High Performance Short Polar Codes: A Concatenation Scheme Using Spinal Codes as the Outer Code

An innovative scheme for concatenating the polar codes with the recently proposed spinal codes is presented in this paper. The primary objective is to improve the performance of the polar codes in the finite-length regime. One effective used way is to concatenate the polar codes with short outer codes. Essentially, the short outer codes that have as high performance as possible is required for concatenation. To this end, the newly invented spinal codes are used as the outer codes, which are characterized by its great error correcting capability even when the message length is short. First, the proposed codes, named spinal-polar, is implemented through an interleaved concatenation scheme. A joint iterative decoding algorithm is proposed accordingly, and the decoding complexity of the algorithm is also analyzed. Second, in order to reduce the decoding complexity of the full concatenation while maintaining the BER performance, the partial concatenation scheme is presented. Finally, we propose a rate allocation algorithm to further improve the BER performance of the designed concatenated codes. Extensive simulations results indicate that the proposed spinal-polar codes have significant performance improvement over the stand-alone polar codes, and the other improvement strategies mentioned earlier have also been proved to be effective.