Golden Space-Time Trellis Coded Modulation

In this paper, we present a concatenated coding scheme for a high rate $2\times 2$ multiple-input multiple-output (MIMO) system over slow fading channels. The inner code is the Golden code \cite{Golden05} and the outer code is a trellis code. Set partitioning of the Golden code is designed specifically to increase the minimum determinant. The branches of the outer trellis code are labeled with these partitions. Viterbi algorithm is applied for trellis decoding. In order to compute the branch metrics a lattice sphere decoder is used. The general framework for code optimization is given. The performance of the proposed concatenated scheme is evaluated by simulation. It is shown that the proposed scheme achieves significant performance gains over uncoded Golden code.Comment: 33 pages, 13 figure

Golden Coded Multiple Beamforming

The Golden Code is a full-rate full-diversity space-time code, which achieves maximum coding gain for Multiple-Input Multiple-Output (MIMO) systems with two transmit and two receive antennas. Since four information symbols taken from an M-QAM constellation are selected to construct one Golden Code codeword, a maximum likelihood decoder using sphere decoding has the worst-case complexity of O(M^4), when the Channel State Information (CSI) is available at the receiver. Previously, this worst-case complexity was reduced to O(M^(2.5)) without performance degradation. When the CSI is known by the transmitter as well as the receiver, beamforming techniques that employ singular value decomposition are commonly used in MIMO systems. In the absence of channel coding, when a single symbol is transmitted, these systems achieve the full diversity order provided by the channel. Whereas this property is lost when multiple symbols are simultaneously transmitted. However, uncoded multiple beamforming can achieve the full diversity order by adding a properly designed constellation precoder. For 2 \times 2 Fully Precoded Multiple Beamforming (FPMB), the general worst-case decoding complexity is O(M). In this paper, Golden Coded Multiple Beamforming (GCMB) is proposed, which transmits the Golden Code through 2 \times 2 multiple beamforming. GCMB achieves the full diversity order and its performance is similar to general MIMO systems using the Golden Code and FPMB, whereas the worst-case decoding complexity of O(sqrt(M)) is much lower. The extension of GCMB to larger dimensions is also discussed.Comment: accepted to conferenc

Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels

The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading MIMO channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upperbound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders, called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension. With turbo codes, they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January 2006 - First review: June 200

Generalized space-time shift keying designed for flexible diversity-, multiplexing- and complexity-tradeoffs

In this paper, motivated by the recent concept of Spatial Modulation (SM), we propose a novel Generalized Space-Time Shift Keying (G-STSK) architecture, which acts as a unified Multiple-Input Multiple-Output (MIMO) framework. More specifically, our G-STSK scheme is based on the rationale that P out of Q dispersion matrices are selected and linearly combined in conjunction with the classic PSK/QAM modulation, where activating P out of Q dispersion matrices provides an implicit means of conveying information bits in addition to the classic modem. Due to its substantial flexibility, our G-STSK framework includes diverse MIMO arrangements, such as SM, Space-Shift Keying (SSK), Linear Dispersion Codes (LDCs), Space-Time Block Codes (STBCs) and Bell Lab’s Layered Space-Time (BLAST) scheme. Hence it has the potential of subsuming all of them, when flexibly adapting a set of system parameters. Moreover, we also derive the Discrete-input Continuous-output Memoryless Channel (DCMC) capacity for our G-STSK scheme, which serves as the unified capacity limit, hence quantifying the capacity of the class of MIMO arrangements. Furthermore, EXtrinsic Information Transfer (EXIT) chart analysis is used for designing our G-STSK scheme and for characterizing its iterative decoding convergence

Bit-Interleaved Coded Multiple Beamforming with Perfect Coding

When the Channel State Information (CSI) is known by both the transmitter and the receiver, beamforming techniques employing Singular Value Decomposition (SVD) are commonly used in Multiple-Input Multiple-Output (MIMO) systems. Without channel coding, there is a trade-off between full diversity and full multiplexing. When channel coding is added, both of them can be achieved as long as the code rate Rc and the number of employed subchannels S satisfy the condition RcS<=1. By adding a properly designed constellation precoder, both full diversity and full multiplexing can be achieved for both uncoded and coded systems with the trade-off of a higher decoding complexity, e.g., Fully Precoded Multiple Beamforming (FPMB) and Bit-Interleaved Coded Multiple Beamforming with Full Precoding (BICMB-FP) without the condition RcS<=1. Recently discovered Perfect Space-Time Block Code (PSTBC) is a full-rate full-diversity space-time code, which achieves efficient shaping and high coding gain for MIMO systems. In this paper, a new technique, Bit-Interleaved Coded Multiple Beamforming with Perfect Coding (BICMB-PC), is introduced. BICMB-PC transmits PSTBCs through convolutional coded SVD systems. Similar to BICMB-FP, BICMB-PC achieves both full diversity and full multiplexing, and its performance is almost the same as BICMB-FP. The advantage of BICMB-PC is that it can provide a much lower decoding complexity than BICMB-FP, since the real and imaginary parts of the received signal can be separated for BICMB-PC of dimensions 2 and 4, and only the part corresponding to the coded bit is required to acquire one bit metric for the Viterbi decoder.Comment: accepted to conference; Proc. IEEE ICC 201

Multiple Beamforming with Perfect Coding

Perfect Space-Time Block Codes (PSTBCs) achieve full diversity, full rate, nonvanishing constant minimum determinant, uniform average transmitted energy per antenna, and good shaping. However, the high decoding complexity is a critical issue for practice. When the Channel State Information (CSI) is available at both the transmitter and the receiver, Singular Value Decomposition (SVD) is commonly applied for a Multiple-Input Multiple-Output (MIMO) system to enhance the throughput or the performance. In this paper, two novel techniques, Perfect Coded Multiple Beamforming (PCMB) and Bit-Interleaved Coded Multiple Beamforming with Perfect Coding (BICMB-PC), are proposed, employing both PSTBCs and SVD with and without channel coding, respectively. With CSI at the transmitter (CSIT), the decoding complexity of PCMB is substantially reduced compared to a MIMO system employing PSTBC, providing a new prospect of CSIT. Especially, because of the special property of the generation matrices, PCMB provides much lower decoding complexity than the state-of-the-art SVD-based uncoded technique in dimensions 2 and 4. Similarly, the decoding complexity of BICMB-PC is much lower than the state-of-the-art SVD-based coded technique in these two dimensions, and the complexity gain is greater than the uncoded case. Moreover, these aforementioned complexity reductions are achieved with only negligible or modest loss in performance.Comment: accepted to journa

Cyclic division algebras: a tool for space-time coding

Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space–Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes