Title: Short Regular Girth-8 QC-LDPC Codes From Exponent Matrices with Vertical Symmetry

Abstract: To address the challenge of constructing short girth-8 quasi-cyclic (QC) low-density parity-check (LDPC) codes, a novel construction framework based on vertical symmetry (VS) is proposed. Basic properties of the VS structure are presented. With the aid of these properties, existing explicit constructions for column weights from three to five which can be transformed into the VS structure are sorted out. Then two novel explicit constructions with the VS structure which guarantee short codes are presented for column weights of three and six. Moreover, an efficient search-based method is also proposed to find short codes with the VS structure. Compared with the state-of-the-art benchmarks, both the explicit constructions and the search-based method presented in this paper can provide shorter codes for most cases. Simulation results show that the new shorter codes can perform almost the same as or better than the longer existing counterparts. Thus, the new shorter codes can fit better with the low-latency requirement for modern communication systems.