"Huh? What did you say?"
Yuki couldn't hear Riku's words. Construction noise echoed outside the club room.
"I said! Information theory..."Riku raised his voice.
"Information theory what?"
"Homework!"
Finally, it got through. Aoi closed the window with a wry smile.
"This is a communication channel with noise."
"Noise?" Yuki asked.
"Things that interfere with the signal. Construction sounds, wind, all kinds of noise."
Riku looked tired. "Conversations are tough when there's noise."
"Yes. In information theory, there's a concept called signal-to-noise ratio. Called SNR."
Aoi wrote on the whiteboard.
"SNR = Signal / Noise"
"The stronger the signal and weaker the noise, the easier communication becomes."
Yuki understood. "That's why even a small voice carries in a quiet place."
"Correct. Conversely, in noisy places, you need a loud voice."
Riku raised his hand. "But just being loud isn't enough. You have to speak clearly."
"Sharp observation," Aoi nodded. "Not just volume, but clarity matters. This becomes an encoding problem."
Yuki wrote in the notebook. "Encoding?"
"Converting messages into forms resistant to noise. For example, when transmitting the alphabet by radio, 'A' becomes 'Alpha,' 'B' becomes 'Bravo.'"
"Why?"
"'B' and 'D' sound similar and are easily confused with noise. But 'Bravo' and 'Delta' are easier to distinguish."
Riku's eyes lit up. "Adding redundancy prevents errors!"
"Exactly. Information amount increases, but so does reliability."
Aoi drew a diagram.
"Channel capacity is limited. When noise increases, capacity decreases. But with smart encoding, capacity can be used effectively."
Yuki remembered. "That's Shannon's limit we learned before."
"Yes. Even with noise, approaching the limit allows nearly error-free communication."
Riku suddenly realized. "Is our conversation encoded too?"
"Natural language is a powerful encoding system," Aoi explained. "Grammar, context, paraphrasing. All serve as noise countermeasures."
Yuki gave an example. "Asking 'Huh?' is also a type of error correction?"
"Precise. It's a feedback loop. The receiver confirms, and the sender retransmits."
"Human conversation is amazing," Riku was impressed.
Aoi continued. "But it's not perfect. Misunderstandings happen. When noise is too strong, no encoding helps."
"Then what do we do?"
"Reduce noise, strengthen the signal, or use better encoding. Three options."
Yuki looked outside. The construction noise continued.
"But completely eliminating noise is impossible, right?"
"Impossible. So we learn to coexist with noise. That's the essence of communication theory."
Riku wrote in his notebook. "Even surrounded by noise, there are things we want to convey."
"That's poetic, Riku," Yuki laughed.
Aoi smiled. "Information theory is the technology of pursuing perfection in an imperfect world."
The construction noise grew louder again. The three looked at each other and laughed.
Even with noise, important messages get through.
Believing that, they continue their conversation today as well.