On the minimum stopping sets of product codes

Document Type: Research Paper

Authors

1 Department of mathematics, Institute for Advanced Studies in Basic Science,

2 Malek ashtar university of technology

Abstract

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.

Keywords

Main Subjects


[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.