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ITC:010117The stay-3/4 flip-1/4 binary Markov chain has entropy rate h2(1/4) and the word 00110 has self-information 9-2 log2 3

Itc Stationary Binary Markov Entropy RateItc Markov Word Self Information

Entropy, typicality, and source codingInformation Theory and Digital Communications · Mixed review

ITC:010118The length-8 two-ones type class under Bern(1/4) has size 28, class probability 5103/16384, and needs 5 enumerative bits

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Itc Bernoulli Type Class ProbabilityItc Enumerative Index Bit Length

Entropy, typicality, and source codingInformation Theory and Digital Communications · Mixed review

ITC:010219The BEC(1/4) has I=(3/4)h2(q), capacity 3/4 bit per use, and two million uses per second give at most 1.5 Mbit/s

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Itc Bec Mutual Information IN QItc Bec Capacity Throughput

Discrete channels, mutual information, and capacityInformation Theory and Digital Communications · Mixed review

ITC:010220Cascading BSC(1/10) with BSC(1/5) yields BSC(13/50) whose uniform mutual information is 1-h2(13/50)

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Itc Cascade Bsc Equivalent CrossoverItc Data Processing Strict Audit

Discrete channels, mutual information, and capacityInformation Theory and Digital Communications · Mixed review

ITC:010221Uniform input through BSC(1/4) has information density log2(3/2) or -1, mean (3/4)log2 3-1, and variance (3/16)(log2 3)^2

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Itc Bsc Information Density ValuesItc Information Density Mean Variance

Discrete channels, mutual information, and capacityInformation Theory and Digital Communications · Mixed review

ITC:010322MAP on the ternary source decides 0 then 1 with error 13/30; ML decides 0 then 2 with error 7/15

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Itc Finite Bayes Posterior Three HypItc Map Versus ML Error Split

Statistical detection and estimationInformation Theory and Digital Communications · Mixed review

ITC:010323The LLR 2y1+y2/2 is the test y1+y2/4>0 with error Q(sqrt(5)/2); equal-gain is worse

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Itc Gaussian Llr Unequal VarianceItc Q Function Linear Statistic

Statistical detection and estimationInformation Theory and Digital Communications · Mixed review

ITC:010424Gray QPSK at (±sqrt(Eb),±sqrt(Eb)) has Pb=Q(sqrt(2Eb/N0)) and exact Ps=2Pb-Pb^2

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Itc Gray Qpsk Coordinate BpskItc Independent Bits Exact Symbol Error

Baseband and passband digital modulationInformation Theory and Digital Communications · Mixed review

ITC:010425Coherent orthogonal BFSK has Pe=Q(sqrt(Eb/N0)); noncoherent envelopes give (1/2)exp[-Eb/(2N0)]

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Itc Coherent Orthogonal Correlator QItc Noncoherent Envelope Half Exp

Baseband and passband digital modulationInformation Theory and Digital Communications · Mixed review

ITC:010426Square 16-QAM with Es=10a^2 has exact Ps=1-[1-(3/2)Q(sqrt(Es/(5N0)))]^2; Gray BER is a shortcut

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Itc Square 16qam Energy And 4pamItc Exact Product Symbol Error Gray Audit

Baseband and passband digital modulationInformation Theory and Digital Communications · Mixed review

ITC:010527Hamming(7,4) encodes 1011 as 0110011; syndrome (0,1,1) corrects bit 6; dmin is 3

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Itc Hamming Lsb Parity Check ColumnsItc Hamming Syndrome Single Flip

Block, convolutional, and coded-modulation foundationsInformation Theory and Digital Communications · Mixed review

ITC:010528CRC of 100101 by 1011 appends 110; every nonzero length-at-most-3 burst is detected

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Itc Crc Shifted Polynomial DivisionItc Crc Short Burst Degree Argument

Block, convolutional, and coded-modulation foundationsInformation Theory and Digital Communications · Mixed review

ITC:010529The (111,101) encoder sends 111000010111; the terminated impulse has weight 5, which is dfree

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Itc Conv Zero State Terminated EncodingItc Conv Free Distance Path Enumeration

Block, convolutional, and coded-modulation foundationsInformation Theory and Digital Communications · Mixed review

ITC:010630The causal ZF inverse of [1,1/2] is the geometric sum; two-tap truncation leaves a -1/4 postcursor

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Itc Causal ZF Geometric InverseItc ZF Truncation Postcursor Noise

ISI, equalization, synchronization, and link budgetsInformation Theory and Digital Communications · Mixed review

ITC:010631The link yields Eb/N0=10 dB, misses the 11 dB target by 1 dB, and supports at most 10^{5.9} bit/s

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Itc Link Budget Ebn0 Decibel IdentityItc Link Budget Margin Rate Inversion

ISI, equalization, synchronization, and link budgetsInformation Theory and Digital Communications · Mixed review

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ITC:010117The stay-3/4 flip-1/4 binary Markov chain has entropy rate h2(1/4) and the word 00110 has self-information 9-2 log2 3

ITC:010118The length-8 two-ones type class under Bern(1/4) has size 28, class probability 5103/16384, and needs 5 enumerative bits

ITC:010219The BEC(1/4) has I=(3/4)h2(q), capacity 3/4 bit per use, and two million uses per second give at most 1.5 Mbit/s

ITC:010220Cascading BSC(1/10) with BSC(1/5) yields BSC(13/50) whose uniform mutual information is 1-h2(13/50)

ITC:010221Uniform input through BSC(1/4) has information density log2(3/2) or -1, mean (3/4)log2 3-1, and variance (3/16)(log2 3)^2

ITC:010322MAP on the ternary source decides 0 then 1 with error 13/30; ML decides 0 then 2 with error 7/15

ITC:010323The LLR 2y1+y2/2 is the test y1+y2/4>0 with error Q(sqrt(5)/2); equal-gain is worse

ITC:010424Gray QPSK at (±sqrt(Eb),±sqrt(Eb)) has Pb=Q(sqrt(2Eb/N0)) and exact Ps=2Pb-Pb^2

ITC:010425Coherent orthogonal BFSK has Pe=Q(sqrt(Eb/N0)); noncoherent envelopes give (1/2)exp[-Eb/(2N0)]

ITC:010426Square 16-QAM with Es=10a^2 has exact Ps=1-[1-(3/2)Q(sqrt(Es/(5N0)))]^2; Gray BER is a shortcut

ITC:010527Hamming(7,4) encodes 1011 as 0110011; syndrome (0,1,1) corrects bit 6; dmin is 3

ITC:010528CRC of 100101 by 1011 appends 110; every nonzero length-at-most-3 burst is detected

ITC:010529The (111,101) encoder sends 111000010111; the terminated impulse has weight 5, which is dfree

ITC:010630The causal ZF inverse of [1,1/2] is the geometric sum; two-tap truncation leaves a -1/4 postcursor

ITC:010631The link yields Eb/N0=10 dB, misses the 11 dB target by 1 dB, and supports at most 10^{5.9} bit/s

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ITC:010117The stay-3/4 flip-1/4 binary Markov chain has entropy rate h2(1/4) and the word 00110 has self-information 9-2 log2 3

ITC:010118The length-8 two-ones type class under Bern(1/4) has size 28, class probability 5103/16384, and needs 5 enumerative bits

ITC:010219The BEC(1/4) has I=(3/4)h2(q), capacity 3/4 bit per use, and two million uses per second give at most 1.5 Mbit/s

ITC:010220Cascading BSC(1/10) with BSC(1/5) yields BSC(13/50) whose uniform mutual information is 1-h2(13/50)

ITC:010221Uniform input through BSC(1/4) has information density log2(3/2) or -1, mean (3/4)log2 3-1, and variance (3/16)(log2 3)^2

ITC:010322MAP on the ternary source decides 0 then 1 with error 13/30; ML decides 0 then 2 with error 7/15

ITC:010323The LLR 2y1+y2/2 is the test y1+y2/4>0 with error Q(sqrt(5)/2); equal-gain is worse

ITC:010424Gray QPSK at (±sqrt(Eb),±sqrt(Eb)) has Pb=Q(sqrt(2Eb/N0)) and exact Ps=2Pb-Pb^2

ITC:010425Coherent orthogonal BFSK has Pe=Q(sqrt(Eb/N0)); noncoherent envelopes give (1/2)exp[-Eb/(2N0)]

ITC:010426Square 16-QAM with Es=10a^2 has exact Ps=1-[1-(3/2)Q(sqrt(Es/(5N0)))]^2; Gray BER is a shortcut

ITC:010527Hamming(7,4) encodes 1011 as 0110011; syndrome (0,1,1) corrects bit 6; dmin is 3

ITC:010528CRC of 100101 by 1011 appends 110; every nonzero length-at-most-3 burst is detected

ITC:010529The (111,101) encoder sends 111000010111; the terminated impulse has weight 5, which is dfree

ITC:010630The causal ZF inverse of [1,1/2] is the geometric sum; two-tap truncation leaves a -1/4 postcursor

ITC:010631The link yields Eb/N0=10 dB, misses the 11 dB target by 1 dB, and supports at most 10^{5.9} bit/s

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Problem results

ITC:010117The stay-3/4 flip-1/4 binary Markov chain has entropy rate h2(1/4) and the word 00110 has self-information 9-2 log2 3View problem statement

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ITC:010117The stay-3/4 flip-1/4 binary Markov chain has entropy rate h2(1/4) and the word 00110 has self-information 9-2 log2 3View problem statement

ITC:010117The stay-3/4 flip-1/4 binary Markov chain has entropy rate h2(1/4) and the word 00110 has self-information 9-2 log2 3

ITC:010117The stay-3/4 flip-1/4 binary Markov chain has entropy rate h2(1/4) and the word 00110 has self-information 9-2 log2 3