Polar Codes for the Deletion Channel: Weak and Strong Polarization

This paper presents the first proof of polarization for deletion channel with a constant rate and regular hidden-Markov input distribution. A key part this work involves representing using trellis describing plus minus polar-decoding operations on that trellis. In particular, can be seen as combining adjacent stages to yield new half many stages. Using viewpoint, we prove weak theorem standard polar codes channel. To achieve strong polarization, modify scheme by adding guard bands repeated zeros between various parts codeword. gives whose approaches mutual information probability error decays exponentially in cube-root block length. We conclude showing capacity proving achieved sequence distributions.