Codeword Design Research Articles

Phase-engineered bosonic quantum codes

Continuous-variable systems protected by bosonic quantum codes have emerged as a promising platform for quantum information. To date, the design of code words has centered on optimizing the state occupation in the relevant basis to generate the distance needed for error correction. Here, we show tuning the phase degree of freedom in the design of code words can affect, and potentially enhance, the protection against Markovian errors that involve excitation exchange with the environment. As illustrations, we first consider phase engineering bosonic codes with uniform spacing in the Fock basis that correct excitation loss with a Kerr unitary and show that these modified codes feature destructive interference between error code words and, with an adapted ``two-level'' recovery, the error protection is significantly enhanced. We then study protection against energy decay with the presence of mode nonlinearities and analyze the role of phase for optimal code designs. We extend the principle of phase engineering to bosonic codes defined in other bases and multiqubit codes, demonstrating its broad applicability in quantum error correction.

Two-Step Codeword Design for Millimeter Wave Massive MIMO Systems With Quantized Phase Shifters

In this paper, a two-step codeword design approach for millimeter wave (mmWave) massive MIMO systems is presented. Ideal codewords are first designed, which ignores the hardware constraints in terms of phase shifter resolution and the number of RF chains. Based on the ideal codewords, practical codewords are then obtained taking the hardware constraints into consideration. For the ideal codeword design in the first step, additional phase is introduced to the beam gain to provide extra degree of freedom. We develop a phase-shifted ideal codeword design (PS-ICD) method, which is based on alternative minimization with each iteration having a closed-form solution and can be extended to design more general beamforming vectors with different beam patterns. Once the ideal codewords are obtained in the first step, the practical codeword design problem in the second step is to approach the ideal codewords by considering the hardware constraints of the hybrid precoding structure in terms of phase shifter resolution and the number of RF chains. We propose a fast search based alternative minimization (FS-AltMin) algorithm that alternatively designs the analog precoder and digital precoder. Simulation results verify the effectiveness of the proposed methods and show that the codewords designed based on the two-step approach outperform those designed by the existing approaches.

TCM-NOMA: Joint Multi-User Codeword Design and Detection in Trellis-Coded Modulation-Based NOMA for Beyond 5G

In this paper, we propose a novel non-orthogonal multiple access (NOMA) scheme based on trellis-coded modulation (TCM). Different from those in the traditional code-domain NOMA, the incoming data streams of multiple users are jointly coded and mapped to the codewords so as to improve the coding gain of the system without any bandwidth extension. Both codeword design and multi-user detection are considered to optimize the TCM for NOMA. The multi-dimensional (MD) constellation is carefully selected and a new set partitioning algorithm is developed for MD signal set labeling. To achieve the trade-off between the BER performance and complexity, a suboptimal two-layer Viterbi algorithm is proposed for joint decoding. Simulation results show that our proposed TCM-based NOMA scheme performs significantly better than the traditional code-domain NOMA and OFDMA schemes in terms of the BER performance under the same channel conditions.

Cognitive Transmitting Frequency Codewords Design for Sparse Stepped Frequency Radar Based on Sensing Matrix Optimization

Cognitive waveform design is of great significance for radar transmitting system to better adapt to the changing electromagnetic environment and target scene. In this paper, a novel cognitive waveform design method of sparse stepped frequency based on sensing matrix optimization is proposed. The proposed cognitive waveform exploits the information returned from the target scene to continuously optimize the transmitted frequency and sensing matrix. Compressive sensing (CS) technique is applied for range-Doppler reconstruction due to the sparse property of the target to be estimated. Comparing with random stepped frequency, this optimized cognitive waveform could further improve the upper limit of the number of detection targets; also increase the accuracy and robustness.

Optimal Design of Cascade LDPC-CPM System Based on Bionic Swarm Optimization Algorithm

The direct-to-home satellite digital video broadcasting has been fast developed in the past decades, and the continuous phase modulation (CPM) is an alternative modulation scheme with the advantages of constant envelope and high spectral efficiency for the band-limited channel and non-linear amplifiers of the satellite transponder. In this paper, CPM cascaded with irregular low density parity check (LDPC) code is studied. A practical system model with global interleaving is proposed for the optimization of degree distribution of the LDPC codes, and code word design is obtained with a modified progressive edge-growth algorithm. Simulation results combined with theoretical analysis clarify the effect of signal-to-noise ratios and two important CPM parameters (modulation index ${h}$ and correlation length ${L}$ ), providing guidance for system design. Simulation on bit error rate performance show the validity of the proposed algorithm. This paper systematically solves the optimal system design of cascade irregular LDPC-CPM and is of great significance for future satellite broadcasting.

An Improved Non-dominated Sorting Genetic Algorithm-II (INSGA-II) applied to the design of DNA codewords

DNA codewords design is critical for many research fields, from DNA computing, to DNA hybridization arrays, to DNA nanotechnology. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Since DNA codewords design can be regarded as a multi-objective optimization problem, and nondominated sorting genetic algorithm II (NSGA-II) has been demonstrated as one of the most efficient algorithms for multi-objective optimization problems, in this paper, we proposed an improved nondominated sorting genetic algorithm II (INSGA-II) for the design of DNA codewords. The novelty of our method is that introduced the constraints to the non-dominated sorting process. The performance of our method is compared with other DNA codewords design methods, and the experiment results in silico showed that the INSGA-II has a higher convergence speed and better population diversity than those of other algorithms, and can provide reliable and effective codewords for the controllable DNA computing.

Trellis Coded Modulation for Non-Orthogonal Multiple Access Systems: Design, Challenges, and Opportunities

Capable of achieving massive connectivity and high reliability, the NOMA technique has been well recognized as a potential candidate for 5G mobile communications. Being a key technique of code-domain NOMA, codebook design has drawn great attention due to its potential to improve the coding gain of the system. Trellis coded modulation (TCM) techniques have been considered as an effective approach to optimize the coding gain through signal set expansion without causing bandwidth expansion. In this article, we propose a framework to apply the multi-dimensional TCM (MD-TCM) techniques in code-domain NOMA to jointly design the superposed codewords. Starting with a basic TCM-based NOMA system, we present the design criteria based on which joint multi-layer codeword design for code-domain NOMA is elaborated. Three TCM-based NOMA applications are extended: TCM-based NOMA for MIMO systems, TCM-based NOMA for cooperative relay systems, and TCM-based NOMA for vehicular systems. Open research issues in these scenarios are also discussed.

Differential spatial modulation for high-rate transmission systems

This paper introduces a new differential spatial modulation (DSM) scheme which subsumes both the previously introduced DSM and high-rate spatial modulation (HR-SM) for wireless multiple input multiple output (MIMO) transmission. By combining the codeword design method of the HR-SM scheme with the encoding method of the DSM scheme, we develop a high-rate differential spatial modulation (HR-DSM) scheme equipped with an arbitrary number of transmit antennas that requires channel state information (CSI) neither at the transmitter nor at the receiver. The proposed approach can be applied to any equal energy signal constellations. The bit error rate (BER) performance of the proposed HR-DSM schemes is evaluated by using both theoretical upper bound and computer simulations. It is shown that for the same spectral efficiency and antenna configuration, the proposed HR-DSM outperforms the DSM in terms of bit error rate (BER) performance.

Modified codewords design for space–time block coded spatial modulation

Two kinds of modified codewords for space–time block coded spatial modulation (STBC-SM) are presented in this study. The first modified codeword introduces a concept of flexible coefficients into the M-ary phase shift keying STBC-SM. A method is proposed to obtain the optimal flexible coefficients. Moreover, the first modified codewords can also be applied to the systems developed from the STBC-SM. In the second provided codewords, super-orthogonal space–time trellis codes are applied in STBC-SM. Therefore, a higher spectral efficiency is obtained compared with the original STBC-SM. Finally, the simulation results and theoretical analysis demonstrate these performance advantages of the two kinds of modified codewords for STBC-SM.

Testing DNA code words properties of regular languages

One aspect of DNA Computing is the possibility of using DNA molecules for solving some “complicated” computational problems. In this context, the DNA code word design problem assumes a fundamental role: given a problem encoded in DNA strands and biochemical processes, the final computation is a concatenation of the input DNA strands that must allow us to recover the solution of the given problem in terms of the input (unique decipherability). Thus the initial set of DNA strands must be a code. In addition, it should satisfy some restrictions, called here DNA properties, in order to prevent them from interacting in undesirable ways. So a new interest towards the design of efficient algorithms for testing whether a language X is a code, has arisen from (wet) DNA Computing, but, as far as we know, only when X is a finite set. In this paper we provide an algorithm for testing whether an infinite but regular set of words is a code that avoids some DNA properties among unwanted intermolecular and intramolecular hybridizations.

SNR Decomposition for Full-Duplex Gaussian Relay Channel

A relay channel (RC), consisting of a source, a relay, and a destination, is a basic transmission unit of cooperative communication networks. The capacity of an RC is not known in general. In this paper, an SNR decomposition (SD) strategy is presented to implement time sharing, which provides a new tractable and achievable rate for a full-duplex Gaussian RC. More specifically, we first expand the SNR of a relay destination channel (SNR-RD) into two terms under the relay power constraint and divide the system into two subbands. Then, we assign the obtained SNR-RD for each subband and employ decode-forward (DF) or compress-forward (CF) according to the assigned SNR-RD. It is shown that the achievable rate of the SD strategy is competitive with that of superposing CF on DF. As the superposition structure requires a sophisticated codeword design, the SD strategy provides another practical combination structure of DF and CF strategies. Approximations for the SNR-RD and bandwidth allocation for subbands are also given. Based on the obtained results, two application scenarios, i.e., mobile relay and quasi-static fading RCs, are also considered. Finally, various numerical results are shown to support our developed theoretical results.

DNA Codeword Design: Theory and Applications

This is a survey of the origin, current progress and applications of a major roadblock to the development of analytic models for DNA computing (a massively parallel programming methodology) and DNA self-assembly (a nanofabrication methodology), namely the so-called CODEWORD DESIGN problem. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves or to their complements and has been recognized as an important problem in DNA computing, self-assembly, DNA memories and phylogenetic analyses because of their error correction and prevention properties. Major recent advances include the development of experimental techniques to search for such codes, as well as a theoretical framework to analyze this problem, despite the fact that it has been proven to be NP-complete using any single concrete metric space to model the Gibbs energy. In this framework, codeword design is reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the key to finding such sets would lie in knowledge of the geometry of these spaces. A new general technique has been recently found to embed them in Euclidean spaces in a hybridization-affinity-preserving manner, i.e., in such a way that oligos with high/low hybridization affinity are mapped to neighboring/remote points in a geometric lattice, respectively. This isometric embedding materializes long-held metaphors about codeword design in terms of sphere packing and error-correcting codes and leads to designs that are in some cases known to be provably nearly optimal for some oligo sizes. It also leads to upper and lower bounds on estimates of the size of optimal codes of size up to 32–mers, as well as to infinite families of solutions to CODEWORD DESIGN, based on estimates of the kissing (or contact) number for sphere packings in Euclidean spaces. Conversely, this reduction suggests interesting new algorithms to find dense sphere packing solutions in high dimensional spheres using results for CODEWORD DESIGN previously obtained by experimental or theoretical molecular means, as well as a proof that finding these bounds exactly is NP-complete in general. Finally, some research problems and applications arising from these results are described that might be of interest for further research.

Joint IR-UWB Power Spectral Lines and Interference Suppression Based on Coded Auxiliary Independent Signaling in Presence of Pulse Attenuation and Timing Jitter

This paper deals with spectral shaping problem in impulse radio ultra-wideband systems based on coded auxiliary independent signaling (AIS), as a modified version of transmitted-reference approach. In this manuscript, the main contribution includes a unified theoretical framework for spectral analysis which is, not only able to address all effective parameters in the emergence of spectral lines and coexistence issues, but also provides a convex optimization based method. This can produce AIS-aided signals using random process characteristics as optimization variables. In particular, the specific novelty insights of this paper are as follows: (i) to propose a new signal model, where each transmitted symbol is represented by a preamble AIS pulse followed by a set of transmitted data pulses that are synthesized in accordance with a codeword design and within this context, the preamble signal is designed to eliminate spectral lines via an adaptive monitoring of data-stream statistics as the optimal policy; (ii) to exploit the proposed spectral optimization strategies to maximize spectral flexibility.

Near Shannon Limit and Low Peak to Average Power Ratio Turbo Block Coded OFDM

In this paper, we present an advanced solution for the long standing problem of large peak to average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. Although the design of low PAPR codewords has been extensively studied and the existence of asymptotically good codes with low PAPR is also proven, still no code has been constructed to satisfy all requirements. The main goal of the paper is to develop a coding scheme that not only generates low PAPR codewords, but it also performs relatively close to the Shannon limit. We achieve this goal by implementing a time-frequency turbo block coded OFDM. In this scheme, we design the frequency domain component to have a tightly bounded PAPR. The time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity. Through comparative performance evaluation we show that utilizing the proposed method, we achieve considerable improvement in terms of PAPR while we slightly loose the performance compared to capacity achieving codes with similar overall block length.

Geometric Approaches to Gibbs Energy Landscapes and DNA Oligonucleotide Design

DNA codeword design has been a fundamental problem since the early days of DNA computing. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves, to each other or to others' complements. Such strands represent so-called domains, particularly in the language of chemical reaction networks (CRNs). The problem has shown to be of interest in other areas as well, including DNA memories and phylogenetic analyses because of their error correction and prevention properties. In prior work, a theoretical framework to analyze this problem has been developed and natural and simple versions of Codeword Design have been shown to be NP-complete using any single reasonable metric that approximates the Gibbs energy, thus practically making it very difficult to find any general procedure for finding such maximal sets exactly and efficiently. In this framework, codeword design is partially reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the size of such sets depends on the geometry of these spaces. Here, the authors describe in detail a new general technique to embed them in Euclidean spaces in such a way that oligonucleotides with high (low, respectively) hybridization affinity are mapped to neighboring (remote, respectively) points in a geometric lattice. This embedding materializes long-held metaphors about codeword design in analogies with error-correcting code design in information theory in terms of sphere packing and leads to designs that are in some cases known to be provably nearly optimal for small oligonucleotide sizes, whenever the corresponding spherical codes in Euclidean spaces are known to be so. It also leads to upper and lower bounds on estimates of the size of optimal codes of size under 20-mers, as well as to a few infinite families of DNA strand lengths, based on estimates of the kissing (or contact) number for sphere codes in high-dimensional Euclidean spaces. Conversely, the authors show how solutions to DNA codeword design obtained by experimental or other means can also provide solutions to difficult spherical packing geometric problems via these approaches. Finally, the reduction suggests a tool to provide some insight into the approximate structure of the Gibbs energy landscapes, which play a primary role in the design and implementation of biomolecular programs.

A DNA assembly model of sentence generation

Recent results of corpus-based linguistics demonstrate that context-appropriate sentences can be generated by a stochastic constraint satisfaction process. Exploiting the similarity of constraint satisfaction and DNA self-assembly, we explore a DNA assembly model of sentence generation. The words and phrases in a language corpus are encoded as DNA molecules to build a language model of the corpus. Given a seed word, the new sentences are constructed by a parallel DNA assembly process based on the probability distribution of the word and phrase molecules. Here, we present our DNA code word design and report on successful demonstration of their feasibility in wet DNA experiments of a small scale.

DNA chips for species identification and biological phylogenies

The codeword design problem is an important problem in DNA computing and its applications. Several theoretical analyses as well as practical solutions for short oligonucleotides (up to 20-mers) have been generated recently. These solutions have, in turn, suggested new applications to DNA-based indexing and natural language processing, in addition to the obvious applications to the problems of reliability and scalability that generated them. Here we continue the exploration of this type of DNA-based indexing for biological applications and show that DNA noncrosshybridizing (nxh) sets can be successfully applied to infer ab initio phylogenetic trees by providing a way to measure distances among different genomes indexed by sets of short oligonucleotides selected so as to minimize crosshybridization. These phylogenies are solidly established and well accepted in biology. The new technique is much more effective in terms of signal-to-noise ratio, cost and time than current methods. Second, it is demonstrated that DNA indexing does provide novel and principled insights into the phylogenesis of organisms hitherto inaccessible by current methods, such as a prediction of the origin of the Salmonella plasmid 50 as being acquired horizontally, likely from some bacteria somewhat related to Yesinia. Finally, DNA indexing can be scaled up to newly available universal DNA chips readily available both in vitro and in silico. In particular, we show how a recently obtained such set of nxh 16-mers can be used as a universal coordinate system in DNA spaces to characterize very large groups (families, genera, and even phylla) of organisms on a uniform biomarker reference system, a veritable and comprehensive "Atlas of Life", as it is or as it could be on earth.

An Efficient Genetic Algorithm Based on the Cultural Algorithm Applied to DNA Codewords Design

An Efficient Genetic Algorithm Based on the Cultural Algorithm Applied to DNA Codewords Design

Codeword design for ultra-wideband (UWB) precoding

A precoding technique applied to symbols transmitted in an ultra-wideband (UWB) system can concentrate the signal power at the receiver for a higher data detection rate. The codeword design problem for optimal UWB precoding is investigated in this work. After the problem formulation, we examine its solution in the full-rank and the reduced-rank subspaces to obtain different tradeoffs between the detection performance and the amount of feedback messages. Furthermore, we propose two subspace selection schemes, each of which corresponds to a code design method. The resultant optimal codewords improve the performance of previous work significantly at the expense of a slightly increased amount of feedback messages. Finally, the performance of a precoded UWB system with various codewords is compared via computer simulation.

DNA Code Word Design for DNA Computing with Real-Time Polymerase Chain Reaction

Problem statement: A number of DNA computing models to solve mathematical graph problem such as the Hamiltonian Path Problem (HPP), Traveling Salesman Problem (TSP), and the Shortest Path Problem (SPP), have been proposed and demonstrated. Normally, the DNA sequences used for the computation should be critically designed in order to reduce error that could occur during a computation. We have proposed a DNA computing readout method tailored specifically to HPP in DNA computing using real-time Polymerase Chain Reaction (PCR). The DNA sequences were designed based on a procedure and DNASequenceGenerator was employed to generate the sequences required for the experiment. The drawback of the previous approach is that a pool of DNA sequences need to be generated by DNASequenceGenerator before the selection is done manually, based on several design constraints. Hence, an automatic and systematic approach is needed to generate the DNA sequences based on design constraints. Approach: In this study, a generate-and-test approach was proposed for the same problem subjected to several design constraints. The generate-and-test algorithm consists of two main levels. The first level considered the basic constraints of DNA sequence design, which were melting temperature, GC-percentage, similarity, continuity, hairpin, and H-measure. This was followed by the second level that includes specific constraints formulated based on five rules, which had been used in previous study. A generated sequence was chosen only if the sequence satisfies all the basic and specific constraints. Results: Sequences designed by generate-and-test approach have higher H-measure value than sequences generated by DNASequenceGenerator. However, the generated sequences show lower value for similarity as well as for additional constraints compared to sequences designed by DNASequenceGenerator. Conclusion: The generated DNA sequences were better compared to the sequences, obtained from DNASequenceGenerator.