"The call is distant."
Riku held the phone away from his ear and looked at it.
"Bad reception," Aoi said.
"But I can somehow hear. Strange, right?"
Yuki was interested. "Even with lots of noise, it gets through."
"That's the power of error-correcting codes."
Aoi drew a diagram on the whiteboard. Sender, channel, receiver.
"Communication channels always have noise mixed in."
"Wireless has radio interference, wired has signal attenuation."
Riku asked. "Then how does it transmit correctly?"
"Add redundancy. Send the same information multiple times."
"Like sending 'hello' as 'hheelllloo'?"
"In principle, yes. But there are smarter methods."
Mira appeared and wrote in her notebook. "Hamming code."
"Hamming code?" Yuki asked.
"One type of error-correcting code. Can detect and correct errors with few added bits."
Aoi continued explaining. "Add 3 parity bits to 4 data bits."
"Send 7 bits and correct 1-bit errors."
Riku was impressed. "That's efficient."
"Shannon's channel coding theorem. Below channel capacity rate, arbitrarily small error rates are achievable."
Yuki asked. "What's channel capacity?"
"The upper limit of information that can be sent reliably even with noise. C = B log₂(1 + S/N)."
"Determined by bandwidth B and signal-to-noise ratio S/N."
Riku thought. "More noise means less capacity?"
"Right. Small S/N reduces sendable information."
"That's why important calls need quiet places."
Aoi continued. "But we can counter with encoding."
"Internet TCP protocol. If packets corrupt, retransmit."
Yuki understood. "That's also a type of error correction?"
"Error detection and retransmission. Called ARQ (Automatic Repeat reQuest)."
"If you can't correct, ask to send again."
Mira wrote again. "FEC vs ARQ."
"FEC (Forward Error Correction) corrects only at receiver."
"ARQ requests retransmission from sender."
Riku laughed. "Human conversation is also ARQ. 'Huh? Say that again.'"
"Exactly. Natural language communication also has error correction mechanisms."
Aoi supplemented. "Grammar, context, redundancy. All counter noise."
Yuki wrote in her notes. "What about a perfect communication channel?"
"With zero noise, redundancy is unnecessary. Just compress."
"But reality has noise."
"So balancing compression and error correction matters."
Riku asked. "What happens if you do both?"
"Compress first, then add error-correcting codes."
"Shannon's separation theorem. Source coding and channel coding can be optimized independently."
Yuki was impressed. "There's proper theory."
"Shannon's information theory built the foundation of communication."
Mira drew a diagram. In a noisy channel, the message arrives safely.
"Messages beyond noise," Aoi said.
"Even with noise, feelings reach."
Riku looked at his phone. "Amazing technology packed in this little machine."
"Encoding, modulation, demodulation, error correction. All cooperating."
Yuki looked out the window. "Radio waves are invisible but flying around."
"Invisible information fills the space."
Aoi smiled gently. "And despite noise, it reaches those who matter."
"That's the beauty of communication."
Mira wrote finally. "Messages to you will surely reach."
"Error correction protects them."
The four nodded quietly.
Even beyond noise, feelings are conveyed. That's the power of information theory.