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The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally treelike, and sparse covariance matrices. We derive a closed set of equations from which the density of eigenvalues can be efficiently calculated. Within this approach, the… (More)

– An approach to analyze the performance of the code division multiple access (CDMA) scheme, which is a core technology used in modern wireless communication systems, is provided. The approach characterizes the objective system by the eigenvalue spectrum of a cross-correlation matrix composed of signature sequences used in CDMA communication, which enable… (More)

The Kronecker channel model of wireless communication is analyzed using statistical mechanics methods. In the model, spatial proximities among transmission/reception antennas are taken into account as certain correlation matrices, which generally yield non-trivial dependence among symbols to be estimated. This prevents accurate assessment of the… (More)

—We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L1-norm minimization utilizing a correlated compression matrix with a statistical mechanics method. We focus on the compression matrix modeled as the Kronecker-type random matrix studied in research on multiple-input multiple-output wireless communication… (More)

PACS 89.70.-a – Information and communication theory PACS 75.10.Nr – Spin-glass and other random models PACS 05.70.Fh – Phase transitions: general studies Abstract.-We provide a scheme for exploring the reconstruction limits of compressed sensing by minimizing the general cost function under the random measurement constraints for generic correlated signal… (More)

A statistical mechanical framework to analyze linear vector channel models in digital wireless communication is proposed for a large system. The framework is a generalization of that proposed for code-division multiple-access systems in Europhys. Lett., 76 (2006) 1193 and enables the analysis of the system in which the elements of the channel transfer… (More)

We propose a systematic method for constructing a sparse data reconstruction algorithm in compressed sensing at a relatively low computational cost for general observation matrix. It is known that the cost of ℓ1-norm minimization using a standard linear programming algorithm is O(N 3). We show that this cost can be reduced to O(N 2) by applying the approach… (More)

A study of the universal threshold in the ℓ 1 recovery by statistical mechanics Abstract—We discuss the universality of the ℓ1 recovery threshold in compressed sensing. Previous studies in the fields of statistical mechanics and random matrix integration have shown that ℓ1 recovery under a random matrix with orthogonal symmetry has a universal threshold.… (More)

We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by using the replica method in two situations: lossy data compression and channel coding. For both the situations, the… (More)

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