The decoding latency of the successive-cancellation decoder for polar codes is of great importance in its practical applications, and it can be reduced by implementing multi-bit decision decoders in the constituent nodes of the decoding tree. In this letter, we develop a matrix analysis method to analyze the corresponding parity submatrix of the decoding tree’s internal node. Two generalized constituent nodes are presented for the fast simplified successive-cancellation (fast-SSC) decoding of linear kernels-mixed multi-kernel polar codes. Results show that the proposed method achieves latency reduction and preserves the error-correction performance.
A method is proposed, called
l-formula, to design efficient successive cancellation (SC) decoding of polar codes with medium-dimensional binary kernels (dimensions up to 16). Our
l-formula method obtains the simplified recursive formulas of the SC decoder in the likelihood ratio domain for any binary kernel. We confirm that the complexity of the SC decoder based on
l-formulas achieves considerable advantages over the straightforward SC decoder for polar codes with medium-dimensional binary kernels.