publication . Article . Preprint . 2020

Union Bound Evaluation for Non-Binary Turbo Coded Modulations

Rami Klaimi; Charbel Abdel Nour; Catherine Douillard; Joumana Farah;
Open Access English
  • Published: 04 Aug 2020 Journal: IEEE Communications Letters, volume 24, issue 6, pages 1,178-1,182 (issn: 1089-7798, eissn: 1558-2558 2373-7891, Copyright policy)
  • Publisher: HAL CCSD
  • Country: France
Abstract
International audience; 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.
Persistent Identifiers
Subjects
free text keywords: non-binary turbo codes, Euclidean distance spectrum, union bound, coded modulation, Index Terms-Non-binary turbo codes, [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], Modelling and Simulation, Electrical and Electronic Engineering, Computer Science Applications, Binary number, Turbo code, Forward error correction, Modulation, Algorithm, Modulation (music), Convolutional code, Euclidean distance, Decoding methods, Computer science
Funded by
EC| EPIC
Project
EPIC
Enabling Practical Wireless Tb/s Communications with Next Generation Channel Coding
  • Funder: European Commission (EC)
  • Project Code: 760150
  • Funding stream: H2020 | RIA
Validated by funder
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.

[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. [OpenAIRE]

[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]

[11] R. Klaimi, C. Abdel Nour, C. Douillard, and J. Farah, “Design of Lowcomplexity convolutional codes over GF(q),” in IEEE Global Commun. Conf., Abu Dhabi, U.A.E., Dec. 2018.

[12] R. Garzón-Bohórquez, R. Klaimi, C. Abdel Nour, and C. Douillard, “Mitigating correlation problems in turbo decoders,” in Intern. Symp. on Turbo Codes & Iterative Inf. Process., Hong Kong, China, Dec. 2018.

[13] R. Klaimi, C. Abdel Nour, C. Douillard, and J. Farah, “Low-complexity decoders for non-binary turbo codes,” in Intern. Symp. on Turbo Codes & Iterative Inf. Process., Hong Kong, China, Dec. 2018. [OpenAIRE]

[14] C. Berrou, S. Vaton, M. Jezequel, and C. Douillard, “Computing the minimum distance of linear codes by the error impulse method,” in IEEE Global Commun. Conf., Taipei, Taiwan, Nov 2002, pp. 1017-1020. [OpenAIRE]

[15] S. Crozier, P. Guinand, and A. Hunt, “Estimating the minimum distance of turbo-codes using double and triple impulse methods,” IEEE Commun. Lett., vol. 9, no. 7, pp. 631-633, 2005.

19 references, page 1 of 2
Any information missing or wrong?Report an Issue