Gregor Kralj (2010) Low-Density Parity-Check codes. EngD thesis.
Transmition of data over various communication systems is lossy, because of all the noise affecting the communication channel. One of the most useful ways to achieve reliable transmision are error correcting codes. Recently, low-density parity-check codes became very popular. These codes can come arbitrarily close to the Shannon limit and because of the technology development their coding and decoding algorithms are reasonably fast. In this graduation thesis, low density parity check (LDPC) codes are studied. The progressive edge growth (PEG) algorithm for generating such codes is presented and iterative decoding algorithm (SPA) is described. For the communication channel model, additive white Gaussian noise channel is used. In the last section of the thesis, efficiency of the presented decoding algorithm is examined for matrices of various dimensions, that were generated with algorithm PEG. The rate of bit errors or the number of iterations for correct decoding was counted for different levels of noise. Results show that in the tested cases, parity check codes of larger dimensions perform better than the parity check codes of lower dimensions.
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