Sparsely Pre-Transformed Polar Codes for Low-Complexity SCL Decoding

Polar codes are the first explicitly constructed error-correcting codes over binary input memoryless channels that achieve provably asymptotic capacity using low-complexity encoding and decoding. Applying upper-triangular pre-transform before polar encoding improves the distance property of the existing polar codes. Although it is known that well-designed pre-transformed polar codes can achieve the normal approximation bound in finite-blocklength regime, achieving that limit requires huge decoding latency, which is undesirable in practical communication system. In this paper, we adopt sparsely applied pre-transform to enhance the weight spectrum of codewords and be decodable under successive cancellation list decoder with small list size. We also propose an algorithm for selecting indices to which pre-transforms are applied. Simulation results confirm that proposed codes surpass 5G standard polar codes with cyclic redundancy check precoding by supporting the effectiveness of sparse pre-transform.