Abstract
Error correcting codes are used to ensure as maximum as possible the correction of errors due to the noisy perturbation of data transmitted in communication channels or stored in digital supports. The decoding of linear codes is in general a NP-Hard problem and many decoders are developed to detect and correct errors. The evaluation of the quality of a decoder is based on its performances in terms of Bit Error Rate and its temporal complexity. The hash table was previously used for alleviating the temporal complexity of the syndrome decoding algorithm. In this paper, we present two new fast and efficient decoding algorithms to decode linear block codes on binary channels. The main idea in the first decoder HSDec is based on a new efficient hash function that permits to find the error pattern directly from the syndrome of the received word. The storage position of each corrigible error pattern is equal to the decimal value of its syndrome and therefore the run time complexity is much reduced comparing to known low complexity decoders. The main disadvantage of HSDec is the spatial complexity, because it requires to previously storing all corrigible error patterns in memory. For reminding this problem, we propose a second decoder HWDec based also on hash, but it requires storing only the weight of each corrigible error pattern instead of the error pattern itself. The temporal complexity of HWDec is more than that of HSDec but its spatial complexity is less than that of HSDec. The simulation results of the proposed decoders over Additive White Gaussian Channel show that they guarantee at 100% the correction of all corrigible error patterns for some Quadratic Residue, BCH, Double Circulant and Quadratic Double Circulant codes (QDC). The proposed decoders are simple and suitable for software implementations and practice use in particular for transmission of Big Data and real time communication systems which requires rapidity of decoding and prefer codes of high rates.
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El Kasmi Alaoui, M.S., Nouh, S., Marzak, A. (2019). Two New Fast and Efficient Hard Decision Decoders Based on Hash Techniques for Real Time Communication Systems. In: Mizera-Pietraszko, J., Pichappan, P., Mohamed, L. (eds) Lecture Notes in Real-Time Intelligent Systems. RTIS 2017. Advances in Intelligent Systems and Computing, vol 756. Springer, Cham. https://doi.org/10.1007/978-3-319-91337-7_40
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DOI: https://doi.org/10.1007/978-3-319-91337-7_40
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