# Investigation of IEEE 802.16e LDPC Code Application in PM-DQPSK System
## 1 Introduction
At present, Low-density parity-check (LDPC) stands out for its ability to complete correct decoding in optical fiber communication systems with extremely low OSNR. LDPC was proposed by [PERSON] in the 1960s, which is a linear block code characterized by a sparse parity check matrix, and it has fewer non-zero elements and more zeros, hence the name. Although it has excellent error correction performance, the advantages of LDPC remained overlooked for decades due to the lack of effective computational methods in the 1960s, and encoders at that time believed that serial codes performed better [5]. [PERSON] studied the LDPC code from a graphical point of view in 1981, and the Tanner diagram shows the decoding process of the LDPC code directly. From [PERSON]'s diagram, the decoding process of LDPC code became visually comprehensible [6]. Until the mid to late 1990s, [PERSON] rediscovered that LDPC code was also a good code with performance close to Shannon limit under AWGN channel, coupled with low realization complexity [7], and popularized [PERSON]'s probabilistic iterative decoding algorithm, which greatly promoted the development of LDPC code [8]. Recent research on LDPC highlights its remarkable performance, nearing the theoretical Shannon limit, which underscores its efficacy in achieving optimal communication reliability. LDPC codes offer advantages over traditional Reed-Solomon (RS) codes and convolutional codes due to their simpler coding structure and lower decoding complexity [9]. Compared with Turbo code, LDPC code is proven to have stronger error correction capability and lower error rate in long coding, and the iterative decoding algorithm of LDPC is a parallel algorithm with low decoding delay [10; 11]. Moreover, LDPC codes have shown better performance relative to polar codes in optical communication systems, especially under high SNR conditions, where LDPC codes generally have lower bit error rates and higher reliability [12]. Additionally, LDPC codes excel in large-scale data transmission and high-rate communication, such as long-distance and high-rate optical communication, owing to their comparatively low decoding complexity. As a result, LDPC codes have been widely recognized as a superior performance and efficient forward error correction coding technique in optical communication systems. The paper discusses the application of IEEE80.216e LDPC codes in optical fiber communication systems to improve system performance. The contents of this paper are as follows: Section 1 introduces the research background and significance; Section 2 discusses the construction of IEEE 802.16e standard LDPC code, where Section 2.1 discusses the construction of IEEE 802.16e Standard H-matrix, and Sections 2.2 and 2.3 discuss the fast iterative coding algorithm and belief propagation (BP) decoding algorithm; Section 3 discusses the PM-DQPSK system and simulation results, where Sections 3.1 and 3.2 discuss the PM-DQPSK coherent optical transmission system setup and the digital signal processing (DSP) algorithm, and the simulation results are discussed in Section 3.3. Finally, the conclusion is given in Section 4.