arXiv subjects
Publications and source records attributed to Takayuki Nozaki.
This paper constructs a non-binary code correcting a single $b$-burst of insertions or deletions with a large cardinality. This paper also proposes a decoding algorithm of this code and evaluates a lower bound of the cardinality of this code. Moreover, we evaluate an asymptotic upper bound on the cardinality of codes which correct a single burst of insertions or deletions.
Fountain codes are erasure correcting codes realizing reliable communication systems for the multicast on the Internet. The zigzag decodable fountain (ZDF) code is one of generalization of the Raptor code, i.e, applying shift operation to generate the output packets. The ZDF code is decoded by a two-stage iterative decoding algorithm, which combines the packet-wise peeling algorithm and the bit-wise peeling algorithm. By the bit-wise peeling algorithm and shift operation, ZDF codes outperform Raptor codes under iterative decoding in terms of decoding erasure rate and overhead. However, the bit-wise peeling algorithm spends long decoding time. This paper proposes a fast bit-wise decoding algorithm for the ZDF codes. Simulation results show that the proposed algorithm drastically reduces the decoding time compared with the existing algorithm.
The random access scheme is a fundamental scenario in which users transmit through a shared channel and cannot coordinate each other. In recent years, successive interference cancellation (SIC) was introduced into the random access scheme. It is possible to decode transmitted packets using collided packets by the SIC. The coded slotted ALOHA (CSA) is a random access scheme using the SIC. The CSA encodes each packet using a local code prior to transmission. It is known that the CSA achieves excellent throughput. On the other hand, it is reported that in the coding theory time shift improves the decoding performance for packet-oriented erasure correcting codes. In this paper, we propose a random access scheme which applies the time shift to the CSA in order to achieve better throughput. Numerical examples show that our proposed random access scheme achieves better throughput and packet loss rate than the CSA.
This paper proposes an erasure correcting code and its systematic form for the distributed storage system. The proposed codes are encoded by exclusive OR and bit-level shift operation. By the shift operation, the encoded packets are slightly longer than the source packets. This paper evaluates the extra length of encoded packets, called overhead, and shows that the proposed codes have smaller overheads than the zigzag decodable code, which is an existing code using exclusive OR and bit-level shift operation.
In the present paper, we derive an upper bound of the average network breakdown probability of packet networks with unreliable relay nodes. We here assume that relay nodes get independently broken with a given node breakdown probability. A survivor graph is the induced subgraph obtained by removing the broken relay nodes and their connecting edges from the original graph. If the survivor network is disconnected, we consider a network breakdown happens. The primal contribution of the paper is to derive an upper bound of the average network breakdown probability, where the expectation is taken over a regular graph ensemble. The proof of the bound is based on a natural one-to-one correspondence between a regular graph and a regular bipartite graph, and also on enumeration of bipartite graphs satisfying certain conditions. This proof argument is inspired by the analysis of weight distribution for low-density parity-check codes. Compared with estimates of the average network breakdown probability obtained by computer experiments, it is observed that the upper bound provides the values which are not only upper bounds but also precise estimates of the network breakdown probability when the node breakdown probability is small.
This paper proposes a fountain coding system which has lower space decoding complexity and lower decoding erasure rate than the Raptor coding systems. The main idea of the proposed fountain code is employing shift and exclusive OR to generate the output packets. This technique is known as the zigzag decodable code, which is efficiently decoded by the zigzag decoder. In other words, we propose a fountain code based on the zigzag decodable code in this paper. Moreover, we analyze the overhead for the received packets, decoding erasure rate, decoding complexity, and asymptotic overhead of the proposed fountain code. As the result, we show that the proposed fountain code outperforms the Raptor codes in terms of the overhead and decoding erasure rate. Simulation results show that the proposed fountain coding system outperforms Raptor coding system in terms of the overhead and the space decoding complexity.
In a previous work, we presented a parallel encoding algorithm for low-density parity-check (LDPC) codes by partitioning hypergraph representation for the LDPC codes. The aim of this research is to analyze the processing time of this encoding algorithm. This paper clarifies that the processing time of the encoding algorithm depends on the minimum cutsize of balanced hypergraph partitions. Moreover, this paper gives the typical minimum cutsize and cutsize distribution for balanced hypergraph bipartitions of random hypergraphs defined from a regular LDPC ensemble.
We report on the temperature and layer thickness variation of spin-orbit torques in perpendicularly magnetized W/CoFeB bilayers. Harmonic Hall voltage measurements reveal dissimilar temperature evolutions of longitudinal and transverse effective magnetic field components. The transverse effective field changes sign at 250 K for a 2 nm thick W buffer layer, indicating a much stronger contribution from interface spin-orbit interactions compared to, for example, Ta. Transmission electron microscopy measurements reveal that considerable interface mixing between W and CoFeB is primarily responsible for this effect.
In this paper, we derive the average weight distributions for the irregular non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we give the exponential growth rate of the average weight distribution in the limit of large code length. We show that there exist $(2,d_c)$-regular non-binary cluster LDPC code ensembles whose normalized typical minimum distances are strictly positive.
We study LDPC codes for the channel with $2^m$-ary input $\underline{x}\in \mathbb{F}_2^m$ and output $\underline{y}=\underline{x}+\underline{z}\in \mathbb{F}_2^m$. The receiver knows a subspace $V\subset \mathbb{F}_2^m$ from which $\underline{z}=\underline{y}-\underline{x}$ is uniformly chosen. Or equivalently, the receiver receives an affine subspace $\underline{y}-V$ where $\underline{x}$ lies. We consider a joint iterative decoder involving the channel detector and the LDPC decoder. The decoding system considered in this paper can be viewed as a simplified model of the joint iterative decoder over non-binary modulated signal inputs e.g., $2^m$-QAM. We evaluate the performance of binary spatially-coupled MacKay-Neal codes by density evolution. The iterative decoding threshold is seriously degraded by increasing $m$. EXIT-like function curve calculations reveal that this degradation is caused by wiggles and can be mitigated by increasing the randomized window size. The resultant iterative decoding threshold values are very close to the Shannon limit.
A scaling law developed by Amraoui et al. is a powerful technique to estimate the block error probability of finite length low-density parity-check (LDPC) codes. Solving a system of differential equations called covariance evolution is a method to obtain the scaling parameter. However, the covariance evolution has not been analytically solved. In this paper, we present the analytical solution of the covariance evolution for irregular LDPC code ensembles.
In this paper, we investigate the error floors of non-binary low-density parity-check (LDPC) codes transmitted over the memoryless binary-input output-symmetric (MBIOS) channels. We provide a necessary and sufficient condition for successful decoding of zigzag cycle codes over the MBIOS channel by the belief propagation decoder. We consider an expurgated ensemble of non-binary LDPC codes by using the above necessary and sufficient condition, and hence exhibit lower error floors. Finally, we show lower bounds of the error floors for the expurgated LDPC code ensembles over the MBIOS channel.
The degradation mechanisms of multilayer graphene spin valves are investigated. The spin injection signals in graphene spin valves have been reported to be linearly dependent on the drain bias voltage, which indicates that the spin polarization of injected spins in graphene is robust against the bias voltage. We present that the disappearance of this robustness is due to two different degradation mechanisms of the spin valves. Our findings indicate that the disappearance of the robustness is due to degradation rather than an intrinsic characteristic of graphene. Thus, the robustness can be greatly enhanced if degradation can be prevented.
Decrease of spin polarization in spintronics devices under an application of bias voltage is one of currently important problems which should be solved. We reveal unprecedented robustness of spin polarization in multi-layer graphene spin valves at room temperature. Surprisingly, the spin polarization of injected spins is constant up to a bias voltage of +2.7 V and -0.6 V in positive and negative bias voltage applications, which is dramatically superior to all spintronics devices. Our finding is induced by suppression of spin scattering due to an ideal interface formation. Furthermore, we firstly report on important accordance between theory and experiment in molecular spintronics by observing the fact that signal intensity in a local scheme is double of that in a non-local scheme as theory predicts, which provides construction of a steadfast physical basis in this field.
Growing demands for the voltage-driven spintronic applications with ultralow-power consumption have led to new interest in exploring the voltage-induced magnetization switching in ferromagnetic metals. In this study, we observed a large perpendicular magnetic anisotropy change in Au(001) / ultrathin Fe80Co20(001) / MgO(001) / Polyimide / ITO junctions, and succeeded in realizing a clear switching of magnetic easy axis between in-plane and perpendicular directions. Furthermore, employing a perpendicularly magnetized film, voltage-induced magnetization switching in the perpendicular direction under the assistance of magnetic fields was demonstrated. These pioneering results may open a new window of electric-field controlled spintronics devices.
The covariance evolution is a system of differential equations with respect to the covariance of the number of edges connecting to the nodes of each residual degree. Solving the covariance evolution, we can derive distributions of the number of check nodes of residual degree 1, which helps us to estimate the block error probability for finite-length LDPC code. Amraoui et al.\ resorted to numerical computations to solve the covariance evolution. In this paper, we give the analytical solution of the covariance evolution.
We implemented a nuclear magnetic resonance (NMR) study on rubrene(C42H28)-Co nano-composites that exhibit an enhanced magnetoresistance (MR) ratio of 80%. The 59Co NMR spin echo experiment enabled clarification of the hyperfine field of Co at the interface between the ferromagnet and the molecules, which has not been investigated for molecular spintronics. An enhanced hyperfine field of the Co was observed in the rubrene-Co nano-composites, which may be related to the enhancement of the MR ratio. This study demonstrates the importance of microscopic investigation of the interface between molecules and ferromagnets that governs spin-dependent transport in molecular spin devices.
We demonstrate spin injection into a graphene thin film with high reliability by using non-local magnetoresistance (MR) measurements, in which the electric current path is completely separated from the spin current path. Using these non-local measurements, an obvious MR effect was observed at room temperature; and the MR effect was ascribed to magnetization reversal of ferromagnetic electrodes. This result is a direct demonstration of spin injection into a graphene thin film. Furthermore, this is the first report of spin injection into molecules at room temperature.