Parallel Concatenation Codes with Polar Component Codes for Incremental Redundancy Hybrid Automatic Repeat reQuest Functionality

Abstract

This article develops a novel method for construction of parallel concatenation codes with Polar Codes as component code. These parallel concatenation codes are similar to the Turbo codes in construction. Actually, it is a combination of the idea of parallel concatenation codes and the coding essential of the Polar codes. The codeword bits of the initial transmission are based on Polar codes in 5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> Generation mobile communication system (5G). The codeword bits of the re-transmission can come from codeword bits from the parallel concatenation codes. The component codes can be identical to the Polar codes in the initial transmission. The generation matrix of this kind of parallel concatenation codes construction is based on that of Polar codes in 5G. The flexible code rate of Incremental Redundancy Hybrid Automatic Repeat reQuest (IR-HARQ) is implemented without increasing hardware complexity (i.e., the maximum mother code length, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> ). The numerical experiments indicate that it has the similar performance with that of the optimal Polar codes under the same codeword bits length and code rate.