Decoding

Question 1

How do you decode the Hamming code?

Answer 1

Ensure there is parity (even number of 1s) in each circle of the Venn diagram; if there is not, flip one bit

Question 2

Where should bits 1 to 7 go in the circles in the Hamming code? (Eg 0110100011️⃣2️⃣3️⃣4️⃣5️⃣6️⃣7️⃣01101)

Answer 2

5️⃣
1️⃣ 2️⃣
3️⃣
7️⃣ 4️⃣ 6️⃣

Question 3

What do N and K represent for a block code?

Answer 3

In a block code, like the Hamming code, N represents the number of bits involved in a code word, and K represents the number of source bits whose information is passed on in the source code.

Question 4

What is the rate of a block code?

Answer 4

K/N
4/7 for Hamming code
1/N for repetition code

Question 5

What did Shannon show regarding codes (in 1948)?

Answer 5

Shannon showed that block codes can be made with rate K/N about 0.53 which have a very very low chance of error - however, they use very large N values.