Error Probability of Multi-Bit Nodes in Polar Codes Considering Effective Bit Count

This letter proposes an enhanced method for calculating the error probability of multi-bit nodes in the SC-decoding tree of polar codes. We prove that the number of effective bits influencing the error probability for a multi-bit node corresponds to the number of information bits under the multi-bit node. Using this fact, we refine the error probability originally proposed in OEB-aided SCL decoding by considering only effective bits, which allows accurate estimation of one-error and multi-error probabilities. Simulation results show that the corrected error probabilities closely match the actual probabilities, even with frozen bits present under multi-bit nodes.