"Is noise a villain?"
To Yuki's question, Aoi answered with interest. "Depends on perspective. Knowing the origins of noise gives you a different view."
Riku played an audio file full of static. "I recorded this yesterday. Can't tell what's being said."
"Typical environmental noise," Aoi explained. "Background sounds, wind, other conversations. Everything's mixed."
Mira wrote in her notebook. "Thermal noise, quantization noise, interference"
"Yes. Noise has multiple sources," Aoi drew classifications on the whiteboard.
"First, thermal noise. Emitted by all electronic devices. With temperature, electrons move randomly. This is unavoidable noise."
Yuki thought. "So it decreases if we cool it?"
"Theoretically. At absolute zero, thermal noise is zero. But practically impossible."
Riku raised his hand. "What's quantization noise?"
"Occurs during digital conversion. When rounding analog signals to discrete values, information is lost."
Aoi drew a diagram. A continuous curve approximated by a staircase shape.
"This rounding error is quantization noise. Higher precision reduces noise, but increases data volume."
"Another tradeoff," Riku smiled wryly.
Mira wrote another example. "Interference: multiple signals overlap"
"Interference," Aoi nodded. "Like Wi-Fi, when multiple transmitters use the same frequency, signals mix. This is also a type of noise."
Yuki was fascinated. "So we can't completely eliminate noise?"
"No. Shannon's channel coding theorem shows that 'even with noise, error-free transmission is possible below channel capacity.' It assumes noise exists."
"Coexisting with noise..."
"Right. Even in a perfect anechoic chamber, thermal noise remains. In space, there's cosmic microwave background radiation. Noise is everywhere."
Riku suddenly thought of something. "Can't we use noise?"
Aoi's eyes lit up. "Sharp! There's a technique called dithering. By intentionally adding noise, you disperse quantization errors."
"Adding noise? Paradoxical."
"Often used in image processing. Adding fine noise makes gradations appear smoother."
Mira supplemented. "Stochastic resonance: noise can enhance signal"
"Stochastic resonance," Aoi explained. "Appropriate noise makes weak signals easier to detect. Also occurs in biological sensory organs."
Yuki organized in the notebook. "Noise is unavoidable, but depending on usage, can become an ally."
"Exactly. Information theory doesn't view noise as an enemy. Rather, understanding noise properties helps find optimal communication methods."
Riku listened to the recording again. "Maybe analyzing this noise reveals patterns."
"Yes. If you know noise's statistical properties, you can filter it. Whether it's white noise or pink noise, characteristics matter."
Mira said quietly. "Noise is information about the channel"
The four fell silent. It was a deep insight.
"Noise itself carries information about the channel," Aoi rephrased. "Knowing what kind of noise is key to understanding the channel."
Yuki smiled. "Noise isn't a villain, but part of communication."
"Perfect silence is less interesting information-theoretically than noisy reality."
Riku laughed. "So I'm also a type of noise?"
"In a sense," Aoi admitted. "But necessary noise."
From outside the club room, city noise could be heard. That too was part of the information.