1. **Stating the problem:** We are given a list of source encodings (binary strings) and corresponding values of $r$. We need to encode each source message using the given $r$ value to find the channel encoding. 2. **Understanding the encoding:** The problem does not specify the exact encoding rule, but a common approach is to repeat each bit $r$ times to form the channel encoding. 3. **Applying the rule:** For each source encoding, repeat each bit $r$ times. 4. **Encoding each message:** - For source encoding $101$ with $r=2$: repeat each bit twice: $1\to11$, $0\to00$, $1\to11$ so channel encoding is $110011$. - For source encoding $100$ with $r=3$: repeat each bit thrice: $1\to111$, $0\to000$, $0\to000$ so channel encoding is $111000000$. - For source encoding $001$ with $r=2$: $0\to00$, $0\to00$, $1\to11$ so channel encoding is $000011$. - For source encoding $011$ with $r=2$: $0\to00$, $1\to11$, $1\to11$ so channel encoding is $001111$. - For source encoding $110$ with $r=3$: $1\to111$, $1\to111$, $0\to000$ so channel encoding is $111111000$. 5. **Final answers:** - $101 \to 110011$ - $100 \to 111000000$ - $001 \to 000011$ - $011 \to 001111$ - $110 \to 111111000$