Abstract
We revisit a capacity achieving scheme for error correctiion over the Gaussian channel, previously introduced by Joseph and Barron. We show that these codes can be iteratively decoded in an efficient way thanks to the approximate message passing algorithm. As in LDPC codes, the decoding by message passing is however not performing until the capacity. We use the spatial coupling technique to saturate the capacity, in a very similar way as in compressed sensing. Finally, we show empirically with simulations that using structured coding matrices leads to good performances even in relatively small sizes.