An improved algorithm of generating shortening patterns for polar codes

The rate matching in polar codes becomes a solution when non-conventional codewords of length N not equal 2n are required. Shortening is employed to design arbitrary rate codes from a mother code with a given rate. Based on the conventional shortening scheme, length of constructed polar codes is limited. In this paper, we demonstrate the presence of favorable and unfavorable shortening patterns. The structure of polar codes is leveraged to eliminate unfavorable shortening patterns, thereby reducing the search space. We generate an auxiliary matrix through likelihood and subsequently select the shortening bits from the matrix. Unlike different existing methods that offer only a single shortening pattern, our algorithm generates multiple favorable shortening patterns, encompassing all possible favorable configurations. This algorithm has a reduced complexity and suboptimal performance, effectively identifying shortening patterns and sets of frozen symbols for any polar code. Simulation results underscore that the shortened polar codes exhibit performance closely aligned with the mother codes. Our algorithm addresses this security concern by making it more difficult for an attacker to obtain the information set and frozen symbols of a polar code. This is done by generating multiple shortening patterns for any polar code.