The simulation model for OFDM (Orthogonal Frequency Division Multiplexing) signal energy characteristics research is developed. The OFDM signal vector-phase states are examined. The momentary amplitudes distribution function is obtained. A hypothesis of amplitude distribution law is verified by the X 2 criterion. The OFDM subcarriers optimal gain method is proposed.
The analytical description of regular LDPC (Low-Density Parity Check) codes correcting ability has been investigated. The statistical dependencies for the maximum number of corrected bits per the code word as a function of LDPC code word length and code rate are given based on multiple experimental analyses of LDPC check matrices. The analytical expressions are proposed for the cases of linear, exponential and polynomial approximations of given results. The most exact analytical formula is proved by criterion of the minimum divergence between the experimental and theoretical results.
The error-correcting capabilities of regular LDPC (Low Density Parity Check) codes and BCH (Bose-Chaudhuri-Hocquenguem) codes are examined. The qualitative analysis and the quantitative assessment of error-correcting abilities are performed for LDPC codes with code word length n=1000 bits and BCH codes with code word length n=1023 bits. The code rates of LDPC and BCH codes are determined for a known signal to noise ratio in the gaussian channel; detected code rates are optimal for predefined modulation type and required information reliability on the receiver side.
The ultra-long LPDC codes are examined. The errors correction by ultra-long LDPC codes is analyzed. The error-correcting capability research method for ultra-long LDPC codes is described in details. The main results in table and graph representations are shown. The comparison of ultra-long LDPC codes and BCH codes is performed by using Plotkin and Varshamov-Gilbert limits approximation criterion.
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