# Post-FEC Performance of Pilot-Aided Carrier Phase Estimation over Cycle Slip
## 1 Introduction  
Recently, thanks to the advanced technology such as high-speed analog-to-digital converter (ADC), integrated optical front end, and digital signal processing (DSP), 100 Gb/s coherent single carrier transmission system has become a reality [1]. Single carrier quadrature phase-shift keying (QPSK) modulation and narrow line-width laser are a key technology in 100 Gbit/s digital coherent communication system. The laser line-width between 100 k and 500 k is commonly used. Carrier phase estimation (CPE) is an important integral part of digital signal processing (DSP) in coherent transmission systems through which laser phase noise and nonlinear phase noise are compensated [2, 3]. Usually, CPE is implemented as a feed-forward structure for efficient hardware implementation, i.e., Viterbi-Viterbi phase estimation (VVPE) [4]. Due to the necessary phase unwrapping algorithm in these estimators, cycle slip (CS) occurs, which can lead to continuous errors that cannot be corrected properly by the forward error correction (FEC) decoder. A common approach to deal with CS is to use differential encoding (DE), however, differential decoding leads to error duplication and introduces penalties to the PRE- forward error correction (FEC) bit error rate (BER), thus leading to degraded POST-FEC BER [5]. A great deal of efforts has been conducted to mitigate or reduce the impact of CS and to improve the PRE-FEC BER and POST-FEC BER. A lot of research works focus on improved CPE algorithms, which can reduce the CS probability and decrease the PRE-FEC BER. For example, joint polarization carrier phase estimation (JP-CPE) [6, 7], pilot-symbols-based CPE (P-CPE) [8], a forward and backward(FWBW) method [9; 10], recursive probability-weighted blind phase search (RW-BPS) [11], filtered carrier-phase estimation (F-CPE) [12], a support vector machine (SVM)-based boundary creation [13], and a signal recovery method by employing soft decision slip state estimation method at pilots [14]. However, most of these improved CPE algorithms mainly focus on the performance of PRE-FEC BER. The POST-FEC performance of the improved CPE algorithms in combination with a concatenated FEC coding scheme should be taken into consideration since CS might deteriorate the performance of FEC [5]. Some other works concentrate on improved FEC encoding/decoding methods, which can reduce differential encoding (DE)-penalty or improve robustness against CS. For example, turbo differential decoding (TDD) and some improved TDD algorithms have been proposed to eliminate error floor for frequent CS [15; 16; 17; 18]. In References [19; 20; 21], novel code designs for BCH codes were proposed and numerically confirmed, which are robust to CS. [PERSON] et al. [22] proposed a phase noise-aware log-likelihood ratio (LLR) calculation based on a Tikhonov model. An alternative LLR calculation method, employing linear or bilinear transform [23], was also investigated to improve robustness against residual phase noise. [PERSON] [20] proposed a new low-density parity-check (LDPC) code structure, which is robust to CS. Clearly, these techniques, which treated CS within FEC coder/decoder block, can improve POST-FEC BER performance effectively. However, most of these techniques suffer from increased processing complexity. In our previous work [24], the pilot-symbols-aided phase unwrapping (PAPU), which utilizes the time-division multiplexed pilot symbols that are transmitted with data, was proposed to do CS detection and correction with the CPE in QPSK modulation. Recently, it has been employed to high-order quadrature amplitude modulation (QAM) over 1500 km standard single-mode fiber transmission [25]. In this paper, since LDPC is one of the most commonly used FEC code [26], we experimentally investigate the performance of the CPE + PAPU scheme combined with a concatenated soft decision (SD)-LDPC coding in a 56 Gbit/s quadrature phase-shift keying (QPSK) coherent communication system with laser line-width of 300 kHz.