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Foundations, Part I: Counting and Combinatorics
foundationsmathematicsCombinatorics Combinatorics is the study of how to count things i.e. the various combinations, pemutations, subgroups that can be formed from a given set of objects/people etc.
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Not All Gray Codes Are Equal: How Bit-to-Symbol Labeling Affects 5GNR LDPC Performance
wirelesscommunication,informationtheory,matlab,5G,constellationGray Coding in QAM: Not All Gray Maps Are Equal
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AI/ML Basics: What Is Softmax and Why Do We Need It?
machine-learningdeep-learningWhy Do We Need the Softmax Function?
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Part II: Determining Error Probability and Union Bound for M-ary Modulation
wireless-communicationinformation-theoryGeneralized Symbol Error Probability Calculation
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Part I: Representing M-ary Digital Modulation as Constellation Points
wireless-communicationinformation-theoryIn M-ary digital modulation, we transmit one of \(M\) possible signals, \(s_1(t),s_2(t),\cdots,s_M(t)\), during each symbol interval of duration \(T\). Typically, \(M\) equals \(2^m\), where \(m\) is the number of bits per symbol. This makes the symbol duration \(T = m\cdot...
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