Linear-Codes-Based Lossless Joint Source-Channel Coding for Multiple-Access Channels

A general lossless joint source-channel coding (JSCC) scheme based on linear codes and random interleavers for multiple-access channels (MACs) is presented and then analyzed in this paper. By the information-spectrum approach and the code-spectrum approach, it is shown that a linear code with a good joint spectrum can be used to establish limit-approaching lossless JSCC schemes for correlated general sources and general MACs, where the joint spectrum is a generalization of the input-output weight distribution. Some properties of linear codes with good joint spectra are investigated. A formula on the "distance" property of linear codes with good joint spectra is derived, based on which, it is further proved that, the rate of any systematic codes with good joint spectra cannot be larger than the reciprocal of the corresponding alphabet cardinality, and any sparse generator matrices cannot yield linear codes with good joint spectra. The problem of designing arbitrary rate coding schemes is also discussed. A novel idea called "generalized puncturing" is proposed, which makes it possible that one good low-rate linear code is enough for the design of coding schemes with multiple rates. Finally, various coding problems of MACs are reviewed in a unified framework established by the code-spectrum approach, under which, criteria and candidates of good linear codes in terms of spectrum requirements for such problems are clearly presented.Comment: 18 pages, 3 figure

Extending the Coyote emulator to dark energy models with standard w0w_0-waw_a parametrization of the equation of state

We discuss an extension of the Coyote emulator to predict non-linear matter power spectra of dark energy (DE) models with a scale factor dependent equation of state of the form w = w_0 + ( 1 - a )w_a . The extension is based on the mapping rule between non-linear spectra of DE models with constant equation of state and those with time varying one originally introduced in ref. [40]. Using a series of N-body simulations we show that the spectral equivalence is accurate to sub-percent level across the same range of modes and redshift covered by the Coyote suite. Thus, the extended emulator provides a very efficient and accurate tool to predict non-linear power spectra for DE models with w_0 - w_a parametrization. According to the same criteria we have developed a numerical code, and we have implemented in a dedicated module for the CAMB code, that can be used in combination with the Coyote Emulator in likelihood analyses of non-linear matter power spectrum measurements. All codes can be found at https://github.com/luciano-casarini/PKequalComment: All codes can be found at https://github.com/luciano-casarini/PKequa

Evaluation of Seismic Response of a Site Class F Site Using Equivalent Linear and Nonlinear Computer Codes

Evaluation of seismic site response and development of site-specific surface response spectra has evolved in recent years through the use of both equivalent linear (EQL) and nonlinear (NL) computer codes. Before the nonlinear computer codes become popular among practitioners, equivalent linear site response analysis programs were used to develop site-specific design spectra for both soft and stiff sites. Nonlinear site response analysis is now used more routinely for projects planned on Site Class F sites. This paper presents the results of seismic response analyses completed for a Site Class F site at Grays Harbor, Washington. Both the equivalent linear (SHAKE2000) and nonlinear (D-MOD2000) computer codes were used to evaluate the site response under the maximum considered earthquake (MCE) using the guidelines set forth in 2006 International Building Code (IBC) and American Society of Civil Engineers (ASCE) 7-05 code. Comparison of surface response spectra, soil shear stress and strain at various soil layers computed using both the equivalent linear and nonlinear computer program. Conclusions regarding the limitations of the equivalent linear code and presents recommendations on the use of the nonlinear computer code in site response analysis for practitioners

Constructing Linear Encoders with Good Spectra

Linear encoders with good joint spectra are suitable candidates for optimal lossless joint source-channel coding (JSCC), where the joint spectrum is a variant of the input-output complete weight distribution and is considered good if it is close to the average joint spectrum of all linear encoders (of the same coding rate). In spite of their existence, little is known on how to construct such encoders in practice. This paper is devoted to their construction. In particular, two families of linear encoders are presented and proved to have good joint spectra. The first family is derived from Gabidulin codes, a class of maximum-rank-distance codes. The second family is constructed using a serial concatenation of an encoder of a low-density parity-check code (as outer encoder) with a low-density generator matrix encoder (as inner encoder). In addition, criteria for good linear encoders are defined for three coding applications: lossless source coding, channel coding, and lossless JSCC. In the framework of the code-spectrum approach, these three scenarios correspond to the problems of constructing linear encoders with good kernel spectra, good image spectra, and good joint spectra, respectively. Good joint spectra imply both good kernel spectra and good image spectra, and for every linear encoder having a good kernel (resp., image) spectrum, it is proved that there exists a linear encoder not only with the same kernel (resp., image) but also with a good joint spectrum. Thus a good joint spectrum is the most important feature of a linear encoder.Comment: v5.5.5, no. 201408271350, 40 pages, 3 figures, extended version of the paper to be published in IEEE Transactions on Information Theor

MacWilliams Identities for Terminated Convolutional Codes

Shearer and McEliece [1977] showed that there is no MacWilliams identity for the free distance spectra of orthogonal linear convolutional codes. We show that on the other hand there does exist a MacWilliams identity between the generating functions of the weight distributions per unit time of a linear convolutional code C and its orthogonal code C^\perp, and that this distribution is as useful as the free distance spectrum for estimating code performance. These observations are similar to those made recently by Bocharova, Hug, Johannesson and Kudryashov; however, we focus on terminating by tail-biting rather than by truncation.Comment: 5 pages; accepted for 2010 IEEE International Symposium on Information Theory, Austin, TX, June 13-1

A Parallel Iterative Method for Computing Molecular Absorption Spectra

We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of "dominant products" to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamical polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a a matrix-free GMRES method to determine the (interacting) density response. The resulting code is about one order of magnitude faster than our previous full-matrix method. This acceleration makes the speed of our TDDFT code comparable with codes based on Casida's equation. The implementation of our method uses hybrid MPI and OpenMP parallelization in which load balancing and memory access are optimized. To validate our approach and to establish benchmarks, we compute spectra of large molecules on various types of parallel machines. The methods developed here are fairly general and we believe they will find useful applications in molecular physics/chemistry, even for problems that are beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.Comment: 20 pages, 17 figures, 3 table