Abstract
Symbolic q-ary multithreshold decoding (qMTD) for q-ary self-orthogonal codes (qSOC) is analyzed. The SER performance of qMTD is shown to be close to the results provided by optimum total search methods, which are not realizable for non-binary codes in general. qMTD decoders are compared with different decoders for Reed-Solomon and LDPC codes. The results of concatenation of qSOC with simple to decode outer codes are described. The complexity of qMTD is also discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berlekamp, E.R.: Algebraic Coding Theory. McGraw-Hill, New York (1968)
Wu, C.: New list decoding algorithms for Reed-Solomon and BCH codes. IEEE Transactions on Information Theory 54, 3611–3630 (2008)
Declercq, D., Fossorier, M.: Extended minsum algorithm for decoding LDPC codes over GF(q). In: IEEE International Symp. on Inf. Theory, pp. 464–468 (2005)
Zhang, F., Pfister, H.: List-Message Passing Achieves Capacity on the q-ary Symmetric Channel for Large q. In: Proc. IEEE Global Telecom. Conf., Washington, DC, pp. 283–287 (November 2007)
Zubarev, U.B., Zolotarev, V.V., Ovechkin, G.V.: Review of error-correcting coding methods with use of multithreshold decoders. Digital Signal Processing (1), 2–11 (2008)
Zolotarev, V.V., Zubarev, Y.B., Ovechkin G.V.: Multithreshold decoders and optimization coding theory. In: Hot line – Telecom, 239 p. (2012)
Zolotarev, V.V., Averin, S.V.: Non-Binary Multithreshold Decoders with Almost Optimal Performance. In: 9th ISCTA 2007, UK, Ambleside (July 2007)
Ovechkin, G.V., Zolotarev, V.V.: Non-binary multithreshold decoders of symbolic self-orthogonal codes for q-ary symmetric channels. In: 11th ISCTA 2009, UK, Ambleside (July 2009)
Zolotarev, V.V., Ovechkin, G.V.: The algorithm of multithreshold decoding for Gaussian channels. Information Processes 8(1), 68–93 (2008)
Ovechkin, G.V., Zolotarev, V.V., Averin, S.V.: Algorithm of multithreshold decoding for self-orthogonal codes over Gaussian channels. In: 11th ISCTA 2009, UK, Ambleside (July 2009)
Ullah, M.A., Okada, K., Ogivara, H.: Multi-Stage Threshold Decoding for Self-Orthogonal Convolutional Codes. IEICE Trans. Fundamentals E93-A(11), 1932–1941 (2010)
Ullah, M.A., Omura, R., Sato, T., Ogivara, H.: Multi-Stage Threshold Decoding for High Rate Convolutional Codes for Optical Communications. In: AICT 2011: The Seventh Advanced international Conference on Telecommunications, pp. 87–93 (2011)
Massey, J.: Threshold decoding. M.I.T. Press, Cambridge (1963)
Davydov, A.A., Zolotarev, V.V., Samoilenko, S.I., Tretiakova, Y.I.: Computer networks. – M.: Science (1981)
Ovechkin, G.V., Ovechkin, P.V.: Optimisation of non-binary self-orthogonal codes structure for parallel coding schemes. In: NIIR FSUE, vol. (2), pp. 34–38 (2009)
Ovechkin, G.V., Ovechkin, P.V.: Usage of non-binary multithreshold decoder in concatenated shemes of errors correction. RSREU Journal, â„–4 (issue 30) (2009)
Ling, S., Xing, C.: Coding theory. A first course, Cambridge (2004)
Web sites of IKI http://www.mtdbest.iki.rssi.ru and RSREU www.mtdbest.ru
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Zolotarev, V., Ovechkin, G., Ovechkin, P., Satibaldina, D., Tashatov, N. (2014). The Performance of Concatenated Schemes Based on Non-binary Multithreshold Decoders. In: SwiÄ…tek, J., Grzech, A., SwiÄ…tek, P., Tomczak, J. (eds) Advances in Systems Science. Advances in Intelligent Systems and Computing, vol 240. Springer, Cham. https://doi.org/10.1007/978-3-319-01857-7_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-01857-7_24
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01856-0
Online ISBN: 978-3-319-01857-7
eBook Packages: EngineeringEngineering (R0)