Keynote: Construction of Low Density Parity Check Codes: BIBD and Vandermonde
                   Bassem Ammar     Bahram Honary

Abstract:
In this presentation we shall go briefly through the properties of LDPC-codes and discuss two methods for constructing LDPC matrices. One of these methods is based on BIBD, which we explain in the first part of the presentation. We shall go through the definition of BIBD and introduce the general methods of finding them. Then we shall explain one particular method called symmetrically repeated differences SRD and explain several designs based on this method. We shall then show how to use BIBD in LDPC construction. Go through the performance of some LDPC-codes based on BIBD [1, 2].
The second part of the presentation introduces a simple method to construct quasi-cyclic LDPC codes. It is based on Vandermonde matrix [4] and we compare it with BIBD method [3].

[1] Ammar, B., Lin, S., Honary, B. and Kou, Y. (2002) “Construction of Low Density Parity Check Codes: A Combinatoric Design Approach,” Information Theory, 2002. Proceedings. 2002 IEEE International Symposium on , 2002 Page: 311 –311.
[2] Ammar, B., Honary, B., Kou, Y., Xu, J. and Lin, S., (2004) “Construction of Low Density Parity Check Codes based on balanced incomplete block designs,” IEEE Transactions on Information Theory, June-2004.
[3] Gabidulin, E., Ammar, B., Honary, B. (2004) “Simple method for constructing quasi-cyclic regular LDPC codes” 9th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2004.
[4] Yang, K. and Helleseth, T.,(2003) “On the minimum distance of Array codes as LDPC Codes”, IEEE Trans. on Inform. Theory, vol 49, pp. 3268-3271, Dec. 2003.