Low complexity iterative decoding of product codes using a generalized array code form of the Nordstrom-Robinson code

Haesik Kim, G. Markarian, V.C., Jr. da Rocha

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

2 Citations (Scopus)

Abstract

This paper proposes encoding and decoding for nonlinear turbo product codes and investigates the performance of nonlinear turbo product codes.
The proposed nonlinear turbo product codes are constructed as N-dimensional product codes where the constituent codes are nonlinear binary codes derived from the linear codes over higher order alphabets, e.g., Preparata or Kerdock codes.
The performance and the complexity of the proposed construction are evaluated using the well known nonlinear Nordstrom-Robinson code which is presented in the Generalized Array Code format with a low complexity trellis.
The proposed construction shows the additional coding gain, reduced error floor and lower implementation complexity. The (64,24,12) nonlinear turbo product code has about effective 2.5dB gain and 1dB gain at a BER of 10-6 when compared to the (64,15,16) linear turbo product code and the (64,24,10) linear turbo product code, respectively.
The (256,64,36) nonlinear turbo product code composed of two Nordstrom-Robinson codes has about 0.7dB gain at a BER of 10-5 when compared to the (256,64,25) linear turbo product code composed of two (16,8,5) Quasi-Cyclic codes.
These are achieved for codes with relatively short block lengths that make them particularly attractive for new emerging standards that aim at efficient mobile data transmission.
Original languageEnglish
Title of host publicationProceedings
Subtitle of host publication6th International Symposium on Turbo Codes & Iterative Information Processing, ISTC 2010
Place of PublicationPiscataway, NJ, USA
PublisherInstitute of Electrical and Electronic Engineers IEEE
Pages88-92
ISBN (Electronic)978-1-4244-6746-4
ISBN (Print)978-1-4244-6744-0
DOIs
Publication statusPublished - 2010
MoE publication typeA4 Article in a conference publication
Event6th International Symposium on Turbo Codes & Iterative Information Processing, ISTC 2010 - Brest, France
Duration: 6 Sep 201010 Sep 2010

Conference

Conference6th International Symposium on Turbo Codes & Iterative Information Processing, ISTC 2010
Abbreviated titleISTC 2010
CountryFrance
CityBrest
Period6/09/1010/09/10

Fingerprint

Iterative decoding
Binary codes
Data communication systems
Decoding

Cite this

Kim, H., Markarian, G., & da Rocha, V. C. . J. (2010). Low complexity iterative decoding of product codes using a generalized array code form of the Nordstrom-Robinson code. In Proceedings: 6th International Symposium on Turbo Codes & Iterative Information Processing, ISTC 2010 (pp. 88-92). Piscataway, NJ, USA: Institute of Electrical and Electronic Engineers IEEE. https://doi.org/10.1109/ISTC.2010.5613809
Kim, Haesik ; Markarian, G. ; da Rocha, V.C., Jr. / Low complexity iterative decoding of product codes using a generalized array code form of the Nordstrom-Robinson code. Proceedings: 6th International Symposium on Turbo Codes & Iterative Information Processing, ISTC 2010. Piscataway, NJ, USA : Institute of Electrical and Electronic Engineers IEEE, 2010. pp. 88-92
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Kim, H, Markarian, G & da Rocha, VCJ 2010, Low complexity iterative decoding of product codes using a generalized array code form of the Nordstrom-Robinson code. in Proceedings: 6th International Symposium on Turbo Codes & Iterative Information Processing, ISTC 2010. Institute of Electrical and Electronic Engineers IEEE, Piscataway, NJ, USA, pp. 88-92, 6th International Symposium on Turbo Codes & Iterative Information Processing, ISTC 2010, Brest, France, 6/09/10. https://doi.org/10.1109/ISTC.2010.5613809

Low complexity iterative decoding of product codes using a generalized array code form of the Nordstrom-Robinson code. / Kim, Haesik; Markarian, G.; da Rocha, V.C., Jr.

Proceedings: 6th International Symposium on Turbo Codes & Iterative Information Processing, ISTC 2010. Piscataway, NJ, USA : Institute of Electrical and Electronic Engineers IEEE, 2010. p. 88-92.

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

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N2 - This paper proposes encoding and decoding for nonlinear turbo product codes and investigates the performance of nonlinear turbo product codes. The proposed nonlinear turbo product codes are constructed as N-dimensional product codes where the constituent codes are nonlinear binary codes derived from the linear codes over higher order alphabets, e.g., Preparata or Kerdock codes. The performance and the complexity of the proposed construction are evaluated using the well known nonlinear Nordstrom-Robinson code which is presented in the Generalized Array Code format with a low complexity trellis. The proposed construction shows the additional coding gain, reduced error floor and lower implementation complexity. The (64,24,12) nonlinear turbo product code has about effective 2.5dB gain and 1dB gain at a BER of 10-6 when compared to the (64,15,16) linear turbo product code and the (64,24,10) linear turbo product code, respectively. The (256,64,36) nonlinear turbo product code composed of two Nordstrom-Robinson codes has about 0.7dB gain at a BER of 10-5 when compared to the (256,64,25) linear turbo product code composed of two (16,8,5) Quasi-Cyclic codes. These are achieved for codes with relatively short block lengths that make them particularly attractive for new emerging standards that aim at efficient mobile data transmission.

AB - This paper proposes encoding and decoding for nonlinear turbo product codes and investigates the performance of nonlinear turbo product codes. The proposed nonlinear turbo product codes are constructed as N-dimensional product codes where the constituent codes are nonlinear binary codes derived from the linear codes over higher order alphabets, e.g., Preparata or Kerdock codes. The performance and the complexity of the proposed construction are evaluated using the well known nonlinear Nordstrom-Robinson code which is presented in the Generalized Array Code format with a low complexity trellis. The proposed construction shows the additional coding gain, reduced error floor and lower implementation complexity. The (64,24,12) nonlinear turbo product code has about effective 2.5dB gain and 1dB gain at a BER of 10-6 when compared to the (64,15,16) linear turbo product code and the (64,24,10) linear turbo product code, respectively. The (256,64,36) nonlinear turbo product code composed of two Nordstrom-Robinson codes has about 0.7dB gain at a BER of 10-5 when compared to the (256,64,25) linear turbo product code composed of two (16,8,5) Quasi-Cyclic codes. These are achieved for codes with relatively short block lengths that make them particularly attractive for new emerging standards that aim at efficient mobile data transmission.

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Kim H, Markarian G, da Rocha VCJ. Low complexity iterative decoding of product codes using a generalized array code form of the Nordstrom-Robinson code. In Proceedings: 6th International Symposium on Turbo Codes & Iterative Information Processing, ISTC 2010. Piscataway, NJ, USA: Institute of Electrical and Electronic Engineers IEEE. 2010. p. 88-92 https://doi.org/10.1109/ISTC.2010.5613809