Simplified Successive Cancellation Decoding of Polar Codes With Medium-Dimensional Binary Kernels

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.