"Sometimes you think you're communicating, but you're not."
Yuki reacted to Riku's musing. "What do you mean?"
"I just asked Aoi-senpai a question, but got a completely different answer."
Aoi smiled wryly. "Because Riku's question was vague."
"This is the problem of channel capacity," Aoi began explaining. "Channels have limits. No matter how much information you try to send, there's an upper limit to what the channel can handle."
Yuki opened the notebook. "What determines channel capacity?"
"Mainly two things. Bandwidth and signal-to-noise ratio."
Aoi wrote an equation on the whiteboard.
"C = B log₂(1 + SNR)"
"C is channel capacity, B is bandwidth, SNR is signal-to-noise ratio."
Riku looked confused. "Sounds difficult."
"Let's think with a concrete example," Aoi continued. "Phone lines. Voice bandwidth is about 3000 Hz. If SNR is about 30 dB..."
Aoi calculated. "Capacity is about 30 kbps. Trying to send more data increases errors."
"That's why phone audio quality is limited," Yuki understood.
"Yes. Physical constraints limit information flow."
Riku thought. "So conversation also has channel capacity?"
"Interesting perspective," Aoi acknowledged. "Human auditory processing also has limits. How much information can be understood per second."
"Is that why speaking fast doesn't get understood?"
"Exactly. When the sender exceeds capacity, the receiver can't process it. Information is lost."
Yuki raised her hand. "But if we speak slowly, everything gets through, right?"
"Theoretically. But it takes time. Another tradeoff."
Aoi drew a new diagram. "Shannon limit. Channel capacity shows the theoretical upper bound. No matter how clever the encoding, you can't exceed this."
"An absolute wall?" Riku asked.
"Yes. But conversely, below capacity, errors can be made arbitrarily close to zero. That's Shannon's channel coding theorem."
Yuki wrote in the notebook. "So to increase channel capacity?"
"Widen bandwidth or increase SNR. Bandwidth has physical constraints, often difficult. So reducing noise is more realistic."
Riku got excited. "So talking in a quiet place increases channel capacity!"
"Correct. Conversing in a library versus at a construction site has completely different transmission efficiency."
"That's why important talks happen in quiet places," Yuki was convinced.
Aoi supplemented. "In communications engineering, either strengthen the signal or reduce noise. Both approaches exist."
"But if the signal is too strong?"
"It interferes with other communications. That's why transmission power is regulated in wireless communication."
Riku's face became serious. "So if everyone talks loudly, nobody can be heard."
"The reverse of the cocktail party effect," Aoi laughed.
Yuki summarized. "Whether it gets through is determined by channel capacity. If the information amount exceeds capacity, it doesn't get through."
"That's why matching the other person's comprehension speed is important," Aoi said.
"Aoi-senpai's explanations are easy to understand because you consider my channel capacity."
Aoi smiled. "Practicing information theory."
Riku nodded. "I'll also think about how to communicate properly."
Channel capacity. It wasn't just theory, but a concept relevant to all of daily life.