信息論與編碼

第一篇 理論基礎篇
第 1 章 緒論··································································································································.2
1.1 信息的內涵及相關概念···································································································.2
1.1.1 信息的定義 ··············································································································.2
1.1.2 信息與情報等概念的區別和聯系 ················································································.3
1.2 信息論及其發展 ··············································································································.4
1.2.1 信息論發展簡介········································································································.4
1.2.2 信息論的應用···········································································································.6
1.3 通信系統一般模型···········································································································.7
1.4 信息論的研究內容···········································································································.9
習題·········································································································································.10
第 2 章 信息度量與信息熵 ········································································································.11
2.1 信源的分類與數學模型·································································································.11
2.1.1 信源分類················································································································.11
2.1.2 信源的數學模型······································································································.12
2.2 離散單符號信源的信息度量·························································································.13
2.2.1 信息量 ···················································································································.13
2.2.2 信息熵 ···················································································································.18
2.2.3 聯合熵與條件熵······································································································.30
2.2.4 互熵與平均互信息 ··································································································.33
2.3 離散序列信源的信息度量·····························································································.39
2.4 連續信源的信息度量·····································································································.40
2.4.1 均勻分布的連續信源的熵 ························································································.41
2.4.2 高斯（正態）分布的連續信源的熵···········································································.41
2.4.3 指數分布的連續信源的熵 ························································································.42
習題·········································································································································.43
第 3 章 信道與信道容量 ············································································································.47
3.1 信道的分類與數學模型·································································································.47
3.1.1 信道分類················································································································.47
3.1.2 信道的數學模型······································································································.48
3.2 信息傳輸率與信道容量·································································································.51
3.2.1 信道疑義度 ············································································································.51
3.2.2 信息傳輸率 ············································································································.51
3.2.3 信道容量················································································································.52
3.3 離散信道及其容量·········································································································.53
3.3.1 強對稱信道的信道容量····························································································.53
3.3.2 準對稱信道的信道容量····························································································.54
3.3.3 一般離散信道的信道容量計算 ·················································································.55
3.4 連續信道及其容量·········································································································.57
3.4.1 高斯信道················································································································.57
3.4.2 廣義平穩信道的信道容量 ························································································.57
3.5 有噪信道編碼定理·········································································································.61
習題·········································································································································.62
第 4 章 無失真信源編碼理論 ····································································································.65
4.1 信源編碼基礎 ················································································································.65
4.1.1 信源編碼基本概念 ··································································································.65
4.1.2 常用編碼格式·········································································································.66
4.2 無失真信源編碼 ············································································································.68
4.2.1 定長碼及其編碼定理·······························································································.68
4.2.2 變長碼及其編碼定理·······························································································.72
4.3 無失真信源編碼定理·····································································································.76
習題·········································································································································.78
第 5 章 限失真信源編碼理論 ····································································································.80
5.1 信息失真及其度量·········································································································.80
5.1.1 失真的定義與度量 ··································································································.80
5.1.2 限失真編碼的基本思想····························································································.81
5.2 信息率失真函數 R（D）及其性質···············································································.81
5.2.1 信息率失真函數 ····································································································.81
5.2.2 R（D）函數的性質·································································································.83
5.2.3 R（D）函數性質證明······························································································.83
5.3 離散信源 R（D）函數 ··································································································.84
5.3.1 無記憶信源 R（D）的計算 ······················································································.84
5.3.2 R（D）函數的疊代算法 ··························································································.89
5.3.3 連續信源 R（D）函數·····························································································.91
5.4 限失真信源編碼定理·····································································································.95
習題·········································································································································.97
第 6 章 安全編碼基礎理論 ········································································································.99
6.1 密碼技術起源與發展·····································································································.99
6.2 安全編碼分類 ··············································································································.100
6.2.1 對稱密碼體制·······································································································.100
6.2.2 非對稱密碼體制····································································································.101
6.2.3 基於身份的密碼體制·····························································································.102
6.2.4 雜湊密碼體制·······································································································.103
6.3 密碼體制的安全性測度·······························································································.103
6.3.1 完善保密性 ··········································································································.103
6.3.2 唯一解距離 ··········································································································.105
習題·······································································································································.106
第二篇 編碼實踐篇
第 7 章 信源編碼方法及實踐 ··································································································.108
7.1 統計編碼方法 ··············································································································.108
7.1.1 香農編碼··············································································································.108
7.1.2 香農-費諾編碼······································································································.111
7.1.3 霍夫曼編碼 ··········································································································.112
7.1.4 香農-費諾-埃利斯編碼···························································································.115
7.2 統計編碼實踐 ··············································································································.116
7.3 預測編碼 ······················································································································.119
7.3.1 無損預測編碼·······································································································.119
7.3.2 有損預測編碼·······································································································.121
7.4 變換編碼 ······················································································································.121
習題·······································································································································.123
第 8 章 信道編碼方法及實踐 ··································································································.124
8.1 信道編碼概述 ··············································································································.124
8.1.1 信道錯誤概率分析 ································································································.124
8.1.2 編碼方法選擇·······································································································.129
8.1.3 檢錯與糾錯 ··········································································································.133
8.2 線性碼 ··························································································································.138
8.2.1 有限域上的線性空間·····························································································.138
8.2.2 線性碼的生成矩陣與校驗矩陣 ···············································································.139
8.2.3 線性碼的漢明重量和系統碼···················································································.141
8.2.4 線性碼的編碼與譯碼·····························································································.142
8.3 循環碼 ··························································································································.145
8.3.1 循環碼數學基礎····································································································.145
8.3.2 循環碼的生成多項式與校驗多項式·········································································.146
8.3.3 循環碼的編碼與譯碼·····························································································.148
8.3.4 循環冗余校驗碼····································································································.153
習題·······································································································································.155
第 9 章 安全編碼方法及實踐 ··································································································.158
9.1 古典密碼 ······················································································································.158
9.1.1 凱撒密碼··············································································································.158
9.1.2 仿射密碼··············································································································.159
9.1.3 維吉尼亞密碼·······································································································.159
9.1.4 希爾密碼··············································································································.161
9.2 近現代密碼體制 ··········································································································.161
9.2.1 數據加密標準（DES）··························································································.162
9.2.2 高級加密標準（AES）··························································································.163
9.2.3 國際數據加密算法（IDEA）··················································································.165
9.2.4 非對稱密碼算法（RSA） ······················································································.166
9.3 安全編碼實踐 ··············································································································.168
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第三篇 工程應用篇
第 10 章 多媒體壓縮應用········································································································.173
10.1 圖像編碼標準 ············································································································.173
10.1.1 無損壓縮和有損壓縮的區別 ·················································································.173
10.1.2 國際圖像壓縮標準·······························································································.174
10.2 音頻編碼 ····················································································································.175
10.2.1 音頻信號的冗余信息 ···························································································.176
10.2.2 常見的音頻編碼技術 ···························································································.177
10.2.3 常見的音頻編碼格式 ···························································································.178
10.3 視頻編碼技術 ············································································································.180
10.3.1 高級視頻編碼（AVC）························································································.180
10.3.2 高效視頻編碼（HEVC） ·····················································································.181
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第 11 章 高可靠傳輸應用 ········································································································.184
11.1 可靠傳輸中的高效壓縮編碼設計 ·············································································.184
11.1.1 應用問題 ············································································································.184
11.1.2 研究與分析·········································································································.185
11.2 可靠通信信號中的編碼識別·····················································································.187
11.2.1 應用問題 ············································································································.187
11.2.2 研究與分析·········································································································.188
11.3 基於信道編碼的可靠傳輸·························································································.193
11.3.1 應用問題 ············································································································.193
11.3.2 研究與分析·········································································································.193
11.4 語音通信中的可靠預測編碼技術 ·············································································.197
11.4.1 應用問題 ············································································································.197
11.4.2 研究與分析·········································································································.197
11.5 數據鏈中的可靠傳輸應用·························································································.201
11.5.1 應用問題 ············································································································.201
11.5.2 研究與分析·········································································································.202
習題·······································································································································.211
第 12 章 安全保密技術應用 ····································································································.212
12.1 密碼系統應用 ············································································································.212
12.2 國密商密標準 ············································································································.215
12.2.1 國密標準 ············································································································.215
12.2.2 商密標準 ············································································································.218
12.2.3 國密與商密的區別·······························································································.221
12.3 區塊鏈技術應用·········································································································.222
習題·······································································································································.225
第四篇 前沿發展篇
第 13 章 語義信息論················································································································.227
13.1 語義信息定義概述·····································································································.227
13.1.1 信息的不同維度··································································································.227
13.1.2 語義信息論的發展與意義·····················································································.229
13.1.3 語義信息的內涵··································································································.229
13.1.4 語義信息的特征··································································································.230
13.2 語義信息的表示與度量·····························································································.232
13.2.1 語義信息表示 ·····································································································.232
13.2.2 語義信息度量 ·····································································································.236
13.3 語義通信模型 ············································································································.237
13.4 語義信息論應用前景·································································································.238
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第 14 章 信息論與人工智能 ····································································································.242
14.1 樣本數據質量評價中的信息論·················································································.242
14.2 通信數據傳輸冗余評價中的信息論 ·········································································.244
14.3 人工智能對信息論的影響·························································································.247
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參考文獻······································································································································.249