Which of the following correctly states Shannon's channel coding theorem?

Answer: A. If the transmission rate is below the channel capacity, suitable coding can make the error rate arbitrarily small

The channel coding theorem shows that at any rate below the channel capacity C, the error rate can be made arbitrarily small by using sufficiently long codes, and that this is impossible at rates above C. The theorem shows that such codes exist but does not give a concrete way to construct them. Today, codes whose performance approaches this limit (the Shannon limit), such as LDPC codes and polar codes, are in practical use.

• A. Correct. Below the channel capacity, codes exist that make errors arbitrarily rare.
• B. At rates above the channel capacity, no code of any kind can make the error rate small.
• C. With methods that simply repeat the same bits, errors do decrease only if the rate is lowered, but the theorem shows that errors can be reduced while keeping a fixed rate below the capacity.