Nonlinear product codes and their low complexity iterative decoding

Haesik Kim, Garik Markarian, Valdemar C Da Rocha Jr.

    Research output: Contribution to journalArticleScientificpeer-review

    3 Citations (Scopus)


    This paper proposes encoding and decoding for nonlinear product codes and investigates the performance of nonlinear product codes. The proposed nonlinear 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, for example, 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 binary product code has an effective gain of about 2.5 dB and 1 dB gain at a BER of 10−6 when compared to the (64, 15, 16) linear product code and the (64, 24, 10) linear product code, respectively. The (256, 64, 36) nonlinear binary product code composed of two Nordstrom‐Robinson codes has an effective gain of about 0.7 dB at a BER of 10−5 when compared to the (256, 64, 25) linear product code composed of two (16, 8, 5) quasi‐cyclic codes.
    Original languageEnglish
    Pages (from-to)588-595
    Number of pages8
    JournalETRI Journal
    Issue number4
    Publication statusPublished - 2010
    MoE publication typeA1 Journal article-refereed


    • Turbo product code
    • nonlinear error control coding


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