GLDPC coded modulation and its squared Euclidean distance distribution

This paper proposes a new coded modulation technique, called generalized low-density parity-check (GLDPC) coded modulation, where individual redundant modulation mapping nodes are connected to code constraint nodes in a pseudorandom manner, and according to predesigned degree distributions. The main contribution of this paper is to derive a compact solution for the distribution of the squared Euclidean distance (SED) of a GLDPC coded modulation ensemble in the general case. In order to allow for the lack of symmetry of the distribution with respect to the transmitted constellation symbol sequence, the SED is averaged with respect to all possible transmitted constellation symbol sequences. This result can be used directly as a design tool for targeting a good system performance in the error floor region. Since the proposed GLDPC coded modulation scheme is also amenable to extrinsic information transfer (EXIT) chart analysis, a high degree of design freedom is thus facilitated.