Study on Error Correction Capability of Simple Concatenated Polar Codes

Abstract

Polar codes ware mathematically proven to achieve the Shannon limit, where the error probability is reduced with the help of frozen bits. Since the frozen bits are detrimental in terms of transmission efficiency, this paper investigates the importance of the frozen bits and the possibility of being replaced by other protected bits via a concatenation with other outer channel coding schemes. We evaluate the impact of frozen bits to the capability of error correction of original Polar codes (OPC) and the concatenated Polar codes (CPC) in short block-length in terms of bit-error-rate (BER) performances. Repetition codes are used as outer channel encoder prior to the Polar codes and are divided into two schemes, i.e., (i) irregular repetition-CPC (IR-CPC) codes and (ii) regular repetition-CPC (RR-CPC) codes. We evaluate BER performances using computer simulations based on Log-Likelihood Ratio (LLR) with the modulation of Binary Phase Shift Keying (BPSK) under Additive White Gaussian Noise (AWGN) and frequency-flat Rayleigh Fading channels. We found that the OPC is better than the IR-CPC codes or RR-CPC codes for the same channel coding rate and block-length. This finding indicates that the frozen bits in OPC has strong contribution to the error correction capability of the Polar codes and may not be replaced by other bits even though the bits are protected by other channel coding schemes.