Recurrent neural network decoding of rotated surface codes based on distributed strategy

Quantum error correction is a crucial technology for realizing quantum computers.These computers achieve faulttolerant quantum computing by detecting and correcting errors using decoding algorithms.Quantum error correction using neural network-based machine learning methods is a promising approach that is adapted to physical systems without the need to build noise models.In this paper,we use a distributed decoding strategy,which effectively alleviates the problem of exponential growth of the training set required for neural networks as the code distance of quantum error-correcting codes increases.Our decoding algorithm is based on renormalization group decoding and recurrent neural network decoder.The recurrent neural network is trained through the ResNet architecture to improve its decoding accuracy.Then we test the decoding performance of our distributed strategy decoder,recurrent neural network decoder,and the classic minimum weight perfect matching(MWPM)decoder for rotated surface codes with different code distances under the circuit noise model,the thresholds of these three decoders are about 0.0052,0.0051,and 0.0049,respectively.Our results demonstrate that the distributed strategy decoder outperforms the other two decoders,achieving approximately a 5%improvement in decoding efficiency compared to the MWPM decoder and approximately a 2%improvement compared to the recurrent neural network decoder.

Tree-Structured Parallel Regeneration for Multiple Data Losses in Distributed Storage Systems Based on Erasure Codes

To reduce the time required to complete the regeneration process of erasure codes, we propose a Tree-structured Parallel Regeneration (TPR) scheme for multiple data losses in distributed storage systems. Under the scheme, two algorithms are proposed for the construction of multiple regeneration trees, namely the edge-disjoint algorithm and edge-sharing algorithm. The edge-disjoint algorithm constructs multiple independent trees, and is simple and appropriate for environments where newcomers and their providers are distributed over a large area and have few intersections. The edge-sharing algorithm constructs multiple trees that compete to utilize the bandwidth, and make a better utilization of the bandwidth, although it needs to measure the available band-width and deal with the bandwidth changes; it is therefore difficult to implement in practical systems. The parallel regeneration for multiple data losses of TPR primarily includes two optimizations: firstly, transferring the data through the bandwidth optimized-paths in a pipe-line manner; secondly, executing data regeneration over multiple trees in parallel. To evaluate the proposal, we implement an event-based simulator and make a detailed comparison with some popular regeneration methods. The quantitative comparison results show that the use of TPR employing either the edge-disjoint algorithm or edge-sharing algorithm reduces the regeneration time significantly.

On the complete weight distributions of quantum error-correcting codes

In a recent paper, Hu et al. defined the complete weight distributions of quantum codes and proved the Mac Williams identities, and as applications they showed how such weight distributions may be used to obtain the singleton-type and hamming-type bounds for asymmetric quantum codes. In this paper we extend their study much further and obtain several new results concerning the complete weight distributions of quantum codes and applications. In particular, we provide a new proof of the Mac Williams identities of the complete weight distributions of quantum codes. We obtain new information about the weight distributions of quantum MDS codes and the double weight distribution of asymmetric quantum MDS codes. We get new identities involving the complete weight distributions of two different quantum codes. We estimate the complete weight distributions of quantum codes under special conditions and show that quantum BCH codes by the Hermitian construction from primitive, narrow-sense BCH codes satisfy these conditions and hence these estimate applies.

Locally Minimum Storage Regenerating Codes in Distributed Cloud Storage Systems

In distributed cloud storage systems, inevitably there exist multiple node failures at the same time. The existing methods of regenerating codes, including minimum storage regenerating(MSR) codes and minimum bandwidth regenerating(MBR) codes, are mainly to repair one single or several failed nodes, unable to meet the repair need of distributed cloud storage systems. In this paper, we present locally minimum storage regenerating(LMSR) codes to recover multiple failed nodes at the same time. Specifically, the nodes in distributed cloud storage systems are divided into multiple local groups, and in each local group(4, 2) or(5, 3) MSR codes are constructed. Moreover, the grouping method of storage nodes and the repairing process of failed nodes in local groups are studied. Theoretical analysis shows that LMSR codes can achieve the same storage overhead as MSR codes. Furthermore, we verify by means of simulation that, compared with MSR codes, LMSR codes can reduce the repair bandwidth and disk I/O overhead effectively.

Construction and Weight Distributions of Binary Linear Codes Based on Deep Holes

Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.

Low complexity DCT-based distributed source coding with Gray code for hyperspectral images

To compress hyperspectral images, a low complexity discrete cosine transform （DCT）-based distributed source coding （DSC） scheme with Gray code is proposed. Unlike most of the existing DSC schemes, which utilize transform in spatial domain, the proposed algorithm applies transform in spectral domain. Set-partitioning-based approach is applied to reorganize DCT coefficients into waveletlike tree structure and extract the sign, refinement, and significance bitplanes. The extracted refinement bits are Gray encoded. Because of the dependency along the line dimension of hyperspectral images, low density paritycheck-（LDPC）-based Slepian-Wolf coder is adopted to implement the DSC strategy. Experimental results on airborne visible/infrared imaging spectrometer （AVIRIS） dataset show that the proposed paradigm achieves up to 6 dB improvement over DSC-based coders which apply transform in spatial domain, with significantly reduced computational complexity and memory storage.

DESIGN OF EXACT REGENERATING HIERARCHICAL CODE FOR DISTRIBUTED STORAGE SYSTEM

Erasure code is widely used as the redundancy scheme in distributed storage system. When a storage node fails, the repair process often requires to transfer a large amount of data. Regenerating code and hierarchical code are two classes of codes proposed to reduce the repair bandwidth cost. Regenerating codes reduce the amount of data transferred by each helping node, while hierarchical codes reduce the number of nodes participating in the repair process. In this paper, we propose a "sub-code nesting framework" to combine them together. The resulting regenerating hierarchical code has low repair degree as hierarchical code and lower repair cost than hierarchical code. Our code can achieve exact regeneration of the failed node, and has the additional property of low updating complexity.

Code Design and Latency Analysis of Distributed Matrix Multiplication with Straggling Servers in Fading Channels

This paper exploits coding to speed up computation offloading in a multi-server mobile edge computing(MEC)network with straggling servers and channel fading.The specific task we consider is to compute the product between a user-generated input data matrix and a large-scale model matrix that is stored distributively across the multiple edge nodes.The key idea of coding is to introduce computation redundancy to improve robustness against straggling servers and to create communication redundancy to improve reliability against channel fading.We utilize the hybrid design of maximum distance separable(MDS)coding and repetition coding.Based on the hybrid coding scheme,we conduct theoretical analysis on the average task uploading time,average edge computing time,and average output downloading time,respectively and then obtain the end-to-end task execution time.Numerical results demonstrate that when the task uploading phase or the edge computing phase is the performance bottleneck,the hybrid coding reduces to MDS coding;when the downlink transmission is the bottleneck,the hybrid coding reduces to repetition coding.The hybrid coding also outperforms the entangled polynomial coding that causes higher uplink and downlink communication loads.

Space-Time-Frequency Coded for Multiband-OFDM Based on IEEE 802.15.3a WPAN

In this paper, Multiband-OFDM UWB system based on IEEE 802.15.3a standard is studied and simulated with spatial, time and frequency (STF)coding scheme. The using of STF coding method can guarantee both full symbol rate and full diversity advantages. The simulation results show that the STF code uses multi- path-rich and random-clustering characteristics of UWB channel environment on the performance of MB- OFDM system.

Distributed Video Coding Using LDPC Codes for Wireless Video

Popular video coding standards like H.264 and MPEG working on the principle of motion-compensated pre-dictive coding demand much of the computational resources at the encoder increasing its complexity. Such bulky encoders are not suitable for applications like wireless low power surveillance, multimedia sensor networks, wireless PC cameras, mobile camera phones etc. New video coding scheme based on the principle of distributed source coding is looked upon in this paper. This scheme supports a low complexity encoder, at the same time trying to achieve the rate distortion performance of conventional video codecs. Current im-plementation uses LDPC codes for syndrome coding.

Trifocal tensor based side information generation for multi-view distributed video code

Distributed video coding （DVC） is a new video coding approach based on Wyner-Ziv theorem. The novel uplink-friendly DVC, which offers low-complexity, low-power consuming, and low-cost video encoding, has aroused more and more research interests. In this paper a new method based on multiple view geometry is presented for spatial side information generation of uncalibrated video sensor network. Trifocal tensor encapsulates all the geometric relations among three views that are independent of scene structure; it can be computed from image correspondences alone without requiring knowledge of the motion or calibration. Simulation results show that trifocal tensor-based spatial side information improves the rate-distortion performance over motion compensation based interpolation side information by a maximum gap of around 2dB. Then fusion merges the different side information （temporal and spatial） in order to improve the quality of the final one. Simulation results show that the rate-distortion gains about 0.4 dB.

Log Likelihood Ratio-Based Relaying for Distributed Turbo Codes

A distributed turbo codes（ DTC） scheme with log likelihood ratio（ LLR）-based threshold at the relay for a two-hop relay networks is proposed. Different from traditional DTC schemes,the retransmission scheme at the relay,where imperfect decoding occurs,is considered in the proposed scheme. By employing a LLR-based threshold at the relay in the proposed scheme,the reliability of decoder-LLRs can be measured. As a result,only reliable symbols will be forwarded to the destination and a maximum ratio combiner（ MRC） is used to combine signals received from both the source and the relay. In order to obtain the optimal threshold at the relay,an equivalent model of decoderLLRs is investigated,so as to derive the expression of the bit error probability（ BEP） of the proposed scheme under binary phase shift keying（ BPSK） modulation. Simulation results demonstrate that the proposed scheme can effectively mitigate error propagation at the relay and also outperforms other existing methods.

PERIOD DISTRIBUTION OF CYCLIC CODES OVER F_q + uF_q +···+u^(m-1)F_q

In this paper, the period distribution of cyclic codes overR = F_q + uF_q +···+u^(m-1)F_q is studied, where um= 0 and q is a prime power. A necessary and sufficient condition for the existence of period of cyclic codes over R is given. The period distributions of cyclic codes over R and their dual codes are determined by employing generator polynomial. The counting formulas of the period distributions of cyclic codes over R and their dual codes are obtained.

Systematic-bit-selection distributed with selective-relaying

An improved distributed turbo coding （DTC） scheme, namely, systematic-bit-selection DTC, is proposed for a two-hop relay network implementing selective-relaying （SR）. In the scheme, source broadcasts a punctured turbo code in order to increase the successful decoding rate of relay. The relay forwards systematic-bit to the destination in case of successful cyclic redundancy check （CRC）. From the two versions of systematic-bit coming from relay and source respectively, the des- tination selects the one with higher signal-to-noise ratio （SNR） for turbo decoding. Simulation re- suits show the improved bit error rate （BER） performance of our scheme.

A Method for Improving Power Distribution Characteristics of Space Time Block Codes

Improving power distribution characteristics of space time block codes(STBCs),namely peak to average power ratio(PAPR),average to minimum power ratio(Ave/min),and probability of transmitting"zero"by antenna,makes easier their practical implementation.To this end,this study proposes to multiply full diversity STB C with a non-singular matrix in multiple input multiple output(MIMO)or multiple input single output(MISO)systems with linear or maximum likelihood(ML)receivers.It is proved that the obtained code achieves full diversity and the order of detection complexity does not change.The proposed method is applied to different types of STBCs.The bit error rate(BER)and power distribution characteristics of the new codes demonstrate the superiority of the introduced method.Further,lower and upper bounds on the BER of the obtained STBCs are derived for all receivers.The proposed method provides trade-off among PAPR,spectral efficiency,energy efficiency,and BER.

An optimized framework for degree distribution in LT codes based on power law

LT codes are practical realization of digital fountain codes, which provides the concept of rateless coding. In this scheme, encoded symbols are generated infinitely from k information symbols. Decoder uses only(1+α)k number of encoded symbols to recover the original information. The degree distribution function in the LT codes helps to generate a random graph also referred as tanner graph. The artifact of tanner graph is responsible for computational complexity and overhead in the LT codes. Intuitively, a well designed degree distribution can be used for an efficient implementation of LT codes. The degree distribution function is studied as a function of power law, and LT codes are classified into two different categories: SFLT and RLT codes. Also, two different degree distributions are proposed and analyzed for SFLT codes which guarantee optimal performance in terms of computational complexity and overhead.

Efficiency and Feasibility of an Integrated Algorithm for Distributed Hydrological M odel Calibration

Increasing complexity of distributed hydrological model （DHM） has lowered the efficiency of convergence.In this study,global sensitivity analysis （SA） was introduced by combining multiobjective （MO） optimization for DHM calibration.Latin Hypercube-once at a time （LH-OAT） was adopted in global parameter SA to obtain relative sensitivity of model parameter,which can be categorized into different sensitivity levels.Two comparative study cases were conducted to present the efficiency and feasibility by combining SA with MO（SA-MO）.WetSpa model with non-dominated sorting genetic algorithm-Ⅱ （NSGA-Ⅱ） algorithm and EasyDHM model with multi-objective sequential complex evolutionary metropolis-uncertainty analysis （MOSCEM-UA）algorithm were adopted to demonstrate the general feasibility of combining SA in optimization.Results showed that the LH-OAT was globally effective in selecting high sensitivity parameters.It proves that using parameter from high sensitivity groups results in higher convergence efficiency.Study case Ⅰ showed a better Pareto front distribution and convergence compared with model calibration without SA.Study case Ⅱ indicated a more efficient convergence of parameters in sequential evolution of MOSCEM-UA under the same iteration.It indicates that SA-MO is feasible and efficient for high dimensional DHM calibration.

ON THE MEAN VALUE AND VARIANCE OF DISTANCE DISTRIBUTION OF NON-LINEAR CODES IN GF(q)

This paper presents the lower bounds and upper bounds for the mean value and variance of distance distribution of non-linear codes in GF(q). By presenting several examples, it is shown that these bounds could be achieved.

Improved scheme with cooperative diversity based on distributed space-time block coding

An improved scheme with cooperative diversity based on distributed space-time block coding （WCD- DSTBC） is proposed, which effectively achieves diversity gains and improves the performance of the system by sharing some single-antenna users＇ antennas to form a virtual antenna array and combining with distributed spacetime block coding （DSTBC） mode. Then the relation between the system BER and the interuser BER for WCDDSTBC scheme is theoretically derived and the closed-form expression of BER for WCD-DSTBC system is obtained. The simulation results show that the proposed WCD-DSTBC scheme achieves distinct gains over the non-cooperative multi-carrier CDMA （MC-CDMA） system. When system BER is le-3 and interuser BER is le-3, about 2.5 dB gain can be gotten. When interuser channel state information （CSI） outgoes the users＇ individual CSI, about 3 dB gain is also achieved.