Quantifying the wave-effect of irregular LDPC codes based on majority-based hard-decoding

Irregular LDPC codes have shown to give performances closer to capacity than their regular counterparts. The intuitive reasoning backed by experimental evidence given by its founder (Luby et al.) was the presence of a wave-effect. It was shown that only with the presence of a carefully optimized irregularity degree profile, comes the better performance. Conventionally this irregularity profile is optimized employing asymptotic assumptions which studies have shown result in poor performance measures in finite-length codes. Also, the conventional techniques are computationally expensive which makes their use inappropriate in cases, e.g. multicarrier, where run-time optimization of the irregularity profile may be needed. This paper proposes a simplistic technique for precise quantification of the wave-effect phenomenon in irregular codes and hence can be used for run-time optimization of irregularity in finite length codes which may not be possible with classical methods.