General differential modulation scheme for quasi-orthogonal space?time block codes with partial or full transmit diversity

A general and simple differential modulation scheme that can be applied to both partial-diversity quasi-orthogonal space-time block codes and full-diversity quasi-orthogonal space-time block codes is reported. A new class of quasi-orthogonal coding structures is presented for various number of transmit antennas. Differential encoding and decoding can be simplified to differential Alamouti codes by grouping the signals in the transmitted matrix and decoupling the detection of data symbols, respectively. For the codes with partial transmit diversity, the new scheme can achieve constant amplitude of transmitted signals, and avoid signal constellation expansion; in addition, it has a linear signal detector with very low complexity. Simulation results show that these partial-diversity codes can provide very useful results at low signal-to-nose ratio for current communication systems. For codes with full transmit diversity achieved by constellation rotation, the proposed scheme has performance equal to the best full-rate quasi-orthogonal schemes previously described in the literature with the benefit of a simpler detector. Moreover, a simple linear detector is also presented for the case when two orthogonal ASK constellations are used. Extension to more than four transmit antennas is also considered.     

Optimising quasi-orthogonal STBC through group-constrained linear transformation

The generic algebraic structure of a quasi-orthogonal space-time block code (QO-STBC) has been derived, and group-constrained linear transformation (GCLT) as a mean to optimise the diversity and coding gains of a QO-STBC with square or rectangular QAM constellations has been proposed. Compared with QO-STBC with constellation rotation (CR), QO-STBC with GCLT requires only half the number of symbols for joint detection, hence lower maximum-likelihood decoding complexity. The optimum GCLT parameters for QO-STBC with square QAM constellation have been derived analytically. The optimised QO-STBCs with GCLT are able to achieve full-transmit diversity and have negligible performance loss compared with QO-STBCs with CR at the same code rate     

DC-free trellis-based error-control codes

Trellis-based error-control (EC) codes, such as convolutional or turbo codes, are integrated with guided scrambling (GS) multimode coding to generate DC-free GS-convolutional/ turbo codes. On the basis of the generators of the convolutional/turbo code, we employ puncturing or flipping to ensure that the EC-coded sequences are DC-free. At the receiver, convolutional/turbo decoding is performed before GS decoding to circumvent the performance degradation that can occur when GS decoding is performed prior to EC decoding. Performance of the new DC-free GS-convolutional/turbo codes is evaluated in terms of both spectral suppression and bit error rate (BER). It is shown that the new codes can provide superior BER performance and approximately the same suppression of low frequencies as the conventional concatenation of convolutional/turbo codes and DC-free GS codes.     

Improving the performance of mobile broadcasting systems using multiple base stations and distributed space?time codes

Error performance of distributed space-time codes used for mobile broadcasting systems consisting of multiple base stations is analysed. The base stations are assumed to operate in a simulcast mode, that is they simultaneously transmit the same message using the same carrier frequency. Mobile users within the intersection of the coverage areas, thus, enjoy a small probability of shadowing and a high probability of at least one line-of-sight (LOS) link. In effect, the base stations establish a virtual multiple-antenna system. The use of a distributed space-time code offers an additional spatial diversity gain. Considering a single user with a fixed (random) position, the impact of shadowing and LOS components on the error performance of the system is analysed and compared with a conventional multiple-antenna system with co-located transmit antennas. Specifically, the analysis shows that already a single LOS link significantly improves the overall system performance. In the case of shadowing, huge diversity gains are obtained in the distributed system. In a system with co-located transmitters, however, the performance improvements compared with a single-antenna system are rather small, when shadowing is taken into account. Altogether, it can be concluded that systems with distributed transmitters are typically superior to conventional multiple-antenna systems (due to macroscopic diversity), and that distributed space-time codes are superior to conventional simulcasting (due to microscopic diversity)     

码率嵌入式高码率差分空时编码

为了提高传输码率,将具有高码率的全分集全码率(FDFR)空时码嵌入到低码率的传统差分空时编码中,提出了一种码率嵌入式的差分空时编码方法,该编码方案具有编码增益高,误码性能好等优点.仿真结果表明,与传统的差分空时编码方案(酉差分空时编码和差分空时分组编码)相比,新编码方法具有很好的误码性能,特别是在高传输码率和接收天线较多情况下,其误码性能优势越明显.     

Differentially coherent code acquisition in the MIMO-aided multi-carrier DS-CDMA downlink

Both differentially coherent and non-coherent code acquisition schemes designed for the multiple-input multiple-output (MIMO)-aided multi-carrier (MC)-DS-CDMA downlink are analysed, when communicating over uncorrelated Rayleigh channels. The attainable mean acquisition time (MAT) performance is studied as a function of both the number of multiple transmit/multiple receive antennas and that of the number of subcarriers. It is demonstrated that in contrast to the expectations, when the number of multiple transmit antennas and/or that of the subcarriers is increased in both the differentially coherent and the non-coherent code acquisition scenarios, the achievable MAT deteriorates over the entire signal-to-interference plus noise ratio (SINR) per chip (E_c/I_o) range considered, except for the scenario of single-carrier (SC)-DS-CDMA using P = 2 transmit antennas and R = 1 receive antenna. As expected, the degree of performance degradation depends upon the specific scheme and the E_c/I_o ratio considered, although paradoxically, the correctly synchronised MIMO-aided system is capable of attaining its target bit error ratio performance at reduced SINR values.     

Low-density parity-check codes for volume holographic memory systems

We investigate the application of low-density parity-check (LDPC) codes in volume holographic memory (VHM) systems. We show that a carefully designed irregular LDPC code has a very good performance in VHM systems. We optimize high-rate LDPC codes for the nonuniform error pattern in holographic memories to reduce the bit error rate extensively. The prior knowledge of noise distribution is used for designing as well as decoding the LDPC codes. We show that these codes have a superior performance to that of Reed-Solomon (RS) codes and regular LDPC counterparts. Our simulation shows that we can increase the maximum storage capacity of holographic memories by more than 50 percent if we use irregular LDPC codes with soft-decision decoding instead of conventionally employed RS codes with hard-decision decoding. The performance of these LDPC codes is close to the information theoretic capacity.     

Concatenated bit-interleaved coded modulation and orthogonal space-time block codes over fading channels

The authors analyse concatenated bit-interleaved coded modulation and orthogonal space-time block codes (OSTBC) over fading channels in the absence and presence of channel state information (CSI) in receiver. The authors derive analytical expressions for bit and frame error probabilities based on which corresponding designing rules are proposed. The analytical results are for arbitrary rate of constituent STBC and arbitrary convolutional code, and for CSI-aware receiver is for any number of transmit and receive antennas. Simulation results are presented to confirm the validity of the proposed designing rules. Moreover, the simulation results show that the proposed system outperforms concatenated trellis coded modulation and OSTBC.     

Hybrid detectors for wireless orthogonal frequency division multiplexing with code division multiplexing systems based on reliability information

Orthogonal frequency division multiplexing with code division multiplexing (OFDM-CDM) is attractive for the next generation high-speed wireless systems due to the fact that the performance of OFDM-CDM systems can be considerably improved by employing a joint detection scheme such as the maximum likelihood (ML) detector. However, the complexity of the ML detector increases rapidly as the number of orthogonal spreading codes and/or the number of bits per modulation symbol increase. In this study, the authors introduce a unified detection model and propose two hybrid detectors, which combine zero forcing (ZF) with successive interference cancellation (SIC) and sphere detection (SD) algorithms, respectively. After obtaining the initial solution from the front-end ZF receiver, the proposed back-end algorithms are adopted to extend the potential solution list and search for the final result. The objective is to utilise the combination of a simplified linear equaliser and a comprehensive detection scheme to achieve enhanced performance and offer alternatives to the more complex and channel-estimation-sensitive minimum mean squared error (MMSE) scheme. The results show that the proposed hybrid detectors are able to achieve superior performance compared to the MMSE scheme and provides a significant performance improvement compared to the conventional OFDM counterpart.     

Modified sum-product algorithms for decoding low-density parity-check codes

The authors deal with the sum-product algorithm (SPA) based on the hyperbolic tangent (tanh) rule when it is applied for decoding low-density parity-check (LDPC) codes. Motivated by the finding that, because of the large number of multiplications required by the algorithm, an overflow in the decoder may occur, two novel modifications of the tanh function (and its inverse) are proposed. By means of computer simulations, both methods are evaluated using random-based LDPC codes with binary phase shift keying (BPSK) signals transmitted over the additive white Gaussian noise (AWGN) channel. It is shown that the proposed modifications improve the bit error rate (BER) performance up to 1 dB with respect to the conventional SPA. These results have also shown that the error floor is removed at BER lower than 10^-6. Furthermore, two novel approximations are presented to reduce the computational complexity of the tanh function (and its inverse), based on either a piecewise linear function or a quantisation table. It is shown that the proposed approximations can slightly improve the BER performance (up to 0.13 dB) in the former case, whereas small BER performance degradation is observed (<0.25 dB) in the latter case. In both cases, however, the decoding complexity is reduced significantly     

Variable-length two-dimensional modulation coding for imaging page-oriented optical data storage systems

We present what is to our knowledge a new class of two-dimensional (2-D) modulation codes, called variable-length 2-D modulation codes, suitable for page-oriented optical data storage (PODS) systems that write and read data in a 2-D bit image format. These codes overcome the inherent spatial intersymbol interference in imaging PODS systems and improve the code rate performance of previous fixed-length 2-D modulation codes. The codes in this new class map one-dimensional input data blocks of variable lengths to 2-D output data blocks of variable lengths and are designed to limit error propagation. In this study we give several examples of fixed-length and variable-length 2-D modulation codes with various properties for imaging PODS systems. We also compare the bit-error-rate performance of these fixed-length and variable-length codes.     

The synthesis of magnetic recording trellis codes with good hamming distance properties

In this paper we present, by means of an example, a systematic procedure to synthesize combined modulation/error correcting trellis codes, suitable for Viterbi decoding. This synthesis is based on firstly selecting a suitable linear convolutional code, secondly by analysing the state system of this code to determine the important Hamming distance building properties, and finally by mapping a code with the desired restrictions on its sequences onto this state system. As an example we develop a R = 3/6 dc free (b,l,c) = (0,3,2) code withd_{min} = 4. This code improves on the best codes in [1]. Codes havingb geq 1, and which will thus be more suitable for magnetic recording, can also be synthesized following the proposed procedure.     

Super-orthogonal space-time-frequency trellis coded OFDM

Super-orthogonal space-time trellis codes (SOSTTCs) given in the literature are full rate and provide full spatial diversity with high coding gain in narrowband quasistatic fading channels. The high number of parallel transitions in their trellis structure restricts their performance in wideband channels where the code performance suffers from multipath. Code design criteria are derived and a computer search based method is proposed to design full-rate optimised SOSTTCs exploiting full spatial and multipath diversity for multiple-input multiple-output orthogonal frequency division multiplexing systems. The proposed codes have codewords defined in space, time, and frequency. We evaluate the codeword error rates of the new 16, 32 and 64-state super-orthogonal space-time-frequency trellis codes for quadrature phase shift keying by computer simulation and show that they provide significant error performance improvement compared to their counterparts with equivalent delay length     

平坦快衰落条件下天线数较多时空时格码的设计

空时格码技术是近年来无线通信领域的一个研究热点，空时格码的设计准则问题一直是该技术的一个难点。在平坦快衰落条件下且天线数目较多时，基于最小平方欧式距离最大化的空时格码设计准则虽然优于经典的距离－积准则，但仍不完善。从平方距离分布与平方距离和方－方和比分布的角度对此进行了改进，得到改进的准则以及性能为目前最优的新码。还对快慢2种衰落条件下码性能差异的原因给出了新的解释，并将改进的码设计准则应用于智贪码的设计。     

Performance of Reed?Solomon codes using the Guruswami?Sudan algorithm with improved interpolation efficiency

List decoding is a novel method for decoding Reed-Solomon (RS) codes that generates a list of candidate transmitted messages instead of one unique message as with conventional algebraic decoding, making it possible to correct more errors. The Guruswami-Sudan (GS) algorithm is the most efficient list decoding algorithm for RS codes. Until recently only a few papers in the literature suggested practical methods to implement the key steps (interpolation and factorisation) of the GS algorithm that make the list decoding of RS codes feasible. However, the algorithm's high decoding complexity is unsolved and a novel complexity-reduced modification to improve its efficiency is presented. A detailed explanation of the GS algorithm with the complexity-reduced modification is given with simulation results of RS codes for different list decoding parameters over the AWGN and Rayleigh fading channels. A complexity analysis is presented comparing the GS algorithm with our modified GS algorithm, showing the modification can reduce complexity significantly in low error weight situations. Simulation results using the modified GS algorithm show larger coding gains for RS codes with lower code rates, with more significant gains being achieved over the Rayleigh fading channels.     

List decoding of repeated codes

Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to their parameters, we show that they have a good performance with this algorithm. We compare, by computer simulations, our algorithm for the repeated code of a Reed–Solomon code against a decoding algorithm of a Reed–Solomon code. Finally, we estimate the decoding capability of the algorithm for Reed–Solomon codes and show that performance is somewhat better than our estimates.     

Frequency-hopping optical orthogonal codes with arbitrary time-blank patterns

We investigate a general scheme of frequency-hopping optical orthogonal codes with a specified distance between adjacent frequency symbols and propose a novel code that allows time blanks between adjacent frequency symbols in code sequences. A time blank represents the absence of frequency symbols in code sequences and makes no interference with frequency components. The insertion of time-blank patterns can provide ample scope to generate much more code sequences than the conventional codes lacking in time-blank patterns, and we show this by constructing an algorithm to generate the proposed code. The performance analysis demonstrates that its performance is superior to that of the conventional codes in terms of the bit error rate. We also derive the upper bound on the proposed code set.     

Performance of differential pulse-position modulation (DPPM) with concatenated coding over optical wireless communications [optical wireless communications]

The concatenation of marker and Reed-Solomon codes in order to correct insertion/ deletion errors in differential pulse-position modulation (DPPM) over optical wireless communications is presented. The concatenated code decoding algorithms with hard-decision and soft-decision detection are presented. The performance of the hard-decision coded DPPM system is evaluated over both nondispersive and dispersive channels via analysis and simulation. It is shown that the coding gain provided by the concatenated code is approximately 4 dB when the code rate is about 0.7 and the channel is nondispersive. Over a dispersive channel, the coded system performs better than the uncoded system when the ratio of delay spread to bit duration is not high. A soft-decision detector is employed to combat intersymbol interference. The soft- decision decoding algorithm, which has low complexity and can be practically implemented, is described. The performance over nondispersive and dispersive channels is evaluated by analysis and simulation. It is shown that the soft-decision system requires approximately 2 dB less transmit power than the hard-decision system for additive white Gaussian noise and low-dispersive channels. Soft decoding also provides a performance improvement in high-dispersive channels.     

Maximum-girth slope-based quasi-cyclic (2, k ⩾ 5) low-density parity-check codes

A class of maximum-girth geometrically structured regular (n, 2, k ⩾ 5) (column-weight 2 and rowweight k) quasi-cyclic low-density parity-check (LDPC) codes is presented. The method is based on cylinder graphs and the slope concept. It is shown that the maximum girth achieved by these codes is 12. A lowcomplexity algorithm producing all such maximum-girth LDPC codes is given. The shortest constructed code has a length of 105. The minimum length n of a regular (2, k) LDPC code with girth g ? 12 determined by the Gallager bound has been achieved by the constructed codes. From the perspective of performance these codes outperform the column-weight 2 LDPC codes constructed by the previously reported methods. These codes can be encoded using an erasure decoding process.     

SISO algorithms based on Max-Log-MAP and Log-MAP turbo decoding

Novel soft-input soft-output (SISO) decoding algorithms suitable for turbo codes are proposed with good compromise between complexity and bit error rate (BER) performance. The algorithms are based on the application of the max/max* (i.e. Jacobian logarithm) operations at different levels when computing the decoder soft-output value. It is observed that some decoding schemes from the authors' previously published work fall into the family of methods described here. The effect is to provide a range of possibilities allowing system designers to make their own choices for turbo code BER performance against complexity