Polar Code Constructions Based on LLR Evolution

Polar code constructions based on mutual information or Bhattacharyya parameters of bit-channels are intended for hard-output successive cancellation (SC) decoders, and thus might not be well designed for use with other decoders, such as soft-output belief propagation (BP) decoders or successive cancellation list (SCL) decoders. In this letter, we use the evolution of messages, i.e., log-likelihood ratios, of unfrozen bits during iterative BP decoding of polar codes to identify weak bit-channels, and then modify the conventional polar code construction by swapping these bit-channels with strong frozen bit-channels. The modified codes show improved performance not only under BP decoding, but also under SCL decoding. The code modification is shown to reduce the number of low-weight codewords, with and without CRC concatenation

Low-Complexity Puncturing and Shortening of Polar Codes

In this work, we address the low-complexity construction of shortened and punctured polar codes from a unified view. While several independent puncturing and shortening designs were attempted in the literature, our goal is a unique, low-complexity construction encompassing both techniques in order to achieve any code length and rate. We observe that our solution significantly reduces the construction complexity as compared to state-of-the-art solutions while providing a block error rate performance comparable to constructions that are highly optimized for specific lengths and rates. This makes the constructed polar codes highly suitable for practical application in future communication systems requiring a large set of polar codes with different lengths and rates.Comment: to appear in WCNC 2017 - "Polar Coding in Wireless Communications: Theory and Implementation" Worksho