  This paper focuses on controlling the absorbing set spectrum for a class of
regular LDPC codes known as separable, circulant-based (SCB) codes. For a
specified circulant matrix, SCB codes all share a common mother matrix,
examples of which are array-based LDPC codes and many common quasi-cyclic
codes. SCB codes retain the standard properties of quasi-cyclic LDPC codes such
as girth, code structure, and compatibility with efficient decoder
implementations. In this paper, we define a cycle consistency matrix (CCM) for
each absorbing set of interest in an SCB LDPC code. For an absorbing set to be
present in an SCB LDPC code, the associated CCM must not be full columnrank.
Our approach selects rows and columns from the SCB mother matrix to
systematically eliminate dominant absorbing sets by forcing the associated CCMs
to be full column-rank. We use the CCM approach to select rows from the SCB
mother matrix to design SCB codes of column weight 5 that avoid all low-weight
absorbing sets (4, 8), (5, 9), and (6, 8). Simulation results demonstrate that
the newly designed code has a steeper error-floor slope and provides at least
one order of magnitude of improvement in the low error rate region as compared
to an elementary array-based code.
