Abstract
The original polar codes, introduced by Arıkan in 2009, are famous for their ability to approach the channel capacity. CRC-aided polar codes were adopted in the 5G standard for uplink and downlink control channels in 2016. Nowadays, there are many types of polar code constructions with various trade-offs between the error-correction capability, flexibility, decoding complexity, design complexity and compactness of the code specifications. This talk will present our recent results on the low-complexity design of compactly specified precoded polar codes with high error-correction capability and low decoding complexity. In general, any precoded polar code can be specified by the set of frozen bit indices (frozen set) and expressions specifying how to compute the values of these frozen bits (frozen bit expressions). Firstly, I will cover the frozen set design, including the optimization criteria, optimization techniques and search space reduction. Secondly, I will outline a simple way to generate frozen bit expressions for long-length codes and the frozen bit expression optimization for short-length codes.