Design of Length-Compatible Polar Codes: A Compound Polar Code's Perspective

Abstract

In this paper, we establish a connection between length-compatible (LC) punctured/shortened polar codes and compound polar codes. Regarding an LC code as a compound code to be transmitted over two different channels, we propose four channel-coded bit mapping rules which generalize some known LC code constructing methods. Performance of the punctured and shortened codes constructed by applying different mapping rules can thus be predicted checking if the Bhattacharyya bound is minimized.