This letter proposes extended single parity check product codes and presents their empirical performances on a Gaussian channel by belief propagation (BP) decoding algorithm. The simulation results show that the codes can achieve close-to-capacity performance in high coding rate. The code of length 9603 and of rate 0.96 is only 0.77 dB away from the Shannon limit for a BER of 10-5.

During the development of a human embryo, the position of eyes moves medially and caudally in the viscerocranium. A statistical model of this process can play an important role in embryology by facilitating qualitative analyses of change. This paper proposes an algorithm to construct a spatiotemporal statistical model for the eyeballs of a human embryo. The proposed modeling algorithm builds a statistical model of the spatial coordinates of the eyeballs independently for each Carnegie stage (CS) by using principal component analysis (PCA). In the process, a q-Gaussian distribution with a model selection scheme based on the Aaike information criterion is used to handle a non-Gaussian distribution with a small sample size. Subsequently, it seamlessly interpolates the statistical models of neighboring CSs, and we present 10 interpolation methods. We also propose an estimation algorithm for the CS using our spatiotemporal statistical model. A set of images of eyeballs in human embryos from the Kyoto Collection was used to train the model and assess its performance. The modeling results suggested that information geometry-based interpolation under the assumption of a q-Gaussian distribution is the best modeling method. The average error in CS estimation was 0.409. We proposed an algorithm to construct a spatiotemporal statistical model of the eyeballs of a human embryo and tested its performance using the Kyoto Collection.