  For LDPC codes operating over additive white Gaussian noise channels and
decoded using message-passing decoders with limited precision, absorbing sets
have been shown to be a key factor in error floor behavior. Focusing on this
scenario, this paper introduces the cycle consistency matrix (CCM) as a
powerful analytical tool for characterizing and avoiding absorbing sets in
separable circulant-based (SCB) LDPC codes. SCB codes include a wide variety of
regular LDPC codes such as array-based LDPC codes as well as many common
quasi-cyclic codes. As a consequence of its cycle structure, each potential
absorbing set in an SCB LDPC code has a CCM, and an absorbing set can be
present in an SCB LDPC code only if the associated CCM has a nontrivial null
space.
  CCM-based analysis can determine the multiplicity of an absorbing set in an
SCB code and CCM-based constructions avoid certain small absorbing sets
completely. While these techniques can be applied to an SCB code of any rate,
lower-rate SCB codes can usually avoid small absorbing sets because of their
higher variable node degree. This paper focuses attention on the high-rate
scenario in which the CCM constructions provide the most benefit. Simulation
results demonstrate that under limited-precision decoding the new codes have
steeper error-floor slopes and can provide one order of magnitude of
improvement in the low FER region.
