General Questions regarding LDPC codes

I am currently learning LDPC codes, I have the following general question regarding LDPC codes,

1) when encountering a term such as LDPC$(672,504)$ are we referring to the code rate or the matrix dimensions? i.e is it $(n,k)$ or $(n,n-k)$? or is it different depending on book?

2) A 3/4 LDPC matrix is used with shortening to have an effective code rate of 1/2 or less. Since the code rate is 1/4 we need to do puncturing is shortening term similar to puncturing?

3) If we have number of bits that we want to encode less than 504, say for example 64, do we need to pad first with zeros to a length of 504 in order to use the LDPC(672,504)? Assuming this notation is referring to 3/4 matrix.

Any references on LDPC would be great.

• When you shorten, you're fixing the redundancy ($n-k$). When you puncture, you're reducing the redundancy $n-k$. – Batman Jun 17 '15 at 16:31
• Yes. This follows from $\frac{x-a}{y-a} \leq \frac{x}{y}$ when $x> a>0, y\geq x$. You can also think of puncturing as deleting columns in a generator matrix while shortening as deleting columns in a parity check matrix (where you use the convention that you left multiply the generator matrix to encode). Shortening decreases rate, puncturing increases rate. – Batman Jun 17 '15 at 16:47