Greedy Check Allocation for Irregular LDPC Codes Optimization in Multicarrier Systems

The capacity approaching performances (Richardson et al., 2001) of different types of low density parity check (LDPC) codes have led them to undergo extensive research in recent years. Along with asymptotic performances analysis, the optimization of ´irregularity´ profile for different channels and the performance analysis of practical finite-length codes has also been extensively explored. With multi-carrier communications becoming the physical layer choice for many emerging wireless systems, a feasible solution for optimizing the irregularity profile of irregular LDPC codes for a frequency selective channel is a problem of particular importance and interest. This paper proposes a simple-to-implement greedy ´check´ allocation (GCA) based method for the construction of BER-optimized irregular LDPC codes using the criterion of Gallager upper bound (Gallager, 1962) for probabilistic decoding. A comparison of our GCA algorithm with some existing works (Mannoni et al., 2002) on the irregular LDPC codes optimization for multicarrier systems based on the classical Gaussian approximation of the ´density evolution´ approach, shows that the same irregularity behavior can be achieved with a much simpler method.