From Short Pre-Coded Polar Codes To Longer Polar Codes

State-of-art polar-like codes, e.g., pre-coded polar codes, show significant gains, e.g., up to 1.5 dB, compared to CRC-aided polar codes of 5G when successive cancellation list (SCL) decoding with limited list sizes, e.g., 8 or 16, are considered. We will briefly revisit exemplary constructions and illustrate that they significantly outperform the 5G codes under overall block error rates (BLERs) for given target undetected BLERs, which might be hot candidates for control channel in 6G as well. Then, we propose such component codes to construct product codes and illustrate that resulting codes are competitive to 5G LDPC codes even for the lowest defined code rates in 5G standard for medium lengths when combined with iterative decoding, where the component code decoding uses the polar code decoding methods of control channel, e.g., SCL decoding.