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On the minimum stopping sets of product codes | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 7، شماره 4، اسفند 2018، صفحه 1-6 اصل مقاله (217.31 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2017.101199.1465 | ||
| نویسندگان | ||
| Morteza Hivadi* 1؛ Akbar Zare Chavoshi2 | ||
| 1Department of mathematics, Institute for Advanced Studies in Basic Science, | ||
| 2Malek ashtar university of technology | ||
| چکیده | ||
| It is shown that the certain combinatorial structures called stopping sets have the important role in analysis of iterative decoding. In this paper, the number of minimum stopping sets of a product code is determined by the number of the minimum stopping sets of the corresponding component codes. As an example, the number of minimum stopping sets of the r-dimensional SPC product code is computed. | ||
| کلیدواژهها | ||
| Stopping set؛ Stopping distance؛ Product code | ||
| مراجع | ||
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[1] G. Battail, Building long codes by combination of simple ones , thanks to weighted-output deco ding, in Pro c. URSI ISSSE Erlangen Germany, 1989. [2] P. Elias, Error-free co ding, IRE Trans. Inform. Theory , 29{37 (1954). [3] K. M. Krishnan and P. Shankar, Computing the stopping distance of a Tanner graph is NP-hard, IEEE Trans. Inform. Theory , 53 (2007) 2278{2280. [4] R. J. McEliece, Are there turbo-codes on Mars? , Shannon Lecture, Pro c. IEEE Int. Symp. Inform. Theory, Chicago, IL, USA, 2004. [5] R. L. Miller, Numb er of minimum-weight co de words in a pro duct co de, Electronics Letters , 14 (1978) 642{643. [6] M. Hivadi and M. Esmaeili, On the Stopping Distance and Stopping Redundancy of Pro duct Co des, IEICE Trans. , E91-A (2008) 2167{2173. [7] W. W. Peterson and E. J. Weldon, Error Correcting Codes , 2nd Ed., MIT Press, 1972. [8] C. Di, D. Proietti, I. E. Telatar, T. J. Richardson and R. L. Urbanke, Finitelength analysis of low-density parity-check co des on the binary erasure channel, IEEE Trans. Inform. Theory , 48 1570{1579 (2002). [9] R. M. Roth, Introduction to Coding Theory , Cambridge University Press, 2006. [10] J. H. Web er and K. A. S. Ab del-Ghaffar, Results on Parity-Check Matrices with Optimal Stopping and/or Dead-End Set Enumerators, IEEE Trans. Inform. Theory , 54 (2008) 1368{1374 . [11] S.-T. Xia and F.-W. Fu, Stopping Set Distributions of Some Linear Codes , Pro c. IEEE Information Theory Work- shop, 2006. | ||
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