On the LLR criterion based shortening design for LDPC codes

In shortening based coding design, a certain amount of known information bits (for instance, all 0 bits) will be inserted into each information packet for encoding and be removed before transmission. Since they are known, the decoder can assume a complete codeword in decoding, even those known bits are not delivered at all. Basically, shortening provides a framework to generate a set of more powerful codewords with shorter size and lower rate from one mother LDPC code. In this paper, a novel log-likelihood ratio (LLR) criterion is proposed to identify those shortening information indices for LDPC codes. Firstly, the LLR criterion is introduced to show how to determine the LLR reliability metric for each individual information bit via a simple noise-free decoding step. Then it is proposed to determine the shortened information indices based on the LLR ordering. The relationship between the proposed shortening scheme and the known approaches are highlighted as well. Finally, the irregular QC-LDPC codes in IEEE 802.11ac standard is utilized as an example to verify the proposed LLR criterion based shortening design. And our analysis unveils that the proposed shortening scheme provides an efficient shortening scheme for LDPC codes with lower computational complexity but better reliability performance.