Noisy-channel coding theorem
Okay kiddo, imagine you have a secret message and you want to send it to your friend who lives far away. But in between you and your friend, there’s a noisy channel (like a scratchy phone line) that might distort or mess up parts of your message.
The noisy-channel coding theorem is a way to protect your message from getting messed up during transmission.
Here’s how it works:
First, you break your message into small pieces called “symbols”. Then you use some math tricks to turn each symbol into a longer sequence of symbols (called a “codeword”) that is more resilient to noise.
When you transmit the codewords, the receiver gets a distorted version of the codewords because of the noise in the channel. But because of the math tricks we used to create the codewords, the receiver can still decode your original message without errors.
Think of it like this: Let’s say your original message is “dog”. But you know that the noisy channel might distort some of the letters, so you turn “dog” into “101010111000”. When your friend receives “101110011000”, they can still decode it back into “dog” because of the extra digits you added to protect against errors.
The noisy-channel coding theorem tells us the maximum amount of protection (the “coding rate”) we can achieve given how noisy the channel is. So we can use this theorem to choose the best code to protect our messages and ensure accurate transmission.
The noisy-channel coding theorem is a way to protect your message from getting messed up during transmission.
Here’s how it works:
First, you break your message into small pieces called “symbols”. Then you use some math tricks to turn each symbol into a longer sequence of symbols (called a “codeword”) that is more resilient to noise.
When you transmit the codewords, the receiver gets a distorted version of the codewords because of the noise in the channel. But because of the math tricks we used to create the codewords, the receiver can still decode your original message without errors.
Think of it like this: Let’s say your original message is “dog”. But you know that the noisy channel might distort some of the letters, so you turn “dog” into “101010111000”. When your friend receives “101110011000”, they can still decode it back into “dog” because of the extra digits you added to protect against errors.
The noisy-channel coding theorem tells us the maximum amount of protection (the “coding rate”) we can achieve given how noisy the channel is. So we can use this theorem to choose the best code to protect our messages and ensure accurate transmission.
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