedded Alamouti Space-Time) codes from [12], 2-group decodable codes from [16], fast-decodable code from [13] and the FGD code from [14]. The entry for 2 antennas with rate 2 and arbitrary constellation is that of the code given in [18] and [19].…”

“…These codes too were fast-decodable. Recently, fast-decodable codes for number of antennas N = 2, 4, 6, 8 were given in [12]. In [13], a rate 3/2 fast-decodable code for 4 antennas was given.…”