Family Of Space-time Block Codes Research Articles

Quantum Codes in Classical Communication: A Space-Time Block Code From Quantum Error Correction

We propose a general framework for noncoherent communication using techniques from the field of quantum error correction (QEC). We first propose an approach for analyzing a classical communication channel as a quantum channel, and develop an extension of the QEC conditions to the classical case. We derive a quantum analogue of the noncoherent multiantenna wireless channel. Restricting to the case in which the number of transmitter and receiver antennas are equal and a power of two, we use the framework to develop a family of space-time block codes for noncoherent multiple-input multiple-output (MIMO) communication. Under a Rayleigh fading assumption, we derive the optimal decoder and bound the probability of symbol detection error. We compare our performance to comparable coherent and noncoherent approaches and achieve competitive performance for various antenna geometries and rates.

Asymptotically-Good, Multigroup Decodable Space-Time Block Codes

For a family of Space-Time Block Codes (STBCs) C1, C2, ... , with increasing number of transmit antennas Ni, with rates Ri complex symbols per channel use, i = 1, 2, ... , we introduce the notion of asymptotic normalized rate which we define as limi→∞ Ri/Ni , and we say that a family of STBCs is Ri asymptotically-good if its asymptotic normalized rate is non-zero, i.e., when the rate scales as a non-zero fraction of the number of transmit antennas. An STBC C is said to be g-group decodable, g ≥ 2, if the information symbols encoded by it can be partitioned into g groups, such that each group of symbols can be ML decoded independently of the others. In this paper we construct full-diversity g-group decodable codes with rates greater than one complex symbol per channel use for all g ≥ 2. Specifically, we construct delay-optimal, g-group decodable codes for number of transmit antennas Nt that are a multiple of g2[g-1/2] with rate Nt/g2g-1 + g2-g/2Nt . Using these new codes as building blocks, we then construct non-delay-optimal g-group decodable codes with rate roughly g times that of the delay-optimal codes, for number of antennas Nt that are a multiple of 2[g-1/2], with delay gNt and rate Nt/2g-1 +g-1/2Nt For each g ≥ 2, the new delay-optimal and nondelay-optimal families of STBCs are both asymptotically-good, with the latter family having the largest asymptotic normalized rates among all known families of multigroup decodable codes with delay T ≤ gNt. Also, for g ≥ 3, these are the first instances of g-group decodable codes with rates greater than 1 reported in the literature.

A New Family of Low-Complexity STBCs for Four Transmit Antennas

Space-Time Block Codes (STBCs) suffer from a prohibitively high decoding complexity unless the low-complexity decodability property is taken into consideration in the STBC design. For this purpose, several families of STBCs that involve a reduced decoding complexity have been proposed, notably the multi-group decodable and the fast decodable (FD) codes. Recently, a new family of codes that combines both of these families namely the fast group decodable (FGD) codes was proposed. In this paper, we propose a new construction scheme for rate-1 FGD codes for 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> transmit antennas. The proposed scheme is then applied to the case of four transmit antennas and we show that the new rate-1 FGD code has the lowest worst-case decoding complexity among existing comparable STBCs. The coding gain of the new rate-1 code is optimized through constellation stretching and proved to be constant irrespective of the underlying QAM constellation prior to normalization. Next, we propose a new rate-2 FD STBC by multiplexing two of our rate-1 codes by the means of a unitary matrix. Also a compromise between rate and complexity is obtained through puncturing our rate-2 FD code giving rise to a new rate-3/2 FD code. The proposed codes are compared to existing codes in the literature and simulation results show that our rate-3/2 code has a lower average decoding complexity while our rate-2 code maintains its lower average decoding complexity in the low SNR region. If a it time-out sphere decoder is employed, our proposed codes outperform existing codes at high SNR region thanks to their lower worst-case decoding complexity.

Space-Time Block Code Designs Based on Quadratic Field Extension for Two-Transmitter Antennas

Space-time block code designs based on algebraic field extension for full rate, large diversity product, and nonvanishing minimum determinant of codewords have received great attention. There are many different types of codes available for two-transmitter antennas, such as cyclotomic space-time block codes, the golden space-time block code, and rotation-based space-time block codes. In this paper, a more general space-time block code design scheme, which is called quadratic space-time block coding, is proposed for the two-transmitter antennas using quadratic field extension. The optimal design of the quadratic space-time block codes in terms of a diversity product criterion is also presented. It is shown that the optimal quadratic space-time block codes designed in this paper do not belong to the existing space-time block code family such as the cyclotomic, golden, and rotation-based space-time block codes. The simulation results demonstrate that the average codeword error rate of the optimal quadratic space-time block code attains about 0.5 dB signal to noise ratio gain over those of the optimal cyclotomic and golden space-time block codes.

Concatenated Alamouti codes using multi-level modulation and symbol mapping diversity technique

A family of space-time block codes (STBCs) for systems with even transmit antennas and any number of receive antennas is proposed. The new codeword matrix is constructed by concatenating Alamouti space-time codes to form a block diagonal matrix, and its dimension is equal to the number of transmit antennas. All Alamouti codes in the same codeword matrix have the same information; thus, full transmit diversity can be achieved over fading channels. To improve the spectral efficiency, multi-level modulations such as multi-quadrature amplitude modulation (M-QAM) are employed. The symbol mapping diversity is then exploited between transmissions of the same information from different antennas to improve the bit error rate (BER) performance. The proposed codes outperform the diagonal algebraic space-time (DAST) codes presented by Damen [Damen et al. IEEE Transactions on Information Theory, 2002, 48(3): 628–636] when they have the same spectral efficiency. Also, they outperform the 1/2-rate codes from complex orthogonal design. Moreover, compared to DAST codes, the proposed codes have a low decoding complexity because we only need to perform linear processing to achieve single-symbol maximum-likelihood (ML) decoding.

A family of space-time block codes achieving full diversity with linear receivers

In this paper, we propose a design scheme for a family of space-time block codes (STBCs) that achieve full diversity when linear receivers, such as zero-forcing (ZF) or minimum mean square error (MMSE) receivers, are used. New STBCs obtained based on this design scheme are characterized by their special structure that combines/overlays orthogonal STBCs (OSTBCs) and Toeplitz codes together, which are called Group Orthogonal-Toeplitz Codes (GOTCs). By choosing different parameters, codes with different symbol rates and orthogonality can be obtained. It is indicated that the existing STBCs achieving full diversity with linear receivers, such as the Toeplitz codes and overlapped Alamouti codes (OACs) recently proposed in the literature and the OSTBCs are three members of the GOTCs with different parameters. It is also shown that the time-reversal space-time block codes (TR-STBCs) and delay diversity codes (DDCs) for frequency selective channels are equivalent to OACs and Toeplitz codes, respectively, and thus they both can achieve full space-frequency diversity with only linear receivers. Furthermore, simulations show that with linear receivers, GOTCs outperforming the above mentioned three codes can be obtained from the proposed design scheme.

Extended balanced space-time block coding for wireless communications

Diversity techniques are very effective tools to increase signal reception quality in Rayleigh fading channels. A well-known method to increase diversity in multi-input multi-output (MIMO) communication is transmit antenna selection (TAS). However, TAS is very sensitive to feedback errors. One of the alternative techniques to TAS is balanced space-time block coding (BSTBC) which guarantees full diversity for any number of transmit antennas, provided that few bits of feedback from the destination to the source are available. The main drawback of the BSTBC is limited coding gain since few numbers of code matrices can be generated in the originally proposed scheme. In this work, the authors extend the balanced space-time block code family to improve its coding performance. In our proposed scheme, larger number of codes can be generated for improved coding gain. The performance of the proposed scheme is investigated for both multi-input single-output (MISO) and cooperative communication cases. Relay selection (RS) algorithm - the TAS equivalent in the cooperative communications - is also considered. Simulation results show that near optimal (infinite feedback) performance can be achieved with four bit extension of the BSTBC and better signal-to-noise ratio can be obtained compared to TAS or RS schemes. The difference in performance becomes more prevalent in the presence of feedback errors.

Space–Time Block Codes Achieving Full Diversity With Linear Receivers

In most of the existing space-time code designs, achieving full diversity is based on maximum-likelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang-Liu-Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zero-forcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang-Liu-Wong's results on Toeplitz codes, in this paper, we propose a design criterion for space-time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol rates of STBC under this criterion are upper bounded by 1. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the 2times2 Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform OSTBC when the number of transmit antennas is above 4.

Space-time error correcting codes

A new space-time block code family for two transmitters, called the space-time error correcting codes (STECCs), is presented. As it is built from any linear forward error correcting code (FEC), a STECC is able to correct errors while achieving high spectral efficiencies. The key principle is the FEC linearity which is exploited to transmit linear combinations of FEC codewords to create a space-time redundancy. The proposed code exhibits interesting performance on an ISI-free block fading channel. This result is all the more true as the number of FEC codewords considered in the combination is high.

Optimal Space–Time Codes for the MIMO Amplify-and-Forward Cooperative Channel

In this work, we extend the nonorthogonal amplify-and-forward (NAF) cooperative diversity scheme to the multiple-input multiple-output (MIMO) channel. A family of space-time block codes for a half-duplex MIMO NAF fading cooperative channel with N relays is constructed. The code construction is based on the nonvanishing determinant (NVD) criterion and is shown to achieve the optimal diversity-multiplexing tradeoff (DMT) of the channel. We provide a general explicit algebraic construction, followed by some examples. In particular, in the single-relay case, it is proved that the Golden code and the 4times4 Perfect code are optimal for the single-antenna and two-antenna cases, respectively. Simulation results reveal that a significant gain (up to 10 dB) can be obtained with the proposed codes, especially in the single-antenna case

Diagonal Block Orthogonal Algebraic Space-Time Block Codes

This paper proposes a new family of space-time block codes whose transmission rate is 1 symbol per channel use. The proposed space-time codes can achieve full transmit diversity with larger coding gain for the constellation carved from the scaled complex integer ring κZ[i]. It is confirmed that the performances of the proposed space-time codes are superior to the existing space-time block codes by our simulation results.

Full-diversity, high-rate space-time block codes from division algebras

We present some general techniques for constructing full-rank, minimal-delay, rate at least one space-time block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algebras of the rational field /spl Qopf/ embedded in matrix rings. The first half of the paper deals with constructions using field extensions of /spl Qopf/. Working with cyclotomic field extensions, we construct several families of STBCs over a wide range of signal sets that are of full rank, minimal delay, and rate at least one appropriate for any number of transmit antennas. We study the coding gain and capacity of these codes. Using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas. We also present a method of constructing STBCs using noncyclotomic field extensions. In the later half of the paper, we discuss two ways of embedding noncommutative division algebras into matrices: left regular representation, and representation over maximal cyclic subfields. The 4/spl times/4 real orthogonal design is obtained by the left regular representation of quaternions. Alamouti's (1998) code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it. Also, we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the STBCs obtained from this construction. Another family of cyclic division algebras discovered by Brauer (1933) is discussed and several examples of STBCs derived from each of these constructions are presented.