Short low-error-floor Tanner codes with Hamming nodes

While it is fairly easy to design good low-density parity-check codes with medium or large block lengths, and with code rates 1/2 or greater, much more effort is required for short lengths and low rates. We propose a code structure which incorporates Hamming codes into a code's graph, leading to a type of a Tanner code. The incorporation of Hamming codes into the graph, which we call "Hamming code doping", tends to lead to larger minimum distances and hence low error-rate floors. We present an iterative decoding algorithm tailored to graphs possessing "Hamming nodes". Further, a density evolution analysis based on the Gaussian approximation is presented, which is a useful tool for finding good codes. Finally, we present numerical results of some Hamming-doped Tanner codes simulated on the AWGN channel. The simulated codes exhibit remarkably low error floors, while simultaneously displaying good decoding thresholds