Diversity performance of precoded orthogonal space-time block codes using limited feedback

Orthogonal space-time block codes (OSTBCs) are simple space-time codes that can be used for open-loop transmit diversity systems. OSTBCs, however, can only be designed for certain numbers of transmit antennas. Channel-dependent linear precoders have been proposed to overcome this deficiency, but it is not clear what conditions the precoder design must satisfy to guarantee full diversity order. In this letter, we show necessary and sufficient conditions for linear precoded OSTBCs to provide full diversity order. We show that limited feedback precoding can achieve full diversity order using fewer bits than limited feedback beamforming. We also present a simplified version of antenna subset selection for OSTBCs that can provide full diversity order with low complexity and only a small amount of feedback.     

Real-valued maximum likelihood decoder for quasi-orthogonal space-time block codes

In this letter, we propose a low complexity Maximum Likelihood (ML) decoding algorithm for quasi-orthogonal space-time block codes (QOSTBCs) based on the real-valued lattice representation and QR decomposition. We show that for a system with rate r = n_s/T, where n_s is the number of transmitted symbols per T time slots; the proposed algorithm decomposes the original complex-valued system into a parallel system with n_s 2 × 2 real-valued components, thus allowing for a simple joint decoding of two real symbols. For a square QAM constellation with L points (L-QAM), this algorithm achieves full diversity by properly incorporating two-dimensional rotation using the optimal rotation angle and the same rotating matrix for any number of transmit antennas (N ⩾4). We show that the complexity gain becomes greater when N or L becomes larger. The complexity of the proposed algorithm is shown to be linear with the number of transmitted symbols n_s.     

On channel orthogonalization using space-time block coding with partial feedback

Orthogonal space-time block codes (OSTBCs) yield full diversity gain even while requiring only a linear receiver. Such full-rate (rate-one) orthogonal designs are available for complex symbol constellations only for N=2 transmit antennas. In this paper, we propose a new family of full-rate space-time block codes (STBCs) using a single parameter feedback for communication over Rayleigh fading channels for N=3,4 transmit antennas and M receive antennas. The proposed rate-one codes achieve full diversity, and the performance is similar to maximum receiver ratio combining. The decoding complexity of these codes are only linear even while performing maximum-likelihood decoding. The partial channel information is a real phase parameter that is a function of all the channel gains, and has a simple closed-form expression for N=3,4. This feedback information enables us to derive (channel) orthogonal designs starting from quasi-orthogonal STBCs. The feedback complexity is significantly lower than conventional closed-loop transmit beamforming. We compare the proposed codes with the open-loop OSTBCs and also with the closed-loop equal gain transmission (EGT) scheme which uses equal power loading on all antennas. Simulated error-rate performances indicate that the proposed channel orthogonalized STBCs significantly outperform the open-loop orthogonal designs, for the same spectral efficiency. Moreover, even with significantly lower feedback and computational complexity, the proposed scheme outperforms the EGT technique for M>N.     

Fast generalized minimum-distance decoding of algebraic-geometryand Reed-Solomon codes

Generalized minimum-distance (GMD) decoding is a standard soft-decoding method for block codes. We derive an efficient general GMD decoding scheme for linear block codes in the framework of error-correcting pairs. Special attention is paid to Reed-Solomon (RS) codes and one-point algebraic-geometry (AG) codes. For RS codes of length n and minimum Hamming distance d the GMD decoding complexity turns out to be in the order O(nd), where the complexity is counted as the number of multiplications in the field of concern. For AG codes the GMD decoding complexity is highly dependent on the curve in consideration. It is shown that we can find all relevant error-erasure-locating functions with complexity O(o₁nd), where o₁ is the size of the first nongap in the function space associated with the code. A full GMD decoding procedure for a one-point AG code can be performed with complexity O(dn²)     

Full Rate Space Time Codes for Large Number of Transmitting Antennas with Linear Complexity Decoding

Among the specification of the 5G networks two crucial aspects are the support of fast mobility and high data rates. With fast mobility, the fading channels phenomenon become crucial, resulting in the need for multiple input/output channel to create spatial diversity. Space time codes (STC) have been shown to be well used with the Multiple Input Multiple Output channel. The Orthogonal STC (OSTC) family of codes is known to achieve full diversity as well as very simple implementation of the Maximum Likelihood (ML) decoder. However, it was also proven that with a complex symbol constellation one cannot achieve a full rate code when the number of transmitting antennas is larger than two. Quasi-OSTC (QSTC) can have full rate even for more than two transmitting antennas but with the penalty of decoding complexity which becomes severe if the constellation size is large. In order to tackle this inherent drawback of the OSTC/QSTC and to be able to support the 5G high data rate demand, we have come up with a different STC code that, when used with a new transmission and decoding methods, achieves full rate while maintaining linear complexity decoding for any number of transmit antennas. It can also be shown that when the transmitter knows the strongest channel (through minimal feedback) the code also achieves full diversity along with better error rate than the OSTC and the QSTC.     

Space-time multiplexing for mimo multiuser downlink channels

In this paper, we study the downlink of a multiuser system, in which antenna arrays are employed at both the transmitter (base station) and the receivers (clients). A space-time modulation technique that can be seen as two-dimensional spreading is introduced. It provides full transmit diversity for every user, and accommodates N_t times the number of users as a single-antenna code-division multi-access (CDMA) scheme, where N_t is the number of transmit antennas. Thus multiple access is provided through spatial as well as code dimensions. In addition, the scheme forms groups of users that are orthogonal to each other. This feature translates into simplified detection strategies without loss of performance. The main detector structure of interest is a two-stage interference canceller because of its low complexity compared to other joint detectors. We will demonstrate that in conjunction with an unequal power allocation scheme, this receiver provides full diversity and suffers from only a small performance loss compared to the full-complexity maximum likelihood (ML) receiver. In a single-user multiple antenna system, the same spreading scheme and unequal power allocation yields a new approach to designing full-rate, full-diversity space-time codes having good performance with successive interference cancellers     

Efficient Decoding for Generalized Quasi-Orthogonal Space–Time Block Codes

Space–time coding can achieve transmit diversity and power gain over spatially uncoded systems without sacrificing bandwidth. There are various approaches in coding structures, including space–time block codes. A class of space–time block codes namely quasi-orthogonal space–time block codes can achieve the full rate, but the conventional decoders of these codes experience interference terms resulting from neighboring signals during signal detection. The presence of the interference terms causes an increase in the decoder complexity and a decrease in the performance gain. In this article, we propose a modification to the conventional coding/decoding scheme that will improve performance, reduce decoding complexity, and improve robustness against channel estimation errors as well.     

Extending orthogonal block codes with partial feedback

During the last few years a number of space-time block codes have been proposed for use in multiple transmit antennas systems. We propose a method to extend any space-time code constructed for m transmit antennas to m p transmit antennas through group-coherent codes (GCCs). GCCs make use of very limited feedback from the receiver (as low as 1 bit). In particular the scheme can be used to extend any orthogonal code (e.g., Alamouti code) to more than two antennas while preserving low decoding complexity, full diversity benefits, and full data rate.     

Adaptive Channel‐Matched Extended Alamouti Space‐Time Code Exploiting Partial Feedback

Since the publication of Alamouti's famous space‐time block code, various quasi‐orthogonal space‐time block codes (QSTBC) for multi‐input multi‐output (MIMO) fading channels for more than two transmit antennas have been proposed. It has been shown that these codes cannot achieve full diversity at full rate. In this paper, we present a simple feedback scheme for rich scattering (flat Rayleigh fading) MIMO channels that improves the coding gain and diversity of a QSTBC for 2ⁿ (n = 3, 4,…) transmit antennas. The relevant channel state information is sent back from the receiver to the transmitter quantized to one or two bits per code block. In this way, signal transmission with an improved coding gain and diversity near to the maximum diversity order is achieved. Such high diversity can be exploited with either a maximum‐likelihood receiver or low‐complexity zero‐forcing receiver.     

Continuous Phase Modulation and Space-Time Coding: A Candidate for Wireless Robotics

The physical layer(s) of wireless robotics take advantage of current standards, like Bluetooth, Wifi, etc., each of them addressing a specific segment of wireless robotics. Wireless robotics has a wide range of needs, comprising low power, robustness and high data rate when video is used as well as the opportunity to use a large number of transceivers. To cover these needs and take benefit from these opportunities, we propose a new physical layer, based on continuous phase modulation (CPM) and space-time coding. CPM, already used in some standards like GSM and Bluetooth, enables the development of low power devices, but presents a low spectral efficiency. Space-time coding on the other hand yields high spectral efficiency as well as enhanced robustness against the wireless channel. Moreover, space-time coding can take benefit of the large number of transceivers using cooperative communications. In this paper, after analysing the opportunities given by wireless robotics as well as its specific needs, we propose a new physical layer based on L ²-orthogonality for non-linear space-time codes. L ²-orthogonality of our codes is ensured by a bank of phase correction functions, maintaining phase continuity, but at the same time enabling low complexity decoding. We show that the code achieves full diversity and has full rate, for any number of transmit/receive antennas and any CPM parameter.     

Space-time turbo codes with full antenna diversity

In attempting to find a spectrally and power efficient channel code which is able to exploit maximum diversity from a wireless channel whenever available, we investigate the possibility of constructing a full antenna diversity space-time turbo code. As a result, both three-antenna and two-antenna (punctured) constructions are shown to be possible and very easy to find. To check the decodability and performance of the proposed codes, we derive non-binary soft-decoding algorithms. The performance of these codes are then simulated and compared with two existing space-time convolutional codes (one has minimum worst-case symbol-error probability; the other has maximal minimum free distance) having similar decoding complexity. As the simulation results show, the proposed space-time turbo codes give similar or slightly better performance than the convolutional codes under extremely slow fading. When fading is fast, the better distance spectra of the turbo codes help seize the temporal diversity. Thus, the performance advantage of the turbo codes becomes evident. In particular, 10^-5 bit-error rate and 10^-3 frame-error rate can be achieved at less than 6-dB E_b/N₀ with 1 b/s/Hz and binary phase-shift keying modulation. The practical issue of obtaining the critical channel state information (CSI) is also considered by applying an iteratively filtered pilot symbol-assisted modulation technique. The penalty when the CSI is not given a priori is about 2-3 dB     

合作通信中四次群最大似然可译分布空时编码

基于Jing-Hassibi的合作分集协议和Rajan等人的普通非正交放大传送（GNAF）协议,提出了具有完全分集和最大似然译码复杂度低的分布空时编码（DSTC）。这些编码是四次群最大似然可译分布空时编码,并且功率在中继之间随时间均匀分布。仿真结果显示这种编码具有较好的性能。     

Design of Spherical Lattice Space–Time Codes

In this paper, we propose a systematic procedure for designing spherical lattice (space–time) codes. By employing stochastic optimization techniques we design lattice codes which are well matched to the fading statistics as well as to the decoder used at the receiver. The decoders we consider here include the optimal albeit of highest decoding complexity maximum-likelihood (ML) decoder, the suboptimal lattice decoders, as well as the suboptimal lattice-reduction-aided (LRA) decoders having the lowest decoding complexity. For each decoder, our design methodology can be tailored to obtain low error-rate lattice codes for arbitrary fading statistics and signal-to-noise ratios (SNRs) of interest. Further, we obtain fundamental lower bounds on the error probabilities yielded by lattice and LRA decoders and characterize their asymptotic behavior.      

Feedback Capacity of the Compound Channel

In this work, we find the capacity of a compound finite-state channel (FSC) with time-invariant deterministic feedback. We consider the use of fixed length block codes over the compound channel. Our achievability result includes a proof of the existence of a universal decoder for the family of FSCs with feedback. As a consequence of our capacity result, we show that feedback does not increase the capacity of the compound Gilbert-Elliot channel. Additionally, we show that for a stationary and uniformly ergodic Markovian channel, if the compound channel capacity is zero without feedback then it is zero with feedback. Finally, we use our result on the FSC to show that the feedback capacity of the memoryless compound channel is given by inf_thetas max_QX I(X; Y |thetas).     

Superimposed codes based on punctured convolutional codes

Punctured convolutional codes of rates k₁/n and k₂ /n are applied to |u|u+v construction, and then a superimposed code of rate (k₁+k₂)/(2n) is constructed. A suboptimal decoding procedure is presented for the superimposed codes, and it reduces the decoding complexity as compared with maximum likelihood decoding for the known convolutional codes     

Fountain Codes Over GF(q)

Binary fountain codes such as Luby transform codes are a class of erasure codes which have demonstrated an asymptotic performance close to the Shannon limit when decoded with the belief propagation algorithm. When these codes are generalized to GF(q) for q > 2, their performance approaches the Shannon limit much faster than the usual binary fountain codes. In this paper, we extend binary fountain codes to GF(q). In particular, we generalize binary Luby transform codes to GF(q) to develop a low complexity maximum likelihood decoder. The proposed codes have numerous advantages, including low coding overhead, low encoding and decoding complexity, and good performance over various message block lengths, making them practical for real‐time applications. Copyright © 2011 John Wiley & Sons, Ltd.     

Two 16-state, rate R=2/4 trellis codes whose free distances meetthe Heller bound

For rate R=1/2 convolutional codes with 16 states there exists a gap between Heller's (1968) upper bound on the free distance and its optimal value. This article reports on the construction of 16-state, binary, rate R=2/4 nonlinear trellis and convolutional codes having d _free=8; a free distance that meets the Heller upper bound. The nonlinear trellis code is constructed from a 16-state, rate R=1/2 convolutional code over Z₄ using the Gray map to obtain a binary code. Both convolutional codes are obtained by computer search. Systematic feedback encoders for both codes are potential candidates for use in combination with iterative decoding. Regarded as modulation codes for 4-PSK, these codes have free squared Euclidean distance d_{E, free}²=16     

Error rate estimation of low-density parity-check codes on binary symmetric channels using cycle enumeration

The performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms can be accurately estimated if the weight J and the number |E_J| of the smallest error patterns that cannot be corrected by the decoder are known. To obtain J and |E_J|, one would need to perform the direct enumeration of error patterns with weight ι ⩽ J. The complexity of enumeration increases exponentially with J, essentially as η^J, where η is the code block length. This limits the application of direct enumeration to codes with small η and J. In this letter, we approximate J and |E_J | by enumerating and testing the error patterns that are subsets of short cycles in the code's Tanner graph. This reduces the computational complexity by several orders of magnitude compared to direct enumeration, making it possible to estimate the error rates for almost any practical LDPC code. To obtain the error rate estimates, we propose an algorithm that progressively improves the estimates as larger cycles are enumerated. Through a number of examples, we demonstrate that the proposed method can accurately estimate both the bit error rate (BER) and the frame error rate (FER) of regular and irregular LDPC codes decoded by a variety of hard-decision iterative decoding algorithms.     

Video transmission over mobile satellite systems

Mobile satellite communication channels are characterized by long transmission delays, variation of these delays, high bit‐error‐rates, shadowing and the multipath effect which severely reduce the quality of video services. Error control techniques including feedback mechanisms, error concealment methods, forward error correction techniques and error resilience schemes are examined in this paper for achieving a high‐integrity video transmission over a mobile satellite channel. The application of three different error resilience algorithms, namely Turbo codes, error‐resilient entropy codes and two‐way decoding using reversible codes is presented. Their joint performance is also examined. Furthermore, a low‐delay and low‐complexity video transcoding algorithm which fully interconnects two very low bit rate video communication standards: MPEG‐4 and H.263 is also elaborated. This transcoder works as a gateway tool which links two heterogeneous multimedia networks, such as a mobile satellite network and a land‐based network, with negligible processing delay and complexity. Copyright © 2000 John Wiley & Sons, Ltd.     

Cooperative Transmission Using Quasi-Orthogonal Space-Time Block Codes with Adaptive Decode-and-Forward Relaying Protocol

In this paper, we propose a cooperative transmission scheme using quasi-orthogonal space-time block codes (QOSTBCs) for multiple-input multiple-output (MIMO) relay networks. Comparing with the conventional cooperative transmission scheme using orthogonal space-time block codes (OSTBCs), the proposed scheme can achieve higher bandwidth efficiency with the same decoding complexity. Moreover, an adaptive decode-and-forward (ADF) relaying protocol is proposed based on one-bit channel state information (CSI) feedback. According to the CSI feedback, a better transmission mode can be selected between the direct transmission and decode-and-forward (DF) cooperative transmission. In addition, the outage performance of the proposed scheme is investigated and a closed-form upper bound on the outage probability is derived. The performance analysis shows that the proposed scheme can achieve a full diversity order, which is higher than that of the direct and DF cooperative transmissions.