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Design of efficiently encodable nonbinary LDPC codes for adaptive coded modulation

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Abstract

This paper is concerned with constructions of nonbinary low-density parity-check (LDPC) codes for adaptive coded modulations (ACM). A new class of efficiently encodable structured nonbinary LDPC codes are proposed. The defining parity-check matrices are composed of scalar circulant sub-matrices which greatly reduce the storage requirement when compared with random LDPC codes. With this special structure of parity-check matrix, an efficient encoding algorithm is presented. Based on the proposed codes, a family of variablerate/variable-field nonbinary LDPC codes is designed for the ACM system. When combined with matched-size signal constellations, the family of constructed codes can achieve a wide range of spectral efficiency. Furthermore, the resultant ACM system can be implemented via a set of encoder and decoder. Simulation results show that the proposed nonbinary LDPC codes for the ACM system perform well.

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References

  1. Gallager R G. Low density parity check codes. IRE Trans Inform Theory, 1962, 8: 21–28

    Article  MATH  MathSciNet  Google Scholar 

  2. MacKay D J C, Neal R M. Near Shannon limit performance of low density parity check codes. Electron Lett, 1997, 33: 457–458

    Article  Google Scholar 

  3. Spielman D A. Linear-time encodable and decodable error-correcting codes. IEEE Trans Inform Theory, 1996, 42: 1723–1731

    Article  MATH  MathSciNet  Google Scholar 

  4. Davey M C, MacKay D J C. Low density parity check codes over GF(q). IEEE Commun Lett, 1998, 2: 165–167

    Article  Google Scholar 

  5. MacKay D J C, Davey M C. Evaluation of gallager codes for short block length and high rate application. In: International Conference on Mathematic and its Applications: Codes, Systems and Graphincal Models, New York, 2000. 113–130

    Google Scholar 

  6. Barnault L, Declercq D. Fast decoding algorithm for nonbinary LDPC codes over GF(q). In: IEEE Information Theory Workshop, Paris France, 2003. 70–73

    Google Scholar 

  7. Zeng L Q, Lan L, Tai Y Y, et al. Dispersed Reed-Solomon codes for iterative decoding and construction of q-ary LDPC codes. In: IEEE Global Telecommunications Conference, St. Louis, 2005. 1193–1198

    Google Scholar 

  8. Zeng L Q, Lan L, Tai Y Y, et al. Constructions of nonbinary quasi-cyclic LDPC codes: a finite field approach. IEEE Trans Commun, 2008, 56: 545–554

    Article  Google Scholar 

  9. Voicila A, Declercq D, Verdier F, et al. Low-complexity, low-memory EMS algorithm for nonbinary LDPC codes. In: IEEE International Conference on Communications, Glasgow, 2007. 671–676

    Google Scholar 

  10. Ma X, Zhang K, Chen H Q, et al. Low complexity X-EMS algorithms for nonbinary LDPC codes. IEEE Trans Commun, 2012, 60: 9–13

    Article  Google Scholar 

  11. Goldsmith A. Wireless Communications. Cambridge: Cambridge University Press, 2005

    Book  Google Scholar 

  12. Caire G, Kumar K R. Information theoretic foundations of adaptive coded modulation. Proc IEEE, 2007, 95: 2269–2273

    Article  Google Scholar 

  13. Kou Y, Lin S, Fossorier M P C. Low-density parity-check codes based on finite geometries: a discovery and new results. IEEE Trans Inform Theory, 2001, 47: 2711–2736

    Article  MATH  MathSciNet  Google Scholar 

  14. Tanner R M, Sridhara D, Sridharan A, et al. LDPC block and convolutional codes based on circulant matrices. IEEE Trans Inform Theory, 2004, 50: 2966–2984

    Article  MATH  MathSciNet  Google Scholar 

  15. Lan L, Zeng L Q, Tai Y Y, et al. Construction of quasi-cyclic LDPC codes for AWGN and binary erasure channels: a finite field approach. IEEE Trans Inform Theory, 2007, 53: 2429–2458

    Article  MathSciNet  Google Scholar 

  16. Fossorier M. Quasi-cyclic low-density parity-check codes from ciuculant permutation matrices. IEEE Trans Inform Theory, 2004, 50: 1788–1793

    Article  MathSciNet  Google Scholar 

  17. Declercq D, Fossorier M. Decoding algorithms for nonbinary LDPC codes over GF(q). IEEE Trans Commun, 2007, 55: 633–643

    Article  Google Scholar 

  18. Zhao S C, Ma X, Zhang X Y, et al. A class of nonbinary LDPC codes with fast encoding and decoding algorithms. IEEE Trans Commun, 2013, 60: 1–6

    Article  Google Scholar 

  19. Goupil A, Colas M, Gelle G, et al. FFT-based BP decoding of general LDPC codes over Abelian groups. IEEE Trans Commun, 2007, 55: 644–649

    Article  Google Scholar 

  20. Zhu H L, Wang J Z. Chunk-based resource allocation in OFDMA systems—Part I: chunk allocation. IEEE Trans Commun, 2009, 57: 2734–2744

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Engineering, Guangzhou University, Guangzhou, 510006, China

    XiuNi Wang

  2. Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou, 510275, China

    Xiao Ma

  3. State Key Laboratory of ISN, Xidian University, Xi’an, 710071, China

    BaoMing Bai

Authors
  1. XiuNi Wang
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  2. Xiao Ma
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  3. BaoMing Bai
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Correspondence to XiuNi Wang.

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Wang, X., Ma, X. & Bai, B. Design of efficiently encodable nonbinary LDPC codes for adaptive coded modulation. Sci. China Inf. Sci. 57, 1–11 (2014). https://doi.org/10.1007/s11432-013-4948-9

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  • DOI: https://doi.org/10.1007/s11432-013-4948-9

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