Concatenations of polar codes with outer BCH codes and convolutional codes

We analyze concatenation schemes of polar codes with outer binary BCH codes and convolutional codes. We show that both BCH-polar and Convolutional-polar (Conv-polar) codes can have frame error rate that decays exponentially with the frame length, which is a substantial improvement over standalone polar codes. With the increase in the cutoff rate of the channel after polarization, long constraint-length convolutional codes with sequential decoding suffice to achieve a frame error rate that decays exponentially with the frame length, whereas the average decoding complexity is low. Numerical results show that both BCH-polar codes and Conv-polar codes can outperform stand-alone polar codes for some lengths and choice of decoding algorithms used to decode the outer codes. For the additive white Gaussian noise channel, Conv-polar codes substantially outperform concatenated Reed Solomon-polar codes with a careful choice of the lengths of inner and outer codes.