In this paper, we describe the trellis coding where quantum computing (QC) is employed to analyze the coding gain and complexity.According to quantum information theory, quantum bits increase the storage capacity as well as speed.High complex trellis based on partial memory code (PUM) is designed and simulated in digital computers.In order to reduce simulation time for trellis decoding, QC is analyzed with PUM coding.From the theoretical analysis, QC in a quantum computer will be the best option because quantum bits can be stored simultaneously in a given moment of time.From this theory, trellis states, paths, metric calculations are stored in lesser time and space than conventional storing procedures.Therefore, QC certainly will improve the trellis coder performance.
In this paper, we describe the trellis coding where quantum computing (QC) is employed to analyze the coding gain and complexity.According to quantum information theory, quantum bits increase the storage capacity as well as speed.High complex trellis based on partial memory code (PUM) is designed and simulated in digital computers.In order to reduce simulation time for trellis decoding, QC is analyzed with PUM coding.From the theoretical analysis, QC in a quantum computer will be the best option because quantum bits can be stored simultaneously in a given moment of time.From this theory, trellis states, paths, metric calculations are stored in lesser time and space than conventional storing procedures.Therefore, QC certainly will improve the trellis coder performance.
Quantum computing is different from classical computing. It is based on quantum mechanics principles, utilizing the attributes such as entanglement and superposition. The significant difference between a quantum computer and a classical computer is the ability to process information astonishingly faster. This is possible due to the quantum entanglement concept. Interests in the quantum entanglement concept have been exponentially growing over the years. In the last decade, significant progress in implementations of quantum computation in quantum information has been achieved. This study selected secondary resource indexed literature from several databases with specific keywords in almost a century. In this paper, quantum computing and its application is presented along with the essence of quantum entanglement role in quantum computing. This study will provide a general understanding of quantum computing and its application and quantum entanglement.
In this paper, we propose a new type of code called Trellis-based Quasi-Cyclic (TQC)-LDPC convolutional code, which is a special case of protograph-based LDPC convolutional codes. The proposed TQC-LDPC convolutional code can be derived from any QC-LDPC block code by introducing trellis-based convolutional dependency to the code. The main advantage of the proposed TQC-LDPC convolutional code is that it allows reduced decoder complexity and input granularity (which is defined as the minimum number of input information bits the code requires to generate a codeword) while maintaining the same bit error-rate as the underlying QC-LDPC block code ensemble. We also propose two related power-efficient encoding methods to increase the code rate of the derived TQC-LDPC convolutional code. The newly derived short constraint length TQC-LDPC convolutional codes enable low complexity trellis-based decoders and one such decoder is proposed and described in this paper (namely, QC-Viterbi). The TQC-LDPC convolutional codes and the QC-Viterbi decoder are compared to conventional LDPC codes and Belief Propagation (BP) iterative decoders with respect to bit-error-rate (BER), signal-to-noise ratio (SNR), and decoder complexity. We show both numerically and through hardware implementation results that the proposed QC-Viterbi decoder outperforms the BP iterative decoders by at least 1 dB for same complexity and BER. Alternatively, the proposed QC-Viterbi decoder has 3 times lower complexity than the BP iterative decoder for the same SNR and BER. This low decoding complexity, low BER, and fine granularity makes it feasible for the proposed TQC-LDPC convolutional codes and associated trellis-based decoders to be efficiently implemented in high data rate, next generation mobile systems.
This paper studies low-complexity high-speed decoder architectures for quasi-cyclic low density parity check (QC-LDPC) codes. Algorithmic transformation and architectural level optimization are incorporated to reduce the critical path. Enhanced partially parallel decoding architectures are proposed to linearly increase the throughput of conventional partially parallel decoders through introducing a small percentage of extra hardware. Based on the proposed architectures, a (8176, 7154) Euclidian geometry-based QC-LDPC code decoder is implemented on Xilinx field programmable gate array (FPGA) Virtex-II 6000, where an efficient nonuniform quantization scheme is employed to reduce the size of memories storing soft messages. FPGA implementation results show that the proposed decoder can achieve a maximum (source data) decoding throughput of 172 Mb/s at 15 iterations
Quantum computer performs operations by adopting the principles of quantum physics and quantum mechanics. With these principles, it performs operations exponentially faster compared to classical computers. The major problem observed in quantum computation is noise and decoherence. The noise and decoherence generate errors while performing the operations on quantum states. As a solution to this Quantum error correction(QEC) methods are introduced. Encoding plays a key role in QEC. In the encoding process, the logical qubits are encoded into physical qubits by appending extra qubits to them. With this, the logical qubit will be strengthened and can be transferred safely. Initially, the experimental results of quantum computation are theoretical or mathematical. But with the existence of quantum computers, it is possible to develop and run new quantum architectures on publicly available quantum computers. Thus in this paper, we developed an efficient algorithm for encoding quantum information using various quantum gates. The developed algorithm is executed on various quantum systems and the performance is analyzed in terms of frequency, run time, error rate, number of qubits, and quantum volume. This analysis helps the researchers to opt an efficient quantum system to perform the experiments.
Quantum computing is a novel kind of computation that solves very complicated problems rapidly by applying concepts from basic physics. Concepts like quantum mechanical computing and quantum algorithms are included in the field of quantum computing study. Researchers have imagined quantum computing as a revolutionary idea among emerging technologies in terms of concepts, methods, and techniques. These are cross-pollinated. Hence, quantum computing becomes more and more multidisciplinary. Quantum computing leverages quantum mechanical phenomena like superposition and quantum interference to deal with some kinds of problems more precisely than conventional computing. Because of its unique characteristics, which set it apart from conventional computers in terms of functionality and operation, quantum computing has grown in popularity. There are possibilities of creating hybrid models, namely approaches for large-scale mixed-integer programming issues, that effectively combine the strengths of quality control techniques with deterministic algorithms to handle combinatorial challenges.
This thesis concentrates on studying three problems in error-correcting codes: optimal encoding, trellis structure, and normalized weight of linear block codes. In general, the research in error-correcting codes can be roughly classified into coding practice and coding theory. The problems in coding practice focus on codes and decoders with more attention on the subject of the tradeoffs between performance and complexity, e.g., soft-decision decoding, bit error probability, or trellis of the codes. On the other hand, coding theory concentrates on the structure of codes based on sophisticated mathematical techniques, with little concern for the decoding complexity, e.g., coset weight distribution, algebraic constructions, or bounds on possible parameters of the codes. In this dissertation, we will present three fundamental topics in coding practice: optimal encoding of linear block codes for bit error probability, trellis structure of linear block codes for trellis-based decoding, and normalized weight of block coded modulation for bandwidth efficient communication systems. The central theme of the thesis is to transform the problems of the above three topics in coding practice into problems in coding theory and to develop the theory associated with the problems. Much of this thesis is devoted to studying what 'optimal' means in different contexts. In summary, we investigated the optimal information bit encoding of a given linear block code for minimizing the probability of an information bit error, with the goal of determining an optimal generator matrix by using the structure of the code. We showed that many natural codes have systematic optimal generator matrices in the quiet region. We analyzed the trellis structure of a self-dual code C to minimize the trellis complexity of the code by considering all equivalent codes of C, with the goal of reducing the soft-decision decoding complexity via permutations on the codeword coordinates. We determined the length/dimension profile of all eight [32, 16, 8] self-dual codes, and find their corresponding optimum permutations. We examined the performance gains achievable by adding interblock memory to block coded modulation systems, with the goal of finding the best codes for normalized distance rather than Hamming distance. We found a large number of best codes for normalized distance for the cases of practical interest.