Ocena jakości systemu przesyłania informacji z kodem dwukrotnie łączonym na bazie kodu Hamminga i rozszerzonego kodu Hamminga

W pracy analizowano metodę dekodowania detekcyjno-korekcyjnego kodów dwukrotnie łączonych na bazie kodu Hamminga i rozszerzonego kodu Hamminga. Podano reguły dekodowania dla czterech możliwych wariantów dekodowania detekcyjno-korekcyjnego. Przedstawiono schemat blokowy układu dekodera. Opracowano charakterystyki probabilistyczne pozwalające ocenić i porównać jakość systemu przesyłania infor-macji z kodem łączonym na bazie kodu Hamminga i rozszerzonego kodu Hamminga oraz z analizowanymi metodami dekodowania.

---

Methods for detection-correction decoding of a twice merged code of the parameters (15,4) based on the Hamming code and extended Hamming code are analysed in the paper. The coding rule (2) has been determined. The rules for decoding have been given for four types of decoding: "pure" correction type (6), two detection-correction types (7) and (8) and "pure" detection type (9). The correctness of the rules has been confirmed by the coefficients shown in Tab.1. The presented decoding rules can also be applied to a code of any length of the information sequence. A block diagram of the decoder is presented in Fig. 2. Fig. 3 shows basic probabilistic characteristics which allow evaluating the quality of the data trans-mission system for one selected method of detection-correction decoding. Comparison of the probabilistic characteristics for the analysed methods of decoding is presented in Figs. 4-6. When analysing the most important characteristic - the probability of the decoder faulty decision versus the probability of an elementary fault - it can be noted that increase in the number of corrected faults t results in increase in the probability of the decoder faulty decision. For small interference intensities the probabilistic characteristics of particular occurrences as a function of the probability of an elementary fault have an exponential character (for the logarithmic scale of both axes the relation is seen as linear).