Determination of quantum toric error correction code threshold using convolutional neural network decoders

Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.     

Experimentally feasible quantum erasure-correcting code for continuous variables

We devise a scheme that protects quantum coherent states of light from probabilistic losses, thus achieving the first continuous-variable quantum erasure-correcting code. If the occurrence of erasures can be probed, then the decoder enables, in principle, a perfect recovery of the original light states. Otherwise, if supplemented with postselection based on homodyne detection, this code can be turned into an efficient erasure-filtration scheme. The experimental feasibility of the proposed protocol is carefully addressed.     

游程长度受限码RLL(4,18)的研究

介绍了一种新的用于高密度光盘存储的游程长度受限码。给出RLL(4,18)码的构造方法和编解码步骤。对RLL(4,18)码的编码器和解码器进行了CPLD实现。对不同游程长度受限码的主要性能参数进行了比较。     

Variable cross-correlation code construction for spectral amplitude coding optical CDMA networks

We present, for the first time, several aspects of incoherent optical code-division multiple access (OCDMA) codes, focusing on the flexible variable cross-correlation code allocation and its potential for future optical networks. We briefly present a new version of the Random Diagonal (RD) codes for Spectral-Amplitude Coding (SAC) OCDMA approaches. We then concentrate on the properties specific to such schemes allowing for its increased scalability and flexibility. The main coding properties are reviewed. The RD codes provide simple matrix constructions compared to the other SAC-OCDMA codes such as Hadamard, MQC and MFH codes. This code possesses such a numerous advantages, including the efficient and easy code construction, simple encoder/decoder design, existence for every natural number n, and variable in-phase cross-correlation and easy to implement using Fiber Bragg Gratings (FBGs). Finally, a new detection scheme called “NAND” detection is developed for the variable cross-correlation RD code.     

Performance of run-length limited (4, 18) code for optical storage systems

In this paper, the authors investigate the performance of recently presented run-length limited (4, 18) code for high density optical storage systems. The construction of the code is described simply. The code has code rate R = 1/3 and density ratio (DR) = 1.67. The bit error rate (BER) performance for decision feedback equalizer (DFE) and partial response maximum likelihood (PRML) detector are simulated, considering signal-to-noise ratio (SNR) and optical channel jitter. The result shows that the performance of the code is acceptable. The encoder and decoder of the code are implemented by complex programmable logic device (CPLD) chip and the hardware resources required for encoder and decoder arelow.     

Fast frequency modulation optical code division multiple access communication system

An optical fast frequency modulation code division multiple access communication system is proposed. In this system, an electrically controlled tunable optical filter (TOF) is used to encode the modulated broadband light source. The code depends on the function set to the controller. Two-dimensional code named functional code is also proposed based on a shifted sine function. The function defines the dynamic coding pattern of the central wavelength of the transmitted narrowband optical signal. Thus, the system will allow for an easy reconfiguration of the transmitter without the need for sophisticated encoder. At the receiver, a synchronized TOF with the same function is used as a decoder. The performance of this system is shown to be better compared with a fast frequency hopping and a spectral amplitude coding systems.     

A Manifold Learning Perspective on Representation Learning: Learning Decoder and Representations without an Encoder

Autoencoders are commonly used in representation learning. They consist of an encoder and a decoder, which provide a straightforward method to map n-dimensional data in input space to a lower m-dimensional representation space and back. The decoder itself defines an m-dimensional manifold in input space. Inspired by manifold learning, we showed that the decoder can be trained on its own by learning the representations of the training samples along with the decoder weights using gradient descent. A sum-of-squares loss then corresponds to optimizing the manifold to have the smallest Euclidean distance to the training samples, and similarly for other loss functions. We derived expressions for the number of samples needed to specify the encoder and decoder and showed that the decoder generally requires much fewer training samples to be well-specified compared to the encoder. We discuss the training of autoencoders in this perspective and relate it to previous work in the field that uses noisy training examples and other types of regularization. On the natural image data sets MNIST and CIFAR10, we demonstrated that the decoder is much better suited to learn a low-dimensional representation, especially when trained on small data sets. Using simulated gene regulatory data, we further showed that the decoder alone leads to better generalization and meaningful representations. Our approach of training the decoder alone facilitates representation learning even on small data sets and can lead to improved training of autoencoders. We hope that the simple analyses presented will also contribute to an improved conceptual understanding of representation learning.     

多阶光存储的调制原理分析与编码设计研究

根据编码理论的状态切分算法，提出一种新型的8阶(1,3)游程长度受限码，在最小记录符上能够存储3.0比特的用户数据，并且编码与译码逻辑简明，可用于未来高密度多阶游程长度调制光盘系统.     

Realization of 2-D OCDMA network using EDW code

The attraction towards two-dimensional optical code division multiple access (2D-OCDMA) systems has increased due to its potential in enhancing the performance of optical access networks and producing optical code-based signals. 2D-OCDMA network systems enable better bit-error-ratio (BER) performance as well as increase the number of supportable users in the optical network. Time-spreading wavelength-hopping is one of the many techniques that has been proposed for 2D-OCDMA. In this paper, we present the simulative study of a 2D-OCDMA system. The developed time-spreading, wavelength-hopping network utilizes enhanced double weight (EDW) code which has enhanced properties such as a cross-correlation value of 1 and has a simple encoder/decoder design. The output BER was satisfactory at above 10^?9 at data rate of 1.25 Gbps for 20 km distance with the ITU-T G.652 standard single mode optical fiber for 3 users.     

Soft decision decoding of the orthogonal complex MIMO codes for three and four transmit antennas

Orthogonality is a much desired property for MIMO coding. It enables symbol-wise decoding, where the errors in other symbol estimates do not affect the result, thus providing an optimality that is worth pursuing. It also paves the way for low complexity soft decision decoding, which for orthogonal complex MIMO codes is known for two transmit (Tx) antennas, i.e. for the Alamouti code. We propose novel soft decision decoders for the orthogonal complex MIMO codes on three and four Tx antennas and extend the old result of maximal ratio combining (MRC) to cover all orthogonal codes up to four Tx antennas.As a rule, a sophisticated transmission scheme encompasses forward error correction (FEC) coding, and its performance is measured at the FEC decoder instead of at the MIMO decoder. We introduce the receiver structure that delivers the MIMO decoder’s soft decisions to the demodulator, which in turn cranks out the logarithm of likelihood ratio (LLR) of each bit and delivers them to the FEC decoder. This significantly improves the receiver, where a maximum likelihood (ML) MIMO decoder makes hard decisions at a too early stage. Further, the additional gain is achieved with stunningly low complexity.     

Hybrid WDMA/OCDM system with the capability of encoding multiple wavelength channels by employing one encoder and one corresponding optical code

<正>A hybrid wavelength division multiple access(WDMA)/optical code division multiplexing(OCDM) system is proposed,where the optical code is not the same as the address of every optical network unit(ONU); rather,the code is a virtual fiber of hybrid passive optical network(PON).To our knowledge,this is the first report analyzing a single encoder/decoder with a single corresponding optical code being exploited to encode/decode multiple wavelength signals simultaneously.This system enables OCDM to become transparent to ONU so that the existing wavelength division multiplexing(WDM) PON can be upgraded. Thus,redesigning the optical line terminal and ONU can be easily accomplished,and greatly decreasing the number of encoder/decoder becomes possible.In experiment,we only employ two encoder/decoder pairs to combine two WDM-PONs in one fiber.Simulation results confirm the feasibility of the proposed system.     

Performance analysis of wavelength/spatial coding system with fixed in-phase code matrices in OCDMA network

This paper proposes a wavelength/spatial (W/S) coding system with fixed in-phase code (FIPC) matrix in the optical code-division multiple-access (OCDMA) network. A scheme is presented to form the FIPC matrix which is applied to construct the W/S OCDMA network. The encoder/decoder in the W/S OCDMA network is fully able to eliminate the multiple-access-interference (MAI) at the balanced photo-detectors (PD), according to fixed in-phase cross correlation. The phase-induced intensity noise (PIIN) related to the power square is markedly suppressed in the receiver by spreading the received power into each PD while the net signal power is kept the same. Simulation results show that the W/S OCDMA network based on the FIPC matrices cannot only completely remove the MAI but effectively suppress the PIIN to upgrade the network performance.     

Low-Complexity Chase Decoding of Reed–Solomon Codes Using Channel Evaluation

A novel time-varying channel adaptive low-complexity chase (LCC) algorithm with low redundancy is proposed, where only the necessary number of test vectors (TVs) are generated and key equations are calculated according to the channel evaluation to reduce the decoding complexity. The algorithm evaluates the error symbol numbers by counting the number of unreliable bits of the received code sequence and dynamically adjusts the decoding parameters, which can reduce a large number of redundant calculations in the decoding process. We provide a simplified multiplicity assignment (MA) scheme and its architecture. Moreover, a multi-functional block that can implement polynomial selection, Chien search and the Forney algorithm (PCF) is provided. On this basis, a high-efficiency LCC decoder with adaptive error-correcting capability is proposed. Compared with the state-of-the-art LCC (TV = 16) decoding, the number of TVs of our decoder was reduced by 50.4% without loss of the frame error rate (FER) performance. The hardware implementation results show that the proposed decoder achieved 81.6% reduced average latency and 150% increased throughput compared to the state-of-the-art LCC decoder.     

量子稀疏图码的反馈式迭代译码

量子稀疏图码的译码可以由基于错误图样的和积译码算法来实现.本文在此基础上构建了一个新的反馈式迭代译码算法.其反馈策略不仅仅重新利用了错误图样,而且还利用了稳定子上相应元素的值和信道的错误模型.由此,本方法一方面可以克服传统的量子和积译码算法中遇到的所谓对称简并错误,另一方面还能反馈更多的有用信息到译码器中,帮助其产生有效的译码结果,大大提高译码器的译码能力.另外,本算法并没有增加量子测量的复杂度,而是对测量中所能获得的信息的更充分利用.     

An Optimized Three-Level Design of Decoder Based on Nanoscale Quantum-Dot Cellular Automata

Quantum-dot Cellular Automata (QCA) has been potentially considered as a supersede to Complementary Metal–Oxide–Semiconductor (CMOS) because of its inherent advantages. Many QCA-based logic circuits with smaller feature size, improved operating frequency, and lower power consumption than CMOS have been offered. This technology works based on electron relations inside quantum-dots. Due to the importance of designing an optimized decoder in any digital circuit, in this paper, we design, implement and simulate a new 2-to-4 decoder based on QCA with low delay, area, and complexity. The logic functionality of the 2-to-4 decoder is verified using the QCADesigner tool. The results have shown that the proposed QCA-based decoder has high performance in terms of a number of cells, covered area, and time delay. Due to the lower clock pulse frequency, the proposed 2-to-4 decoder is helpful for building QCA-based sequential digital circuits with high performance.     

Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes

Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity.     

脉宽对光码分多址编解码器性能的影响

光码分多址系统中,光编解码是影响系统性能的关键因素之一。给出了低折射率相移超结构光纤光栅(SSFBG)光码分多址编解码器的数学模型,采用自相关峰旁瓣比(P/W)、自互相关峰比(P/C)两个参量作为衡量编解码器性能的主要指标,仿真研究了不同脉宽及不同光栅(码片)长度条件下超结构光纤光栅编解码器的性能,得到了编解码器的P/W、P/C随输入脉冲宽度及编解码器长度的变化曲线。从对编解码器性能仿真分析的结果可以看出,当光源脉宽与编解码器的长度满足一定的匹配条件时,可获得较理想编解码效果,即可以根据输入脉冲的宽度来选择长度合适的编解码器,从而获得较好的系统的性能。     

High Differential Group Index of Dispersion Compensating Fibers for OCDMA Encoder/Decoder

We report the LPG pair device that can be used as a pulse duplicator or an OCDMA encoder/decoder. Due to the ring core region of dispersion compensating fiber (DCF), we can shorten the device length by a third and obtain surrounding insensitive LPG devices.     

Universal Coding for Classical-Quantum Channel

We construct a universal code for a stationary and memoryless classical-quantum channel as a quantum version of the universal coding by Csiszár and Körner. Our code is constructed utilizing a combination of irreducible representations, a decoder introduced through the quantum information spectrum, and the packing lemma.     

Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication.However,the existing decoders are generally incapable of checking node duplication of belief propagation(BP)on quantum low-density parity check(QLDPC)codes.Based on the probability theory in the machine learning,mathematical statistics and topological structure,a GF(4)(the Galois field is abbreviated as GF)augmented model BP decoder with Tanner graph is designed.The problem of repeated check nodes can be solved by this decoder.In simulation,when the random perturbation strength p=0.0115-0.0116 and number of attempts N=60-70,the highest decoding efficiency of the augmented model BP decoder is obtained,and the low-loss frame error rate(FER)decreases to 7.1975×10^-5.Hence,we design a novel augmented model decoder to compare the relationship between GF(2)and GF(4)for quantum code[[450,200]]on the depolarization channel.It can be verified that the proposed decoder provides the widely application range,and the decoding performance is better in QLDPC codes.