Index Modulated Polar Codes

Abstract

Polar codes with short code length under successive cancellation (SC) decoding are inferior to other advanced codes of similar block length. Although more sophisticated algorithms, such as SC list (SCL) decoding and SC stack (SCS) decoding were introduced to address the problem, the complexity of these algorithms has also increased. In this paper, we first propose a novel construction of Polar codes, named index modulated Polar (IM-Polar) codes. This scheme conveys information not only by the information bits in non-frozen channels as conventional Polar codes, but also by the indices of channels, which are activated according to the incoming bit stream. Moreover, we give a specific implementation of IM-Polar codes under cyclic redundancy check (CRC) aided SCL (CA-SCL) decoding. In this implementation, repetition-assisted encoding is employed to improve the accuracy of index detection. It is shown via simulations that the proposed implementation of IM-Polar codes can provide gain of 0.2--0.3 dB over the classical CRC-aided Polar (CA-Polar) codes with code rate 0.357 and code length 128 at the bit error ratio (BER) of $10^{-4}$.