{"id":76453,"date":"2023-05-13T02:09:00","date_gmt":"2023-05-12T18:09:00","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=76453"},"modified":"2026-06-01T10:14:03","modified_gmt":"2026-06-01T02:14:03","slug":"chapter-2%ef%bc%9ainformation-measures-for-discrete-systems-2-4-data-processing-inequality-2-5-fanos-inequality","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-electrical-and-computer-engineering\/information-theory-107-academic-year-college-of-electrical-and-computer-engineering-prof-po-ning-chen\/chapter-2%ef%bc%9ainformation-measures-for-discrete-systems-2-4-data-processing-inequality-2-5-fanos-inequality","title":{"rendered":"Chapter 2\uff1aInformation Measures for Discrete Systems, 2.4 Data processing inequality, 2.5 Fano\u2019s inequality"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"76453\" class=\"elementor 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class=\"elementor-heading-title elementor-size-default\">Chapter 2\uff1aInformation Measures for Discrete Systems, 2.4 Data processing inequality, 2.5 Fano\u2019s inequality\n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7aec5b11 elementor-widget elementor-widget-video\" data-id=\"7aec5b11\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/15SwirHhsqk&quot;,&quot;modestbranding&quot;:&quot;yes&quot;,&quot;lazy_load&quot;:&quot;yes&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 *\/\n.elementor-widget-video .elementor-widget-container{overflow:hidden;transform:translateZ(0)}.elementor-widget-video .elementor-wrapper{aspect-ratio:var(--video-aspect-ratio)}.elementor-widget-video .elementor-wrapper 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100%;-webkit-mask-repeat:var(--divider-pattern-repeat);mask-repeat:var(--divider-pattern-repeat);background-color:var(--divider-color);-webkit-mask-image:var(--divider-pattern-url);mask-image:var(--divider-pattern-url)}.elementor-widget-divider--no-spacing{--divider-pattern-size:auto}.elementor-widget-divider--bg-round{--divider-pattern-repeat:round}.rtl .elementor-widget-divider .elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-da19150 elementor-widget elementor-widget-shortcode\" data-id=\"da19150\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">\n<table id=\"tablepress-247\" class=\"tablepress tablepress-id-247\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">Week<\/th><th class=\"column-2\">Course Content<\/th><th class=\"column-3\">Course Video<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Overview: The philosophy behind information theory<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=70724\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 1:Introduction<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76411\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Appendix A:Overview on Suprema and Limits<br \/>\nA.1 Supremum and maximum<br \/>\nA.2 Infimum and minimum<br \/>\nA.3 Boundedness and suprema operations<br \/>\nA.4 Sequences and their limits<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76417\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Appendix A:Overview on Suprema and Limits<br \/>\nReview A.1-A.4<br \/>\nA.5 Equivalence<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76423\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Appendix B:Overview in Probability and Random Processes<br \/>\nB.1 Probability space<br \/>\nB.2 Random variables and random processes<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76429\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Appendix B:Overview in Probability and Random Processes<br \/>\nB.3 Statistical properties of random sources<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76435\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Appendix B:Overview in Probability and Random<br \/>\nProcesses<br \/>\nB.5 Ergodicity and law of large numbers<br \/>\nB.6 Central limit theorem<br \/>\nB.7 Convexity, concavity and Jensen\u2019s inequality<br \/>\nB.8 Lagrange multipliers tech. &amp; KKT conditions<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76441\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 2\uff1aInformation Measures for Discrete Systems<br \/>\n2.1.1 Self-information<br \/>\n2.1.2 Entropy<br \/>\n2.1.3 Properties of entropy<br \/>\n2.1.4 Joint entropy and conditional entropy<br \/>\n2.1.5 Properties of joint and conditional entropy<br \/>\n2.2 Mutual information<br \/>\n2.2.1 Properties of m<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76447\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 2\uff1aInformation Measures for Discrete Systems<br \/>\n2.4 Data processing inequality<br \/>\n2.5 Fano\u2019s inequality<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76453\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 2\uff1aInformation Measures for Discrete Systems<br \/>\n2.6 Divergence and variational distance<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76459\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 2\uff1aInformation Measures for Discrete System<br \/>\n2.7 Convexity\/concavity of information measures<br \/>\n2.8 Fundamentals of hypothesis testing<br \/>\n2.9 R\u00b4enyi\u2019s information measures<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76465\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 3\uff1aLossless Data Compression<br \/>\n3.1 Principles of data compression<br \/>\n3.2.1 Block codes for DMS<br \/>\n3.2.2 Block Codes for Stationary Ergodic Sources<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76471\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 3\uff1aLossless Data Compression<br \/>\n3.3 Variable-Length Code for Lossless Data Comp.<br \/>\n3.3.1 Non-singular Codes and Uniquely Decodable Codes<br \/>\n3.3.2 Prefix or Instantaneous Codes<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76477\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 3\uff1aLossless Data Compression<br \/>\n3.3.3 Examples of Binary Prefix Codes<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76483\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 3\uff1aLossless Data Compression<br \/>\n3.3.4 Universal Lossless Variable-Length Codes<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76489\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 4:Data Transmission and Channel Capacity<br \/>\n4.3 Block codes for data transmission over DMCs(1\/3)<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76495\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 4:Data Transmission and Channel Capacity<br \/>\n4.3 Block codes for data transmission over DMCs(2\/3)<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76501\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 4:Data Transmission and Channel Capacity<br \/>\n4.3 Block codes for data transmission over DMCs(3\/3)<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76507\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 4:Data Transmission and Channel Capacity<br \/>\n4.5 Calculating channel capacity<br \/>\n4.5.1 Symmetric, Weakly Symmetric, and Quasi-symmetric Channels<br \/>\n4.5.2 Karuch-Kuhn-Tucker cond. for chan. capacity<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76513\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 4:Data Transmission and Channel Capacity<br \/>\n4.4 Example of Polar Codes for the BEC<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76519\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 4:Data Transmission and Channel Capacity<br \/>\n4.6 Lossless joint source-channel coding and Shannon\u2019s separation principle<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76525\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5\uff1aDifferential Entropy and Gaussian Channels<br \/>\n5.1 Differential entropy<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76531\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5\uff1aDifferential Entropy and Gaussian Channels<br \/>\n5.1 Differential entropy<br \/>\n5.2 Joint &amp; cond. diff. entrop., diverg. &amp; mutual info<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76537\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5\uff1aDifferential Entropy and Gaussian Channels<br \/>\n5.3 AEP for continuous memoryless sources<br \/>\n5.4 Capacity for discrete memoryless Gaussian chan<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76543\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5\uff1aDifferential Entropy and Gaussian Channels<br \/>\n5.5 Capacity of Uncorrelated Parallel Gaussian Chan<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76549\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5\uff1aDifferential Entropy and Gaussian Channels<br \/>\n5.6 Capacity of correlated parallel Gaussian channels<br \/>\n5.7 Non-Gaussian discrete-time memoryless channels<br \/>\n5.8 Capacity of band-limited white Gaussian channel<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76555\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 6\uff1aLossy Data Compression and Transmission<br \/>\n6.1.1 Motivation<br \/>\n6.1.2 Distortion measures<br \/>\n6.1.3 Frequently used distortion measures<br \/>\n6.2 Fixed-length lossy data compression<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76561\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 6\uff1aLossy Data Compression and Transmission<br \/>\n6.3 Rate-distortion theorem<br \/>\nAEP for distortion typical set<br \/>\nShannon\u2019s lossy source coding theorem<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76567\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 6\uff1aLossy Data Compression and Transmission<br \/>\n6.4 Calculation of the rate-distortion function<br \/>\n6.4.2 Rate distortion func \/ the squared error dist<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76573\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 6\uff1aLossy Data Compression and Transmission<br \/>\n6.5 Lossy joint source-channel coding theorem<br \/>\n6.6 Shannon limit of communication systems(1\/2)<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76579\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 6\uff1aLossy Data Compression and Transmission<br \/>\n6.6 Shannon limit of communication systems(2\/2)<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76585\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-33 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Preface and Introduction<br \/>\nChapter 1:Generalized Information Measures for Arbitrary Systems with Memory<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76591\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-34 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 2:General Data Compression Theorems<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76597\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-35 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 3:Measure of Randomness for Stochastic Processes<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76603\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-36 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 4:Channel Coding Theorems and Approximations of Output Statistics for Arbitrary Channels<\/td><td class=\"column-3\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&amp;p=76609\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-3 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-5f099062\" data-id=\"5f099062\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5b79cc32 elementor-widget-divider--view-line_text elementor-widget-divider--element-align-center elementor-widget elementor-widget-divider\" data-id=\"5b79cc32\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t\t<span class=\"elementor-divider__text 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href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item 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href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/self-learning-courses-for-high-school-students\" class=\"elementor-item\" tabindex=\"-1\">Self-learning courses for high school students<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-121578\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/pre-university-courses\" class=\"elementor-item\" tabindex=\"-1\">Pre-University Courses<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5381\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\" class=\"elementor-item\" tabindex=\"-1\">College of Science<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5377\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5376\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-electrical-and-computer-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Electrical and Computer Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5380\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-management\" class=\"elementor-item\" tabindex=\"-1\">College of Management<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5375\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-computer-science\" class=\"elementor-item\" tabindex=\"-1\">College of Computer Science<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5374\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biological-science-and-technology\" class=\"elementor-item\" tabindex=\"-1\">College of Engineering Bioscience<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5379\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-humanities-and-social-sciences\" class=\"elementor-item\" tabindex=\"-1\">College of Humanities Arts and Social Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5378\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-hakka-affair-culture\" class=\"elementor-item\" tabindex=\"-1\">College of Hakka Affair Culture<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118070\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-law\" class=\"elementor-item\" tabindex=\"-1\">School of Law<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118069\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-nursing-2\" class=\"elementor-item\" tabindex=\"-1\">School of Nursing<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118071\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-photonics\" class=\"elementor-item\" tabindex=\"-1\">College of Photonics<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-125874\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biomedical-science-and-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Biomedical Science and Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\" tabindex=\"-1\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\" tabindex=\"-1\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\" tabindex=\"-1\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\" tabindex=\"-1\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\" tabindex=\"-1\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\" tabindex=\"-1\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\" tabindex=\"-1\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Chapter 2\uff1aInfo&hellip;<\/p>\n","protected":false},"featured_media":0,"parent":70712,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","format":"standard","meta":{"footnotes":""},"categories":[4321],"tags":[],"class_list":["post-76453","course_page","type-course_page","status-publish","format-standard","hentry","category-information-theory-107-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Chapter 2\uff1aInformation Measures for Discrete Systems, 2.4 Data processing inequality, 2.5 Fano\u2019s inequality - NYCU OCW<\/title>\n<meta name=\"description\" content=\"Chapter 2\uff1aInformation Measures for Discrete Systems, 2.4 Data 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