Could LDPC code achieve rate compatibility?

(1) May I ask if LDPC code can achieve rate compatibility? For example, can the bit rate be set to R=1/2, 1/3, 2/3 for the same input information length K=1000?
(2) If possible, may I ask what theory was used to implement it?

Yes, they can have rate adaptability. In the implementation that we have here, which follows 5G-NR, it is based on code puncturing.

This is performed in the rate-matching stage of the transmission.


Modify an existing code appropriately to increase or decrease its bit rate. There are various ways to implement rate compatible codes, and we mainly discuss achieving variable bit rates through punctures. Delete refers to the use of code C at the sending end to encode an information sequence, and then delete certain symbols at pre selected positions in the sequence to be sent (without sending these symbols), in order to improve transmission efficiency.
Is the basic principle like this?

Some of the parity bits are removed, therefore increasing the code rate. This is explained in the image below (zoom in). At the receiver, those not transmitted bits get assigned a zero-valued LLRs, reflecting total uncertainty about them, and then the whole thing gets passed to the decoder.

This can be implemented in different ways. For the 5G-NR LDPC codes in the simulator, you can find more information about the used puncturing scheme here (Section 5.4.2):