한국통신학회논문지 (The Journal of Korean Institute of Communications and Information Sciences)

  • 제31권3A호
  • /
  • Pages.207-213
  • /
  • 2006
  • /
  • 1226-4717(pISSN)
  • /
  • 2287-3880(eISSN)
한국통신학회 (The Korean Institute of Commucations and Information Sciences)
권호 표지

LDPC 부호와 RA 부호의 최소 거리 검색 알고리즘

Minimum Distance Search Algorithms of LDPC Codes and RA Codes

  • 정규혁 (단국대학교 정보컴퓨터학부)
  • 발행 : 2006.03.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문은 반복 부분을 이용하여 단지 유효한 부호어만을 검색함으로서 RA 부호의 최소 거리를 구하기 위한 계산량을 줄인다. LDPC 부호도 RA 부호와 같이 반복 부분을 가지므로 제안된 알고리즘은 LDPC 부호의 최소거리 계산에도 적응된다. 최소 거리는 높은 신호대 잡음비에서 부호의 성능을 결정한다. 따라서 오류 마루를 추정하는 것을 가능하게 한다. 제안된 알고리즘은 부호 구조에 어떠한 제한도 두지 않고 최소 거리를 구할 수 있다. 실제적 의미가 있는 큰 길이의 인터리버를 가진 LDPC 부호와 RA 부호의 최소 거리가 본 논문에서 구해지며 이에 따른 오류 마루를 구하며 또한 이 오류 마루는 반복 복호의 성능과 비교된다.

In this paper, we reduce the computational complexity to find the minimum distance of RA codes by searching only valid codewords using repetition part. Since LDPC codes have repetition part like RA codes, we also apply this algorithm for computing the minimum distance of LDPC codes. The minimum distance dominates the code performance at high signal-to-noise ratios(SNRs) and in turn allows an estimate of the error floor. The proposed algorithm computes the minimum distance without any constraint on code structures. The minimum distances of LDPC codes and RA codes with large interleavers of practical importance are computed and used to obtain the error floor, which is compared with the performance of the iterative decoding.

키워드

참고문헌

  1. C. Berrou and A. Glavieux, 'Near optimum error correcting coding and decoding: turbo-codes,' IEEE Trans. Commun., vol. 44, pp. 1261-1271, October 1996 https://doi.org/10.1109/26.539767
  2. S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, 'Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding,' IEEE Trans. Inform. Theory, pp. 909-926, May 1998
  3. R. Gallager, 'Low Density Parity Check Codes,' MIT press, 1963
  4. D. J. C. MacKay, 'Good error-correcting codes based on very sparse matrices,' Electronic Letters, vol. 33, pp. 457-458, March 1997 https://doi.org/10.1049/el:19970362
  5. S. Y. Chung, G. D. Forney, T. J. Richardson, and R. L. Urbanke, 'On the design of low-density parity-check codes within 0.0045 db of the shannon limit,' Communication letters, vol. 5, pp. 58-60, February 2001 https://doi.org/10.1109/4234.905935
  6. T. M. Duman and M. Salehi, 'New performance bounds for turbo codes,' IEEE Trans. Commun., vol. 46, pp. 565-567, May 1998 https://doi.org/10.1109/26.668715
  7. G. Poltyrev, 'Bounds on the decoding error probability of binary linear codes via their spectra,' IEEE Trans. Inform. Theory, vol. 40, pp. 1284-1292, July 1994 https://doi.org/10.1109/18.335935
  8. I. Sason and S. Shamai, 'Improved upper bounds on the decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum,' IEEE Trans. Inform. Theory, vol. 46, pp. 24-47, January 2000 https://doi.org/10.1109/18.817506
  9. A. M. Viterbi and A. J. Viterbi, 'Improved union bound on linear codes for the inputbinary awgn channel with applications to turbo codes,' Proc. IEEE Symposium on Information Theory, p. 29, August 1998
  10. H. J. D. Divsalar and R. J. McEliece, 'Coding Theorems for 'Turbo-like' Codes,' 2Pro. 36th Annual Allerton Conf. on Commun., Contol, and Comp, Monticello, IL, USA, pp. 201-210, September 1998
  11. R. Garello, P. Pierleoni, and S. Benedetto, 'Computing the free distance of turbo codes and serially concatenated codes with interleavers: Algorithms and applications,' IEEE J. Select. Areas Commun., vol. 19, pp, 800-812, May 2001 https://doi.org/10.1109/49.924864
  12. L. Ping, and K. Y. Wu, 'Concatenated tree codes: A low-complexity, high-performance approach,' IEEE Trans. Inform. Theory, pp. 791-799, February 200 1
  13. G. D. Forney, 'The Viterbi Algorithm,' Proc. of IEEE, pp. 268-278, March 1973 https://doi.org/10.1109/PROC.1973.9030