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Union Bound Evaluation for Non-Binary Turbo Coded Modulations

Authors: Rami Klaimi; Charbel Abdel Nour; Catherine Douillard; Joumana Farah;

Union Bound Evaluation for Non-Binary Turbo Coded Modulations

Abstract

A method to compute the truncated union bound of non-binary turbo codes mapped to high order modulations isproposed in this letter. It calls for the estimate of the truncated Euclidean distance spectrum. To this end, we identify the error events that limit the Euclidean distance of non-binary turbo codes based on memory-1 convolutional codes defined over GF(q), q > 2. Application examples are elaborated for codes over GF(64). The resulting bounds are found to accurately predict the asymptotic performance of the coded modulation scheme.

International audience

Country
France
Subjects by Vocabulary

Microsoft Academic Graph classification: Binary number Modulation (music) Turbo code Forward error correction Limit (mathematics) Mathematics Discrete mathematics Euclidean distance Convolutional code Decoding methods

Keywords

Index Terms-Non-binary turbo codes, non-binary turbo codes, coded modulation, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Electrical and Electronic Engineering, union bound, Computer Science Applications, [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT], Modeling and Simulation, Euclidean distance spectrum

19 references, page 1 of 2

[1] A. Alvarado, “On bit-interleaved coded modulation with QAM constellations,” Master's thesis, Chalmers Univ. of Technology, Sweden, 2008.

[2] G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inform. Theory, vol. 44, no. 3, pp. 927-946, 1998. [OpenAIRE]

[3] G. Liva, E. Paolini, B. Matuz, S. Scalise, and M. Chiani, “Short turbo codes over high order fields,” IEEE Trans. Commun., vol. 61, no. 6, pp. 2201-2211, June 2013.

[4] L. Dolecek, D. Divsalar, Y. Sun, and B. Amiri, “Non-binary protograph based LDPC codes: enumerators, analysis, and designs,” IEEE Trans. on Inf. Theory, vol. 60, no. 7, pp. 3913-3941, July 2014.

[5] G. Durisi, T. Koch, and P. Popovski, “Toward massive, ultrareliable, and low-latency wireless communication with short packets,” Proceedings of the IEEE, vol. 104, no. 9, pp. 1711-1726, 2016.

[6] G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and ratematched low-density parity-check coded modulation,” IEEE Trans. on Commun., vol. 63, no. 12, pp. 4651-4665, 2015.

[7] J. J. Boutros, F. Jardel, and C. Méasson, “Probabilistic shaping and nonbinary codes,” in IEEE Int. Symp. Inform. Th. (ISIT), Aachen, Germany, Jun 2017, pp. 2308-2312.

[8] F. Steiner, G. Liva, and G. Böcherer, “Ultra-sparse non-binary LDPC codes for probabilistic amplitude shaping,” in IEEE Global Commun. Conf., Singapore, Dec 2017, pp. 1-5.

[9] P. Robertson and T. Wörz, “Bandwidth-efficient turbo trellis-coded modulation using punctured component codes,” IEEE J. Sel. Areas Commun., vol. 16, no. 2, pp. 206-218, Feb 1998.

[10] T. Matsumine and H. Ochiai, “Capacity-approaching non-binary turbo codes: A hybrid design based on exit charts and union bounds,” IEEE Access, vol. 6, pp. 70 952-70 963, 2018. [OpenAIRE]

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citations
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
views
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