On q-ary LDPC Code Design for a Low Error Floor

This paper explores protograph-based and ACE-based methods for constructing q-ary low-density parity-check (LDPC) matrices. The ACE approach maximizes approximate cycle extrinsic message degree, explicitly avoiding small q-ary stopping sets and implicitly avoiding small absorbing sets. In addition to ACE, this paper applies linear-dependent-set maximization (LDSM) to the binary image of the q-ary LDPC matrix. Performance is studied for binary and q-ary instances of erasure channels and additive white Gaussian noise channels. The combination of the ACE approach and LDSM provides dramatic error floor improvement for the binary erasure channel and both binary and q-ary AWGN channels.