Robust decoding schemes for polar coding over compound channels

We consider the problem of designing robust and low complexity decoding schemes for polar coding over a given finite class of channels. We propose two schemes based on multiple runs of the polar successive cancellation decoder, where at each run a different metric adapted to a channel in the class is used in the decoder's decision procedure. The first scheme is a modified polar coding scheme which accommodates Cyclic Redundancy Check bits to help the decoder eliminate the estimates that do not pass the test. We show that this scheme achieves the symmetric capacity of the channel with a vanishing rate loss of O(1√N), where N is the blocklength of the code. The second scheme involves a polar decoding algorithm which implements a generalized likelihood ratio test. We show that over classes of channels which satisfy certain mild conditions, this scheme achieves the symmetric capacity of the channel. The analyses reveal that the decay of the error probability of both schemes is exponential in the square root of the blocklength, which is similar to the polar successive cancellation decoder operating with the knowledge of the true channel. Finally, we compare the schemes in terms of their performances and complexity, and discuss the extension to infinite classes of channels.