Scenario-Simplified Successive Cancellation Decoding of Polar Codes for Channel With Deletions

Abstract

Successive cancellation-based decoding algorithm and corresponding polarization theorems for polar codes over channels with deletions have been proposed recently. In that decoding algorithm, each node in the conventional successive cancellation decoding trellis is divided into many different scenarios according to different deletion patterns. The number of scenarios increases with the square of the number of deletion errors $d$ which results in high decoding complexity. In this paper, to reduce the decoding complexity, we propose the scenario-simplified successive cancellation decoding algorithm for the polar codes over the deletion channel. In the proposed decoding algorithm, we use exact upper and lower bounds to identify the feasible scenarios of each node in the decoding trellis and avoid calculating the impossible scenarios. And by rearranging the scenario index table, the operations of calculating indices of scenarios can be simplified. We also investigate the joint-weight for each scenario. By setting a threshold $\tau $ to prune the scenarios with low joint-weight probabilities, the complexity can be reduced further. For polar codes of length $N=512$ and $d = 10$ , we can reduce 42.5% stored scenarios and 46.8% computed scenarios when $\tau = 10^{-5}$ with a negligible performance loss.