"Riku, you failed again?"
Yuki looked at the sighing Riku.
"It doesn't get through. My feelings."
Aoi approached with interest. "A communication problem."
"Romance is communication?" Riku was confused.
"In a sense. Encode a message, send it, the other person decodes it."
Yuki asked, "But isn't Riku's message too long?"
"True," Riku admitted. "But I don't want to cut my feelings."
Aoi opened the notebook. "There's a field called rate-distortion theory."
"Rate-distortion?"
"It deals with the tradeoff between compression rate and information degradation. How much compression gives acceptable distortion."
Yuki thought. "Like image compression?"
"Yes. JPEG is lossy compression. Doesn't fully restore but looks almost the same."
Riku said, "So my feelings can be compressed too?"
"Perhaps. But you need to decide what can be lost and what must be preserved."
Aoi drew a diagram. "Horizontal axis is compression rate R, vertical axis is distortion D. The rate-distortion function R(D) shows the minimum bit rate when allowing distortion D."
"Difficult..."
Yuki translated. "Basically, how much can you cut safely."
"Yes. And human perception has limits. Imperceptible information can be removed without problem."
Riku asked, "So what parts are important in romantic messages?"
Aoi thought. "The essential emotion. The core 'I like you' should be preserved."
"But why I like them, how much I like them, since when... aren't all important?"
"Information-wise, it might be redundant. Parts the other person can infer can be omitted."
Yuki supplemented, "That you like someone is already conveyed. So instead of 'I still like you today,' saying 'I liked this about you today' has more information."
Riku's eyes widened. "I see. Just send new information."
"Differential encoding," Aoi nodded. "Send only changes from last time. Efficient."
"But," Riku said anxiously, "what if over-compression causes misunderstanding?"
"That's distortion D. You need to decide the acceptable range of misunderstanding."
Yuki said, "Zero percent distortion is impossible, right?"
"Not without lossless compression. But romance might be okay with lossy."
"Lossy?"
"Even if not perfectly conveyed, it's fine if the essence gets through. Reconstruction happens in the other person's brain."
Yuki added, "And everyone reconstructs messages slightly differently based on their own experiences and context."
"That's the beauty and challenge of human communication," Aoi agreed.
"Lossy?"
"Even if not perfectly conveyed, it's fine if the essence gets through. Reconstruction happens in the other person's brain."
Riku pondered. "So it depends on the other person's comprehension?"
"Yes. Decoder performance is important. If the other person understands context, you can convey more with less information."
Aoi drew a graph. "What's interesting about rate-distortion theory is that optimal compression methods exist. Random coding is near-optimal."
"Random?" Riku was surprised.
"Strictly, probabilistic encoding. Natural expressions can be more efficient than perfectly calculated words."
Yuki smiled. "Basically, speak honestly."
"In a sense. Over-designed words are noise-vulnerable."
Riku took a deep breath. "Got it. Brief but preserve essence."
"Good policy," Aoi acknowledged.
Yuki added, "But don't worry too much about compression rate. Feelings can have some redundancy."
"Redundancy can create reassurance," Aoi supplemented. "It becomes error correction capability."
Riku laughed. "Romance is difficult."
"Communication is difficult too," Aoi said. "But that's why information theory exists."
The three discussed transmission efficiency in the sunset club room.
Perfect communication doesn't exist. But optimal compression exists.
That was rate-distortion theory's teaching.