Article Contents
Article Contents

# An approach to the performance of SPC product codes on the erasure channel

• Product codes can be used to correct errors or recover erasures. In this work we consider the simplest form of a product code, this is, the single parity check (SPC) product code. This code has a minimum distance of four and is thus guaranteed to recover all single, double, and triple erasure patterns. The code is actually capable of recovering a higher number of erasure patterns. We count the number of uncorrectable erasure patterns of size $n \times n$ with $t$ erasures, for $t=8$, $2n-3$, $2n-2$ and $2n-1$, using the relation between erasure patterns and bipartite graphs.
Mathematics Subject Classification: Primary: 14G50; Secondary: 97K30.

 Citation:

•  [1] M. Z. Abu-Sbeih, On the number of spanning trees of $K_n$ and $K_{m,n}$, Discrete Math., 84 (1990), 205-207.doi: 10.1016/0012-365X(90)90377-T. [2] R. Amutha, K. Verraraghavan and S. K. Srivatsa, Recoverability study of SPC product codes under erasure decoding, Inf. Sci., 173 (2005), 169-179.doi: 10.1016/j.ins.2004.07.011. [3] R. Diestel, Graph Theory, Springer-Verlag, New York, 2000.doi: 10.1007/b100033. [4] P. Elias, Coding for noisy channels, IRE International Convention Record, pt. 4, 1955, 37-46. [5] P. Giblin, Graphs, Surfaces and Homology, 3rd edition, Cambridge Univ. Press, New York, 2010.doi: 10.1017/CBO9780511779534. [6] N. Hartsfield and J. S. Werth, Spanning trees of the complete bipartite graph, in Topics in Combinatorics and Graph Theory (eds. R. Bodendieck and R. Henn), Physica-Verlag, 1990, 339-346. [7] M. A. Kousa, A novel approach for evaluating the performance of SPC product codes under erasure decoding, IEEE Trans. Commun., 50 (2002), 7-11. [8] M. A. Kousa and A. H. Mugaibel, Cell loss recovery using two-dimensional erasure correction for ATM networks, in Proc. 7th Int. Conf. Telecommun. Syst., 1999, 85-89. [9] A. Muqaibel, Enhanced upper bound for erasure recovery in SPC product codes, ETRI J., 31 (2009), 518-524. [10] D. M. Rankin and T. A. Gulliver, Single parity check product codes, IEEE Trans. Commun., 49 (2001), 1354-1362. [11] J. M. Simmons and R. G. Gallager, Design of error detection scheme for class C service in ATM, IEEE/ACM Trans. Netw., 2 (1994), 80-88.