Algebra-Assisted Construction of Quasi-Cyclic LDPC Codes for 5G New Radio

Abstract

Quasi-cyclic LDPC (QC-LDPC) codes have been accepted as the standard codes of 5G enhanced mobile broadband data channel. These standard codes are designed to support multiple lifting sizes and possess rate-compatible property, which can help adapt various information lengths and code rates well. In this paper, we propose an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">algebra-assisted</i> method for constructing QC-LDPC codes with such properties. We will first review the encoding mechanism and requirements of 5G LDPC codes, and present <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cycle analysis</i> for such emerging codes. We then propose a metric, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">weighted average number of cycles</i> (WANC), from the perspective of cycle structure for constructing the QC-LDPC codes that can support <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple lifting sizes</i> . Based on the WANC metric and algebraic methods, we develop a simple and practical algorithm to construct this kind of QC-LDPC codes. We finally apply the proposed algorithm to construct the exponent matrices for cases of 5G LDPC codes and the standard LDPC codes of consultative committee for space data systems, respectively. Simulation results show that the proposed WANC metric and designed algorithm are feasible and effective, and thus can be utilized to design other similar QC-LDPC codes.