本論探討5G(BG2)低密度同位檢查碼遭遇馬可夫高斯脈衝雜訊，在兩種不同的解碼器之效能比較。
由於5G初始規範只考慮到AWGN雜訊，並無考慮地當5G傳輸時遇到脈衝雜訊干擾，由於常見的脈衝雜訊通道模型，屬於無記憶性型，其發生雜訊的時機具有隨機性，無法去描述真實通道的特性，故發展出基於馬可夫鏈特性的雜訊碼可夫高斯通道模型(Markov-Gaussian Channel)。所以本文將會分別使用已知通道狀態條件以及脈衝統計特徵的Optimum解碼器，以及不知通道狀態條件以及脈衝統計特徵，只能以常態狀態下假設通道參數的Refined解碼器，來探討脈衝雜訊對5G影響。
本文將5G(BG2)短碼來實驗以脈衝發生機率P、發生脈衝時脈衝個數DB以及脈衝平均能量大小來比較5G效能，最後探討這三種變數哪一種對5G效能響較大。

In this paper ,we study of 5G(BG2) Low-Density Parity Check Coding Subject to Markovian Gaussian Impulse Noise. And Performance comparison between two different decoders.
Since the initial 5G specification only considers AWGN noise, impulse noise interference is not considered when 5G is transmitted. The common impulse noise models. they are memoryless, which mean that their occurrences are random. However, they can’t describe the characteristics of the real channel. A memory channel such as Markov-Gaussian is introduced to address the characteristics of the real channel. Therefore, this paper will use Optimum decoders with known channel state conditions and pulse statistics. And without knowing the channel state conditions and pulse statistical characteristics, we can only use the Refined decoder assuming the channel parameters in the normal state to explore the impact of pulse noise on 5G.
This paper compares 5G performance with 5G (BG2) short code with the pulse generation probability P, the number of pulses DB when the pulse is generated, and the average energy of pulse. Finally, it discusses which of these three variables has a greater impact on 5G performance.

[1] R. Tanner, "A recursive approach to low complexity codes," IEEE Transactions on Information Theory, vol. 27, no. 5, pp. 533-547, 1981.

[2] T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 619-637, 2001

[3] T. Richardson and R. Urbanke, “Efficient encoding of Low-DensityParity-Check Codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 638–656, 2001.

[4] T. K. Moon, Error Correction Coding: Mathematical Methods and Algorithms. Wiley, 2005.

[5] M. Chiani, A. Conti, and A. Ventura, “Evaluation of Low-Density Parity-Check Codes Over Block Fading Channels,” IEEE Conf. Commun., vol.3 pp. 1183–1187, June. 2000.

[6] Richardson, T., and S. Kudekar. "Design of Low-Density Parity Check Codes for 5g New Radio." IEEE Communications Magazine 56, no. 3 (2018): 28-34.

[7]Huaan li, Baoming Bai, (Member, IEEE), Xijin Mu, Ji Zhang, and Hengzhou Xu, "Algebra-Assisted Construction of Quasi-Cyclic LDPC Codes for 5G New Radio "IEEE Transactions on Information Theory ,July 31, 2018.

[8]Naveen Chelikani ,"5G-NR DL-SCH LDPC Channel Coding Base Graph selection and Coding Procedure" D 16, 2019.

[9] J. Thorpe1,"Low-Density Parity-Check (LDPC) Codes Constructed from Protographs"August 15, 2003

[10] P. Banelli, "Bayesian Estimation of a Gaussian Source in Middleton's Class-A Impulsive Noise," IEEE Signal Processing Letters, vol. 20, no. 10, pp. 956-959, 2013.

[11] Fathi L, Jourdain G, Arndt M, editors. A Bernoulli-Gaussian model for multipath channel estimation in downlink WCDMA. IEEE/SP 13th Workshop on Statistical Signal Processing, 2005; 2005 17-20 July 2005.

[12] A. William Eckford, Low-Density Parity-Check Codes for Gilbert Elliot and Markov- Modulated Channels, University of Toronto,2004

[13] D. Fertonani, A. Barbieri, and G. Colavolpe, "Reduced-Complexity BCJR Algorithm for Turbo Equalization," IEEE Transactions on Communications, vol. 55, no. 12, pp. 2279-2287, 2007.

[14] R. J. McEliece, "On the BCJR trellis for linear block codes," IEEE Transactions on Information Theory, vol. 42, no. 4, pp. 1072-1092, 1996.

[15] 林峻毅"A study of Finite Field -based Quasi-cyclic LDPC Codes over Markov Gaussian Channels",碩士論文--國立臺灣科技大學電機工程系,2018

[16] 3GPP TSG RAN 15 NR,TS 38.212 v15.3.0, " Multiplexing and channel coding", October 2018