A concatenated scheme to improve the performance of polar codes on symmetric memoryless channels

The performance of Polar codes has been proved to achieve the Shannon capacity when N, the block length, tends to infinity. However, finite block length performance of Polar codes is rather poor compared to other capacity approaching codes such as LDPC (Low-Density Parity-Check) codes. In this paper, we propose a concatenated scheme with a polar code as an inner code and a Reed-Solomon code as an outer code to improve the performance over the binary erasure channel. Since the error pattern at the output of the polar decoder is not uniform, it is necessary to carefully devise an interleaver to map those bits with higher error probability to certain symbols of the Reed-Solomon code. To use the proposed scheme on other symmetric channels, one has to redesign the polar code component using density evolution technique which may not be practical. We therefore use a simplified scheme where the design is achieved using the erasure channel code design. We then show that the proposed concatenated scheme outperforms polar codes as well as Spatially-Coupled LDPC codes of the same rate and block length on symmetric channels.