From product codes to structured generalized LDPC codes

Product codes, due to their relatively large minimum distance, are often seen as a natural solution for applications requiring low error floors. In this paper, we show by means of an ensemble weight enumerator analysis that the minimum distance multiplicities of product codes are much higher than those obtainable by other generalized LDPC (GLDPC) constructions employing the same component codes. We then propose a simple construction of quasi-cyclic GLDPC codes which leads to significantly lower error floors while leaving the decoder architecture of product codes almost untouched.