Improved shortening algorithm for irregular QC-LDPC codes using known bits

Shortening is a technique to achieve rate and length adaptable low-density-parity-check (LDPC) codes. Other than the puncturing and extending techniques, shortening aims to remove certain information columns, i.e., the columns standing for the known information bits, from a given parity check matrix. In this paper, we first review the recently suggested largest-extrinsic-sum (LES) algorithm which is especially designed for quasic-cyclic (QC) LDPC codes, and then propose a method based on smallest-row-variance priority (SRVP). Moreover, we obtain both theoretical analysis and simulation results of the codes in 802.11n and 802.16e standards, which shows that: 1) the proposed SRVP algorithm always achieves better Eb/No threshold than the existing LES algorithm and generally, the shortened codes outperform the original codes; 2) severe performance degradation occurs when too many information bits are shortened for low rate codes. The proposed algorithm as well as the corresponding performance evaluations is instructive to practical applications.