system bit rate vs channel coding We are  usually asked about the full system bit rate. However, we use channel encoding in practical systems, for example conventional coding with rate $(1/3)$. My question is about the full system bit rate in such system which employs channel coding. Should it be calculated including the coding bits or after extracting the code bits? I mean if we have system whose bit rate of $12bps$ and employs channel encoding of rate $(1/3)$. Should the bit rate be $12bps$ or $4bps$ since the other $8$ bits are used for coding?
Both indicators are used. It depends what you mean in speaking of your indicators.
One of common usages is to compare systems where we use indicators of the same type. For example,

to compare 5G NR and LTE RANs, we usually use max throughput which is defined as the multiplication of number of antennas, number of subcarriers and QAM order per subframe. There is no error probability here.
To compare channel decoders e.g. iterative belief propagation LDPC decoder and Ordered Statistic decoder, it does not make sense anymore if error probability is ignored and, therefore, the code dimension (number of bits before encoding) must be used.