LDPC Codes Over GF(q) With Alterable Subset for PAPR Reduction in OFDM Systems

Abstract

Non-binary low-density parity-check (NB-LDPC) codes can exhibit more considerable coding gain than their binary counterparts in numerous cases. To further exploit the benefit of NB-LDPC codes, in this letter, a novel type of non-binary LDPC codes, alterable subset non-binary LDPC (AS-NB-LDPC) codes, is proposed for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) systems. Firstly, we design the alteration scheme of AS-NB-LDPC codes to make <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -ary LDPC codes generate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> valid codewords through one alterable subset, and the codeword with the minimum PAPR is selected for transmission. Then inspired by the invertible subset for binary LDPC codes, the necessary and sufficient conditions for alterable subset generation are derived. Furthermore, we propose an improved progressive edge growth (PEG) construction method to obtain AS-NB-LDPC codes with favorable frame error rate (FER) performance. Simulation results verify the effectiveness of the proposed NB-LDPC codes.