👉 Sender math, also known as sender's inequality or the sender's bound, is a fundamental concept in information theory that quantifies the relationship between the entropy of a source and the capacity of a communication channel. It states that for any discrete memoryless source, the mutual information between the source and the received message cannot exceed the entropy of the source multiplied by the channel's capacity. Mathematically, this is expressed as \( I(X;Y) \leq H(X) \cdot C \), where \( I(X;Y) \) is the mutual information, \( H(X) \) is the entropy of the source, and \( C \) is the channel capacity. This inequality highlights that the amount of information that can be reliably transmitted through a channel is limited by both the source's inherent uncertainty and the channel's ability to transmit information without error.
