New filling procedure to reduce delay ofburst-error correcting array codes

There exist lots of (3, L)-regular quasi-cyclic (QC) LDPC codes constructed from finite fields, protographs, array codes, and computer search under some design rules. For a given code length and rate, how to select the best one from these codes is considerable. In this paper, we study (3, L)-regular QC LDPC codes from the perspective of graph isomorphism, and non-isomorphic (3, L)-regular QC LDPC codes are determined. By analyzing the cycle structures of the resulting non-isomorphic codes, an efficient algorithm for counting cycles is presented. Also proposed is a simplified exhaustive search of non-isomorphic (3, L)-regular QC LDPC codes free of cycles of length less than g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , where g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is the estimated optimal girth value for a given code length. Based on these two algorithms, we can easily construct a (3, L)-regular QC LDPC code with optimized cycle distribution for a given L and code length. Numerical results show that the constructed codes have better performance under the iterative decoding algorithms.

Constructing error-correcting binary codes using transitive permutation groups

Using Labusch-type solid solution strengthening models parameterized with DFT-computed solute-dislocation interaction energies, we perform a computational search for 63 solutes across the periodic table to find those that lower anisotropy ratios (non-basal to basal CRSS) of magnesium potentially increasing its ductility per the von Mises criterion. For this purpose, we compute changes in strength for solutes as a function of composition and temperature, and compute anisotropy ratios for solutes that include both rare earth and non-rare earth elements. We specifically focus on solute-dislocation interaction energies in the following DFT-optimized dislocations as representative of three non-basal plastic deformation modes: $\ensuremath{\langle}c+a\ensuremath{\rangle}$ edge, $(10\overline{1}2)$ tension twinning edge, and the $(10\overline{1}1)$ compression twinning edge. We find that solute-induced changes in non-basal deformation modes can be approximated using a second-order polynomial in the size misfit of the solutes, which permits rapid screening of solutes. Our approach to identify solutes known to improve strengthening incorporates solute solubility, and suggests other solutes that not have been previously explored for strengthening. The 8 rare-earth solutes that our method suggests as the best, ordered by increasing anisotropy ratios at their optimal concentrations, are: Gd, Tb, Dy, Nd, Ho, Er, Tm, and Yb. The 12 non-rare-earth solutes that our method suggests as the best, ordered by increasing anisotropy ratios, are: Y, Mn, Sc, Pb, Ca, Ag, Bi, Tl, Zn, Li, Ga, and Al. Of these, Gd, Nd, Er, Yb, Y, Mn, Ca, Zn, Li, and Al are used in commercial Mg alloys.

Let Aq (n, d) denote the maximum size of a q-ary code with length n and minimum distance d. For most values of n and d, only lower and upper bounds on Aq (n, d) are known. In this paper new lower bounds on and updated tables of Aq (n, d) for q ∈ {3, 4, 5} are presented. The new bounds are obtained through an extensive computer search for codes with prescribed groups of automorphisms. Groups that act transitively on the (coordinate,value) pairs as well as groups with certain other closely related actions are considered.

In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat such error patterns in the quantum regime. Our contributions are as follows. Firstly, we derive an upper bound for the correctable burst errors of QBECCs, the quantum Reiger bound (QRB). Secondly, we propose two constructions of QBECCs: one by heuristic computer search and the other by concatenating two quantum tensor product codes (QTPCs). We obtain several new QBECCs with better parameters than existing codes with the same coding length. Moreover, some of the constructed codes can saturate the quantum Reiger bounds. Finally, we perform numerical experiments for our constructed codes over Markovian correlated depolarizing quantum memory channels, and show that QBECCs indeed outperform standard QECCs in this scenario.

This paper describes a new code generator that meets both the requirements of production code developers in terms of efficiency and reliability, and of the system engineer doing the control design. It works with MATLAB/Simulink block diagrams, supports automatic scaling, and generates highly-efficient production-ready C code for microcontrollers. The development environment is enhanced by a number of supporting tools to analyze fixed-point effects, profile code sizes and execution times, validate models with automated test series, output ASAP2 calibration information, and generate documentation.