Message Passing Decoding of Codes from Complete Graphs
Francisco Chamera and Khumbo Kumwenda
We describe iterative decoding of binary codes from incidence matrices of complete graphs. Parameters for these codes are well known. The codes are also known to be low density parity-check (LDPC). We determine cases where they are decodable by bit flipping (BF) and sum product (SP) decoding algorithms.
Let c be a codeword from the binary code from an incidence matrix of a complete graph. Suppose c is sent through the binary symmetric channel (BSC) with parameter p. Let N and k be the length and dimension of the code respectively. We show that errors occurring in the first k positions are correctable by SP while those occurring in the last N-k positions are correctable by BF.
Keywords: Binary Symmetric Channel, Bit flipping; Complete graphs; Incidence matrix; LDPC codes; Linear code; Sum product; Tanner graph.
Pages: 75 – 88 | Full PDF Paper
The Method Topological Roughness of Systems
Abstract: Method of research of roughness of systems, which is called “the method of topological roughness” and constructed according to the Andronov-Pontryagin concept of roughness, is under consideration. The method is used for research of roughness and bifurcations of dynamic and synergetic systems of various physical nature, chaos in these systems too.
Keywords: roughness of dynamical systems, method of topological roughness, concept of roughness according to Andronov-Pontryagin, topological structure of dynamic systems, singular points, number of conditionality of matrix, synergetic systems of various physical nature.
Pages: 89 – 95 | Full PDF Paper
Linear Mixed Modeling for Mustard Yield Prediction in Haryana State (India)
U. Verma, H. P. Piepho, K. Hartung, J. O. Ogutu, A. Goyal
Abstract: Crop forecasting is a formidable challenge. Such predictions before harvest are needed by the national and state governments for various policy decisions relating to storage, distribution, pricing, marketing, import-export, etc. This study deals in developing a methodology for pre-harvest crop yield prediction of major mustard growing districts in Haryana (India). Zonal yield models using agro-meteorological parameters were generated using multiple linear regression and mixed model procedures. The common weather-based approach to yield forecast is linear regression with constant coefficients over time. This may be restrictive and of limited prediction power since it does not account for the year-to-year dependence in the yield variable. A mixed model procedure provided a flexible way to fit a multi-level model for crop yield prediction. The linear mixed effects models with random time/weather effects at district, zone and state level were fitted for crop yield estimation. The percent deviation(s) of district-level yield forecasts from the real time yield(s) data show a preference for using linear mixed models. The purpose of this paper is also to show the usefulness of the mixed model framework for pre-harvest crop yield forecasting.
Keywords: Multiple linear regression, linear mixed model, weather variables, pre-harvest crop forecast and percent relative deviation.
Pages: 96 – 105 | Full PDF Paper