# What is the probability of binary digits produced

An information source produces a long sequence of three independent symbols A,B,C with probabilities 16/20, 3/20, and 1/20 respectively; 100 such symbols are produced per second. The information is to be transmitted via a noiseless binary channel which can transmit up to 100 binary digits per second. Design a suitable compact instantaneous code and find the probabilities of the binary digits produced.

I need help with this question. For compact instantaneous code, I used the huffman's encoding. How do i find the probability of binary digits produced? Can someone help me please?

• What have you tried so far? We won't give you the complete answer, but we can help you. What's your Huffman encoding? I suppose something like '0', '10' and '11' ?
– Ben
Aug 31, 2022 at 16:08
• i got 1, 01 and 00 for A,B and C respectively. Firstly i wanted to check if huffman is suitable for compact instantaneous code and for probability of binary digits, i'm brainstorming if it can be assumed similar to rolling a dice multiple times and getting the probability. It might help if you could give an idea how to approach it for second question. Aug 31, 2022 at 16:15
• Ok, so 80% of time, the number '1' will be generated, 15% of the time the number "01" will be generate and 5% of the time the number "00" will be generated. So for a sequence of 100 symbols, you should generate 105 zeroes and 15 ones, right ?
– Ben
Aug 31, 2022 at 17:23
• since symbol A happens much more often than either B or C, it seems to me that you might want to do run-length encoding for A and when the run ends a two-bit encoding for B and C. Aug 31, 2022 at 18:56
• What's the entropy of your process, i.e., what's the best compression you'll ever achieve? How close to it are you with your chosen Huffman encoding? Aug 31, 2022 at 23:37