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研究生(外文):Chun-Hao Chen
論文名稱(外文):Decoding Metric based on Viterbi Algorithm over Markov-Gaussian Channel
指導教授(外文):Der-Feng Tseng
口試委員(外文):Der-Feng Tseng
外文關鍵詞:virtual statechannel statebranch metricViterbi algorithmMG model
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在數位傳輸的通道中,有著一些無法以傳統AWGN來表達的脈衝環境,我們稱之為脈衝雜訊,常見的有Class A model和Bernoulli-Gaussian通道模型。但以上兩種雜訊皆屬於無記憶型,無法確切的表達出實際通道的特性(i.e. 連續性的脈衝雜訊),因此就衍生出基於馬可夫鏈特性的記憶型Markov - Gaussian(MG)通道模型。此外,在接收端解碼的過程中所知道脈衝雜訊的統計資訊有限,因此本文也將在未知資訊的條件下進行模擬。


本文主要利用電腦軟體以Markov-Gaussian通道模型來模擬傳送通道中的脈衝雜訊環境,並使用BPSK調變的方式,搭配常見的迴旋碼編碼器和維特比演算 法,並增加通道狀態和虛擬狀態及改進分支度量來達到降低位元錯誤率(BER)的 目標。
It is well known that communication systems are prone to impulse noise; it becomes more and more common to have coexistent systems overlap partial or full bandwidth, inevitably introducing interference to each other if no sophisticated coordinating mechanism is enabled. Nevertheless, the cost arising from the refined coordinating algorithm can be mounting, especially when the number of devices increases to a certain extent, plaguing the coordinator to, if not impossible, maintain a stable network.

In this thesis, a self-arbitrating mechanism is introduced to a low-cost communication device in the presence of impulse noise, which can either instantly occur in each time instant or take place based on whether or not the occurrence of impulse was true in the previous time instant. The study aims at blunting the effect of occurrence of impulses while the statistics of impulse noise is not assumed at the decoder. In the scenario regarding the memory channel noise model, a first-order Markov chain, characterized by the transition probabilities and the probability of impulse occurrence, is used. Without assuming the aforementioned probabilities as well as the power strength of impulse noise, the decoder, additionally taking into account the noise (or channel) state, implements a two-dimensional trellis search owing to virtual state’s help, in a manner similar to the Viterbi algorithm. When compared with other existing methods forgoing the statistics of impulse under the same simulation setups, the proposed decoding algorithm enjoys several decibel gain in terms of signal-to-noise ratio at a bit error probability of 1.0E-5 . Furthermore, the proposed decoder is attested to be robust in numerous scenarios and even performs fairly close to the maximum likelihood decoder, which nevertheless assumes the statistics of impulse are available.
第 1 章 緒論 1
1.1 研究背景 1
1.2 研究目的 1
1.3 章節概述 2

第 2 章 脈衝雜訊的模擬環境 3
2.1 簡介 3
2.2 脈衝雜訊的創建 3
2.2.1 Bernoulli-Gaussian (BG) 脈衝雜訊模型 4
2.2.2 Markov-Gaussian (MG) 脈衝雜訊模型 4
2.2.3 通道記憶性 (Channel Memory) 5
2.2.4 BG 脈衝雜訊和 MG 脈衝雜訊模型比較 6
2.3 迴旋碼 (Convolutional Code) 7
2.4 交錯器 (Interleaver) 10
2.4.1 交錯器與脈衝雜訊通道 10
2.4.2 轉移機率矩陣T與TI 之雜訊模型 12

第 3 章 系統架構及通道編碼 (Channel Coding) 14
3.1 系統模型 14
3.2 維特比解碼器 (Viterbi Decoder) 15
3.2.1 格狀圖 (Trellis Diagram) 15
3.2.2 維特比演算法 (Viterbi Algorithm) 15
3.3 Proposed Decoding Metric 17
3.3.1 概念及介紹 17
3.3.2 求取最大似然路徑 18
3.3.3 分支度量 25
3.3.4 分支度量中的參數 29
3.3.5 最大似然解碼 (Maximum Likelihood Decoding) 30
3.4 α-償罰函數解碼器 (α-Penalty Function Decoder) 31
3.5 歐式距離解碼器 (Euclidean Distance Decoder, EDD) 31

第 4 章 模擬結果 32
4.1 記憶型 MG 脈衝雜訊 32
4.1.1 α 參數 32
4.1.2 雜訊平均能量比值 Rd 34
4.1.3 狀態機率 PB,d 36
4.1.4 平均叢發長度DB,d 38
4.1.5 穩健性(Robustness)及不同解碼方式比較 40
4.2 非記憶型 MG 脈衝雜訊 44
4.2.1 α-補償函數解碼器與歐式距離解碼器 44
4.2.2 雜訊平均能量比值 Rd 46
4.2.3 狀態機率 PB,d 48
4.2.4 穩健性(Robustness)及不同解碼方式比較 50

第 5 章 結論與未來研究方向 53
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[8] M. Ghosh, “Analysis of the effect of impulse noise on multicarrier and single carrier QAM systems,” IEEE Trans. Commun., vol. 44, pp. 145 – 147, Feb. 1996.

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