Codeword Matrix Research Articles

Golden codeword–based modulation schemes for single‐input multiple‐output systems

SummaryThe Golden code has full rate and full diversity. The Golden codeword matrix contains two pairs of super symbols. Based on one pair of super symbols, two modulation schemes, Golden codeword–based M‐ary quadrature amplitude modulation (GC‐MQAM) and component‐interleaved GC‐MQAM (CI‐GC‐MQAM), are proposed for single‐input multiple‐output (SIMO) systems. Since the complexities of the maximum likelihood detection for the proposed GC‐MQAM and CI‐GC‐MQAM are proportional to O(M2) and O(M4), respectively, low complexity detection schemes for the proposed GC‐MQAM and CI‐GC‐MQAM are further proposed. In addition, the theoretical average bit error probabilities (ABEPs) for the proposed GC‐MQAM and CI‐GC‐MQAM are derived. The derived ABEPs are validated through Monte Carlo simulations. Simulation and theoretical results show that the proposed GC‐MQAM can achieve the error performance of signal space diversity. Simulation and theoretical results further show that the proposed CI‐GC‐16QAM, ‐64QAM, and ‐256QAM with three receive antennas can achieve approximately 2.2, 2.0, and 2.1 dB gain at a bit error rate of 4 × 10−6 compared with GC‐16QAM, ‐64QAM, and ‐256QAM, respectively.

Human cell structure-driven model construction for predicting protein subcellular location from biological images.

The systematic study of subcellular location pattern is very important for fully characterizing the human proteome. Nowadays, with the great advances in automated microscopic imaging, accurate bioimage-based classification methods to predict protein subcellular locations are highly desired. All existing models were constructed on the independent parallel hypothesis, where the cellular component classes are positioned independently in a multi-class classification engine. The important structural information of cellular compartments is missed. To deal with this problem for developing more accurate models, we proposed a novel cell structure-driven classifier construction approach (SC-PSorter) by employing the prior biological structural information in the learning model. Specifically, the structural relationship among the cellular components is reflected by a new codeword matrix under the error correcting output coding framework. Then, we construct multiple SC-PSorter-based classifiers corresponding to the columns of the error correcting output coding codeword matrix using a multi-kernel support vector machine classification approach. Finally, we perform the classifier ensemble by combining those multiple SC-PSorter-based classifiers via majority voting. We evaluate our method on a collection of 1636 immunohistochemistry images from the Human Protein Atlas database. The experimental results show that our method achieves an overall accuracy of 89.0%, which is 6.4% higher than the state-of-the-art method. The dataset and code can be downloaded from https://github.com/shaoweinuaa/. dqzhang@nuaa.edu.cn Supplementary data are available at Bioinformatics online.

No-zero-entry full diversity space-time block codes with linear receivers

In MIMO systems, Toeplitz codes, overlapped Alamouti codes (OACs), and embedded Alamouti codes (EACs) can achieve full diversity when linear receivers are used. However, these codes have a large number of zero entries in their codeword matrix. Due to the zero entries in the design, the peak-to-average power ratio (PAPR) is high, and the transmitting antennas need to be switched on and off imposing severe hardware constrains. To solve this problem, in this paper, we propose a design scheme for no-zero-entry full diversity space-time block codes (NZE-STBCs). New no-zero-entry Toeplitz codes (called NZE-TCs) are designed first, and are then combined/overlaid with orthogonal space-time block code, Alamotui code, to construct no-zero-entry overlapped Alamouti codes (NZE-OACs) and no-zero-entry embedding Alamouti codes (NZE-EACs). The full diversity properties of proposed NZE-TCs, NZE-OACs, and NZE-EACs with linear receiver are derived. Simulation results show that our proposed codes outperform the Toeplitz codes, OACs, and EACs under peak power constraint, while performing the same under average power constraint.

No-Zero-Entry Space-Time Block Codes Over Time-Selective Fading Channels for MIMO Systems

In MIMO systems, space-time block code (STBC) is good solution for improving system performance. Among the STBCs, coordinate interleaved orthogonal designs (CIODs) combined with QR-decomposition-based decision-feedback decoding (QR-DDF) allow achieving good performance for time-selective fading channels. However, half of entries in codeword matrix of CIODs are zeros. These zero entries result in high peak-to-average power ratio (PAPR) and also impose a severe constraint on hardware implementation of the code when turning off some of the transmitting antennas whenever a zero is transmitted. In this paper, we propose a new design of space-time block codes without zero entry in codeword matrix (NZE-STBCs) for time-selective fading channels. The main advantage of the proposed NZE-STBCs is that its peak-to-average ratio (PAPR) is 3 dB lower than that of CIODs, and its hardware implementation is also easier due to eliminating on-off switchers without sacrificing performance. Moreover, similar as CIODs, the proposed NZE-STBCs can use low complexity QR-DDF decoder over time-selective fading channels to enhance performance and reduce decoding complexity. Simulation results show that the proposed NZE-STBCs outperform CIODs for three transmit antennas while performing the same for two and four transmit antennas.

Single-Symbol Maximum Likelihood Decodable STBCs with Fewer Zero-Entries

Two generalized constructions of single-symbol maximum likelihood (ML) decodable space-time block codes (SSDCs), the coordinate interleave orthogonal design (CIOD) and the generalized CIOD (GCIOD), have been proposed by Khan et al. Their main disadvantage is that there are too many zero entries in the codeword matrix. The transmission of these zero-valued symbols causes switching off some of the transmit antennas resulting in a high peak-to-average power ratio and also imposing a severe constraint on hardware implementation of the code. Based on the orthogonal construction of orthogonal space-time block codes and coordinate interleaving, a new generalized construction of SSDCs is proposed. Our proposed codes not only maintain the desirable properties of high rate, full transmit diversity and single-symbol ML decoding similar to CIODs and GCIODs, but also have fewer zero entries in its codeword matrix than CIODs and GCIODs.

New design of single-symbol decodable STBCs for MIMO communication system

Single-symbol maximum-likelihood (ML) decodable space-time block codes (SSDCs) can achieve a maximal symbol rate of 6/7 for multiple-input multiple-output (MIMO) communication system with five or six transmit antennas by using rate-efficient generalized coordinate interleaved orthogonal designs (RE-GCIODs). Unfortunately, there are many zero entries in the codeword matrix of RE-GCIODs. The zero entries result in high peak-to-average power ratio (PAPR) and also impose a severe constraint on hardware implementation. In this paper, for MIMO communication systems with five or six transmit antennas and one receive antenna, a new SSDC is proposed. By combining Alamouti code and orthogonal space-time block code (OSTBC), desirable properties like RE-GCIODs can be achieved and are derived, including maximal symbol rate up to 6/7, full diversity and single-symbol ML decodability. Moreover, by reducing the number of zero entries in the codeword matrix, the peak-to-average power ratio (PAPR) of our proposed code is lower than RE-GCIODs. Simulation results show that the proposed codes outperform RE-GCIODs under peak power constraint while performing almost same under average power constraint.

New design of no-zero-entry single symbol ML decodable STBCs based on group precoding

In multiple-input multiple-output (MIMO) systems, space–time block codes (STBCs) from orthogonal designs (ODs) and coordinate interleaved orthogonal designs (CIOD) have been attracting wider attention due to their amenability for fast (single symbol) maximum-likelihood (ML) decoding, and full-rate with full-rank over quasi-static fading channels. However, most of these codes, for transmitting antennas more than 4, have large number of zero entries in their codeword matrix. Due to the zero entries in the design, the transmitting antennas need to be switched on and off imposing severe hardware constraints. To solve this problem, we propose a method to generate a new class of no-zero-entry single symbol maximum likelihood decodable STBCs (NZESSDCs), which is based on coordinate interleaving and group precoding technique. The ability of the proposed group precoding based NZESSDCs (called G-NZESSDCs) on single symbol ML Decoding and full diversity are analyzed and derived. The performance evaluation is accomplished by numerical simulation and is compared with recently reported NZESSDCs (called C-NZESSDCs). Compared with C-NZESSDCs, the proposed G-NZESSDCs have same bit-error-rate (BER) performance and better peak-to-average ratio (PAPR) performance.

Ternary Bradley-Terry model-based decoding for multi-class classification and its extensions

A multi-class classifier based on the Bradley-Terry model predicts the multi-class label of an input by combining the outputs from multiple binary classifiers, where the combination should be a priori designed as a code word matrix. The code word matrix was originally designed to consist of +1 and −1 codes, and was later extended into deal with ternary code {+1,0,−1}, that is, allowing 0 codes. This extension has seemed to work effectively but, in fact, contains a problem: a binary classifier forcibly categorizes examples with 0 codes into either +1 or −1, but this forcible decision makes the prediction of the multi-class label obscure. In this article, we propose a Boosting algorithm that deals with three categories by allowing a ‘don’t care’ category corresponding to 0 codes, and present a modified decoding method called a ‘ternary’ Bradley-Terry model. In addition, we propose a couple of fast decoding schemes that reduce the heavy computation by the existing Bradley-Terry model-based decoding.

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.

Semiorthogonal Space–Time Block Codes

In this paper, a new class of full-diversity, rate-one space-time block codes (STBCs) called semiorthogonal algebraic space-time block codes (SAST codes) is proposed. SAST codes are delay optimal when the number of transmit antennas is even. The SAST codeword matrix has a generalized Alamouti structure where the transmitted symbols are replaced by circulant matrices and the commutativity of circulant matrices simplifies the detection of transmit symbols. SAST codes with maximal coding gain are constructed by using rate-one linear threaded algebraic space-time (LTAST) codes. Compared with LTSAT codes, SAST codes not only reduce the complexity of maximum-likelihood detection, but also provide remarkable performance gain. They also outperform other STBC with rate one or less. SAST codes also perform well with suboptimal detectors such as the vertical-Bell Laboratories layered space-time (V-BLAST) nulling and cancellation receiver. Finally, SAST codes attain nearly 100% of the Shannon capacity of open-loop multiple-input-single-output (MISO) channels.

The Icosian Code and the $E_8$ Lattice: A New $4\,\times\,4$ Space–Time Code With Nonvanishing Determinant

This paper introduces a new rate-2, full-diversity space-time code for four transmit antennas and one receive antenna. The 4times4 codeword matrix consists of four 2times2 Alamouti blocks with entries from <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ,radic5) , and these blocks can be viewed as quaternions which in turn represent rotations in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . The Alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron. This algebraic structure is different from the Golden code, but the complex entries are taken from a common underlying field. The minimum determinant is bounded below by a constant that is independent of the signal constellation, and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> lattice.