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Toshiyuki Tanaka

Publications and source records attributed to Toshiyuki Tanaka.

54 records · Page 3Linked to original sources
arXiv2011

Improvement of BP-Based CDMA Multiuser Detection by Spatial Coupling

Kudekar et al. proved that the belief-propagation (BP) threshold for low-density parity-check codes can be boosted up to the maximum-a-posteriori (MAP) threshold by spatial coupling. In this paper, spatial coupling is applied to randomly-spread code-division multiple-access (CDMA) systems in order to improve the performance of BP-based multiuser detection (MUD). Spatially-coupled CDMA systems can be regarded as multi-code CDMA systems with two transmission phases. The large-system analysis shows that spatial coupling can improve the BP performance, while there is a gap between the BP performance and the individually-optimal (IO) performance.

cs.IT↗
arXiv2011

Large-System Analysis of Joint Channel and Data Estimation for MIMO DS-CDMA Systems

This paper presents a large-system analysis of the performance of joint channel estimation, multiuser detection, and per-user decoding (CE-MUDD) for randomly-spread multiple-input multiple-output (MIMO) direct-sequence code-division multiple-access (DS-CDMA) systems. A suboptimal receiver based on successive decoding in conjunction with linear minimum mean-squared error (LMMSE) channel estimation is investigated. The replica method, developed in statistical mechanics, is used to evaluate the performance in the large-system limit, where the number of users and the spreading factor tend to infinity while their ratio and the number of transmit and receive antennas are kept constant. The performance of the joint CE-MUDD based on LMMSE channel estimation is compared to the spectral efficiencies of several receivers based on one-shot LMMSE channel estimation, in which the decoded data symbols are not utilized to refine the initial channel estimates. The results imply that the use of joint CE-MUDD significantly reduces rate loss due to transmission of pilot signals, especially for multiple-antenna systems. As a result, joint CE-MUDD can provide significant performance gains, compared to the receivers based on one-shot channel estimation.

cs.IT↗
arXiv2010

Effects of Single-Cycle Structure on Iterative Decoding for Low-Density Parity-Check Codes

We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For fixed numbers of BP iterations, the bit error probability approaches a limit as blocklength tends to infinity, and the limit is obtained via density evolution. On the other hand, the difference between the bit error probability of codes with blocklength $n$ and that in the large blocklength limit is asymptotically $α(ε,t)/n + Θ(n^{-2})$ where $α(ε,t)$ denotes a specific constant determined by the code ensemble considered, the number $t$ of iterations, and the erasure probability $ε$ of the BEC. In this paper, we derive a set of recursive formulas which allows evaluation of the constant $α(ε,t)$ for standard irregular ensembles. The dominant difference $α(ε,t)/n$ can be considered as effects of cycle-free and single-cycle structures of local graphs. Furthermore, it is confirmed via numerical simulations that estimation of the bit error probability using $α(ε,t)$ is accurate even for small blocklengths.

cs.IT↗
arXiv2010

Channel Polarization on q-ary Discrete Memoryless Channels by Arbitrary Kernels

A method of channel polarization, proposed by Arikan, allows us to construct efficient capacity-achieving channel codes. In the original work, binary input discrete memoryless channels are considered. A special case of $q$-ary channel polarization is considered by Sasoglu, Telatar, and Arikan. In this paper, we consider more general channel polarization on $q$-ary channels. We further show explicit constructions using Reed-Solomon codes, on which asymptotically fast channel polarization is induced.

cs.IT↗
arXiv2010

Non-Binary Polar Codes using Reed-Solomon Codes and Algebraic Geometry Codes

Polar codes, introduced by Arikan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error probability of non-binary polar codes constructed on the basis of Reed-Solomon matrices by numerical simulations. It is confirmed that 4-ary polar codes have significantly better performance than binary polar codes on binary-input AWGN channel. We also discuss an interpretation of polar codes in terms of algebraic geometry codes, and further show that polar codes using Hermitian codes have asymptotically good performance.

cs.IT↗
arXiv2010

Statistical Mechanical Analysis of a Typical Reconstruction Limit of Compressed Sensing

We use the replica method of statistical mechanics to examine a typical performance of correctly reconstructing $N$-dimensional sparse vector $bx=(x_i)$ from its linear transformation $by=bF bx$ of $P$ dimensions on the basis of minimization of the $L_p$-norm $||bx||_p= lim_{epsilon to +0} sum_{i=1}^N |x_i|^{p+epsilon}$. We characterize the reconstruction performance by the critical relation of the successful reconstruction between the ratio $alpha=P/N$ and the density $rho$ of non-zero elements in $bx$ in the limit $P,,N to infty$ while keeping $alpha sim O(1)$ and allowing asymptotically negligible reconstruction errors. We show that the critical relation $alpha_c(rho)$ holds universally as long as $bF^{rm T}bF$ can be characterized asymptotically by a rotationally invariant random matrix ensemble and $bF bF^{rm T}$ is typically of full rank. This supports the universality of the critical relation observed by Donoho and Tanner ({em Phil. Trans. R. Soc. A}, vol.~367, pp.~4273--4293, 2009; arXiv: 0807.3590) for various ensembles of compression matrices.

cs.IT↗
arXiv2009

Finite-Length Analysis of Irregular Expurgated LDPC Codes under Finite Number of Iterations

Communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding is considered. The average bit error probability of an irregular LDPC code ensemble after a fixed number of iterations converges to a limit, which is calculated via density evolution, as the blocklength $n$ tends to infinity. The difference between the bit error probability with blocklength $n$ and the large-blocklength limit behaves asymptotically like $α/n$, where the coefficient $α$ depends on the ensemble, the number of iterations and the erasure probability of the BEC\null. In [1], $α$ is calculated for regular ensembles. In this paper, $α$ for irregular expurgated ensembles is derived. It is demonstrated that convergence of numerical estimates of $α$ to the analytic result is significantly fast for irregular unexpurgated ensembles.

cs.IT↗
arXiv2009

Performance and Construction of Polar Codes on Symmetric Binary-Input Memoryless Channels

Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this paper, a new construction method for arbitrary symmetric binary memoryless channel (B-MC) with linear complexity in the blocklength is proposed. Furthermore, new upper and lower bounds of the block error probability of polar codes are derived for the BEC and the arbitrary symmetric B-MC, respectively.

cs.IT↗
arXiv2008

Re`class'ification of `quant'ified classical simulated annealing

We discuss a classical reinterpretation of quantum-mechanics-based analysis of classical Markov chains with detailed balance, that is based on the quantum-classical correspondence. The classical reinterpretation is then used to demonstrate that it successfully reproduces a sufficient condition for cooling schedule in classical simulated annealing, which has the inverse-logarithmic scaling.

physics.comp-ph↗
arXiv2008

Optimization of sequences in CDMA systems: a statistical-mechanics approach

Statistical mechanics approach is useful not only in analyzing macroscopic system performance of wireless communication systems, but also in discussing design problems of wireless communication systems. In this paper, we discuss a design problem of spreading sequences in code-division multiple-access (CDMA) systems, as an example demonstrating the usefulness of statistical mechanics approach. We analyze, via replica method, the average mutual information between inputs and outputs of a randomly-spread CDMA channel, and discuss the optimization problem with the average mutual information as a measure of optimization. It has been shown that the average mutual information is maximized by orthogonally-invariant random Welch bound equality (WBE) spreading sequences.

cs.IT↗
arXiv2008

Microscopic Analysis for Decoupling Principle of Linear Vector Channel

This paper studies the decoupling principle of a linear vector channel, which is an extension of CDMA and MIMO channels. We show that the scalar-channel characterization obtained via the decoupling principle is valid not only for collections of a large number of elements of input vector, as discussed in previous studies, but also for individual elements of input vector, i.e. the linear vector channel for individual elements of channel input vector is decomposed into a bank of independent scalar Gaussian channels in the large-system limit, where dimensions of channel input and output are both sent to infinity while their ratio fixed.

cs.IT↗
arXiv2007

Asymptotic Analysis of General Multiuser Detectors in MIMO DS-CDMA Channels

We analyze a MIMO DS-CDMA channel with a general multiuser detector including a nonlinear multiuser detector, using the replica method. In the many-user, limit the MIMO DS-CDMA channel with the multiuser detector is decoupled into a bank of single-user SIMO Gaussian channels if a spatial spreading scheme is employed. On the other hand, it is decoupled into a bank of single-user MIMO Gaussian channels if a spatial spreading scheme is not employed. The spectral efficiency of the MIMO DS-CDMA channel with the spatial spreading scheme is comparable with that of the MIMO DS-CDMA channel using an optimal space-time block code without the spatial spreading scheme. In the case of the QPSK data modulation scheme the spectral efficiency of the MIMO DS-CDMA channel with the MMSE detector shows {\it waterfall} behavior and is very close to the corresponding sum capacity when the system load is just below the transition point of the {\it waterfall} behavior. Our result implies that the performance of a multiuser detector taking the data modulation scheme into consideration can be far superior to that of linear multiuser detectors.

cs.IT↗
arXiv2007

Spectral Density of Sparse Sample Covariance Matrices

Applying the replica method of statistical mechanics, we evaluate the eigenvalue density of the large random matrix (sample covariance matrix) of the form $J = A^{\rm T} A$, where $A$ is an $M \times N$ real sparse random matrix. The difference from a dense random matrix is the most significant in the tail region of the spectrum. We compare the results of several approximation schemes, focusing on the behavior in the tail region.

cond-mat.stat-mech↗
arXiv2007

Hierarchical Decoupling Principle of a MIMO-CDMA Channel in Asymptotic Limits

We analyze an uplink of a fast flat fading MIMO-CDMA channel in the case where the data symbol vector for each user follows an arbitrary distribution. The spectral efficiency of the channel with CSI at the receiver is evaluated analytically with the replica method. The main result is that the hierarchical decoupling principle holds in the MIMO-CDMA channel, i.e., the MIMO-CDMA channel is decoupled into a bank of single-user MIMO channels in the many-user limit, and each single-user MIMO channel is further decoupled into a bank of scalar Gaussian channels in the many-antenna limit for a fading model with a limited number of scatterers.

cs.IT↗
arXiv2002

Typical performance of low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Theoretical framework for dealing with general symmetric channels is provided, based on which Gallager and MacKay-Neal codes are studied as examples of LDPC codes. It has been shown that the basic properties of these codes known for particular channels, including the property to potentially saturate Shannon's limit, hold for general symmetric channels. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.

cond-mat.dis-nn↗
arXiv2000

Application of two-parameter dynamical replica theory to retrieval dynamics of associative memory with non-monotonic neurons

The two-parameter dynamical replica theory (2-DRT) is applied to investigate retrieval properties of non-monotonic associative memory, a model which lacks thermodynamic potential functions. 2-DRT reproduces dynamical properties of the model quite well, including the capacity and basin of attraction. Superretrieval state is also discussed in the framework of 2-DRT. The local stability condition of the superretrieval state is given, which provides a better estimate of the region in which superretrieval is observed experimentally than the self-consistent signal-to-noise analysis (SCSNA) does.

cond-mat.dis-nn↗