Quantum Graphical Models and Belief Propagation

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersely-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.Comment: 58 pages, 9 figure

5G無線通信における誤り訂正符号化方式の評価に関する研究

早大学位記番号:新8267早稲田大

System capacity enhancement for 5G network and beyond

A thesis submitted to the University of Bedfordshire, in fulfilment of the requirements for the degree of Doctor of PhilosophyThe demand for wireless digital data is dramatically increasing year over year. Wireless communication systems like Laptops, Smart phones, Tablets, Smart watch, Virtual Reality devices and so on are becoming an important part of people’s daily life. The number of mobile devices is increasing at a very fast speed as well as the requirements for mobile devices such as super high-resolution image/video, fast download speed, very short latency and high reliability, which raise challenges to the existing wireless communication networks. Unlike the previous four generation communication networks, the fifth-generation (5G) wireless communication network includes many technologies such as millimetre-wave communication, massive multiple-input multiple-output (MIMO), visual light communication (VLC), heterogeneous network (HetNet) and so forth. Although 5G has not been standardised yet, these above technologies have been studied in both academia and industry and the goal of the research is to enhance and improve the system capacity for 5G networks and beyond by studying some key problems and providing some effective solutions existing in the above technologies from system implementation and hardware impairments’ perspective. The key problems studied in this thesis include interference cancellation in HetNet, impairments calibration for massive MIMO, channel state estimation for VLC, and low latency parallel Turbo decoding technique. Firstly, inter-cell interference in HetNet is studied and a cell specific reference signal (CRS) interference cancellation method is proposed to mitigate the performance degrade in enhanced inter-cell interference coordination (eICIC). This method takes carrier frequency offset (CFO) and timing offset (TO) of the user’s received signal into account. By reconstructing the interfering signal and cancelling it afterwards, the capacity of HetNet is enhanced. Secondly, for massive MIMO systems, the radio frequency (RF) impairments of the hardware will degrade the beamforming performance. When operated in time duplex division (TDD) mode, a massive MIMO system relies on the reciprocity of the channel which can be broken by the transmitter and receiver RF impairments. Impairments calibration has been studied and a closed-loop reciprocity calibration method is proposed in this thesis. A test device (TD) is introduced in this calibration method that can estimate the transmitters’ impairments over-the-air and feed the results back to the base station via the Internet. The uplink pilots sent by the TD can assist the BS receivers’ impairment estimation. With both the uplink and downlink impairments estimates, the reciprocity calibration coefficients can be obtained. By computer simulation and lab experiment, the performance of the proposed method is evaluated. Channel coding is an essential part of a wireless communication system which helps fight with noise and get correct information delivery. Turbo codes is one of the most reliable codes that has been used in many standards such as WiMAX and LTE. However, the decoding process of turbo codes is time-consuming and the decoding latency should be improved to meet the requirement of the future network. A reverse interleave address generator is proposed that can reduce the decoding time and a low latency parallel turbo decoder has been implemented on a FPGA platform. The simulation and experiment results prove the effectiveness of the address generator and show that there is a trade-off between latency and throughput with a limited hardware resource. Apart from the above contributions, this thesis also investigated multi-user precoding for MIMO VLC systems. As a green and secure technology, VLC is achieving more and more attention and could become a part of 5G network especially for indoor communication. For indoor scenario, the MIMO VLC channel could be easily ill-conditioned. Hence, it is important to study the impact of the channel state to the precoding performance. A channel state estimation method is proposed based on the signal to interference noise ratio (SINR) of the users’ received signal. Simulation results show that it can enhance the capacity of the indoor MIMO VLC system

Bias-tailored quantum LDPC codes

Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, the XZZX code, exhibits considerably improved performance under biased noise. In this work, we demonstrate that quantum low density parity check codes can be similarly bias-tailored. We introduce a bias-tailored lifted product code construction that provides the framework to expand bias-tailoring methods beyond the family of 2D topological codes. We present examples of bias-tailored lifted product codes based on classical quasi-cyclic codes and numerically assess their performance using a belief propagation plus ordered statistics decoder. Our Monte Carlo simulations, performed under asymmetric noise, show that bias-tailored codes achieve several orders of magnitude improvement in their error suppression relative to depolarising noise.Comment: 21 Pages, 13 Figures. Comments welcome

Decoding algorithms for surface codes

Quantum technologies have the potential to solve computationally hard problems that are intractable via classical means. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build error corrected qubits given their two-dimensional architecture, a requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that it can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum-like tradeoff, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art surface code decoding algorithms is provided. The core operation of these methods is described along with existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface code decoding is also provided.Comment: 54 pages, 31 figure

Ultra-Wideband Secure Communications and Direct RF Sampling Transceivers

Larger wireless device bandwidth results in new capabilities in terms of higher data rates and security. The 5G evolution is focus on exploiting larger bandwidths for higher though-puts. Interference and co-existence issues can also be addressed by the larger bandwidth in the 5G and 6G evolution. This dissertation introduces of a novel Ultra-wideband (UWB) Code Division Multiple Access (CDMA) technique to exploit the largest bandwidth available in the upcoming wireless connectivity scenarios. The dissertation addresses interference immunity, secure communication at the physical layer and longer distance communication due to increased receiver sensitivity. The dissertation presents the design, workflow, simulations, hardware prototypes and experimental measurements to demonstrate the benefits of wideband Code-Division-Multiple-Access. Specifically, a description of each of the hardware and software stages is presented along with simulations of different scenarios using a test-bench and open-field measurements. The measurements provided experimental validation carried out to demonstrate the interference mitigation capabilities. In addition, Direct RF sampling techniques are employed to handle the larger bandwidth and avoid analog components. Additionally, a transmit and receive chain is designed and implemented at 28 GHz to provide a proof-of-concept for future 5G applications. The proposed wideband transceiver is also used to demonstrate higher accuracy direction finding, as much as 10 times improvement

Finite-Length Scaling Laws for Spatially-Coupled LDPC Codes

This thesis concerns predicting the finite-length error-correcting performance of spatially-coupled low-density parity-check (SC-LDPC) code ensembles over the binary erasure channel. SC-LDPC codes are a very powerful class of codes; their use in practical communication systems, however, requires the system designer to specify a considerable number of code and decoder parameters, all of which affect both the code’s error-correcting capability and the system’s memory, energy, and latency requirements. Navigating the space of the associated trade-offs is challenging. The aim of the finite-length scaling laws proposed in this thesis is to facilitate code and decoder parameter optimization by providing a way to predict the code’s error-rate performance without resorting to Monte-Carlo simulations for each combination of code/decoder and channel parameters.First, we tackle the problem of predicting the frame, bit, and block error rate of SC-LDPC code ensembles over the binary erasure channel under both belief propagation (BP) decoding and sliding window decoding when the maximum number of decoding iterations is unlimited. The scaling laws we develop provide very accurate predictions of the error rates.Second, we derive a scaling law to accurately predict the bit and block error rate of SC-LDPC code ensembles with doping, a technique relevant for streaming applications for limiting the inherent rate loss of SC-LDPC codes. We then use the derived scaling law for code parameter optimization and show that doping can offer a way to achieve better transmission rates for the same target bit error rate than is possible without doping.Last, we address the most challenging (and most practically relevant) case where the maximum number of decoding iterations is limited, both for BP and sliding window decoding. The resulting predictions are again very accurate.Together, these contributions make finite-length SC-LDPC code and decoder parameter optimization via finite-length scaling laws feasible for the design of practical communication systems