Coding gain by Integrated Interleaving ECC

We have shown that the coding scheme can be applied to codes with a sum-product(SP) decoding algorithm \cite{kamabekatouMag}. We suppose that we use two different codes, $C_{1}$ and SC_{2}$, with different error correcting capabilities as constituent codes. Without loss of generality, we can assume that $C_{2}$ is stronger than $C_{ 1 }$ and the rate of SC_{2}$, therefore, less than that of $C_{ 1 }$. From the construction of our IIEC scheme we may expect that the error correcting capability of SC_{ 1 }$ and $C_{2}$ is better than SC_{ 1 }$ and worse than SC_{2}$. However, we can show analitically and experimentally that there are cases in which the error correcting capability of the IIEC is {\sl better} than $C_{2}$, the stronger code. This may suggest that the modified IIEC can be used not only to correct burst errors but also to improve the error correcting capability of good codes, e.g. long LDPC (low density parity check) codes, paying a small rate loss.