If the maximum allowable code-word length is $672$ bits and assuming we are using an LDPC parity check matrix with rate $1/2$, $3/4$, what is the maximal number of data bits in each LDPC code-word?
My solution is that $\text{max} = 3*672/4$, but the correct answer provided in the book is $168$ Does anyone know why this is the answer? Thanks.
For an $(n,k)$ code, the parity check matrix is an $(n-k)\times n $ matrix. Then, a parity check matrix with ratio 3/4 means $\frac{n-k}{n}=\frac{3}{4}$, i.e., the code rate, which is defined as $\frac{k}{n}$, is $\frac{1}{4}$. Then, it is easy to see that $672\times \frac{1}{4}= 168$ bits.