C=max I(X;Y). Shannon capacity theorem.
graph TD
D1["Def: Channel\np(y|x) conditional"]
D2["Def: Capacity\nC = max I(X;Y)"]
D3["Def: DMC\nmemoryless"]
D4["Def: Input constraint\nE[cost(X)]≤B"]
T1["Thm: Shannon capacity\nC = max I(X;Y)"]
T2["Thm: Coding thm\nRC ⇒ unreliable"]
T4["Thm: AWGN\nC = ½ log(1+SNR)"]
T5["Thm: Blahut–Arimoto\nalg for C"]
D1 --> D2
D2 --> D3
D3 --> T1
T1 --> T2
T2 --> T3
classDef definition fill:#b197fc,color:#fff
classDef theorem fill:#51cf66,color:#fff
class D1,D2,D3,D4 definition
class T1,T2,T3,T4,T5 theorem
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Frontier: math.IT