193 research outputs found
Lowering the Error Floor of LDPC Codes Using Cyclic Liftings
Cyclic liftings are proposed to lower the error floor of low-density
parity-check (LDPC) codes. The liftings are designed to eliminate dominant
trapping sets of the base code by removing the short cycles which form the
trapping sets. We derive a necessary and sufficient condition for the cyclic
permutations assigned to the edges of a cycle of length in the
base graph such that the inverse image of in the lifted graph consists of
only cycles of length strictly larger than . The proposed method is
universal in the sense that it can be applied to any LDPC code over any channel
and for any iterative decoding algorithm. It also preserves important
properties of the base code such as degree distributions, encoder and decoder
structure, and in some cases, the code rate. The proposed method is applied to
both structured and random codes over the binary symmetric channel (BSC). The
error floor improves consistently by increasing the lifting degree, and the
results show significant improvements in the error floor compared to the base
code, a random code of the same degree distribution and block length, and a
random lifting of the same degree. Similar improvements are also observed when
the codes designed for the BSC are applied to the additive white Gaussian noise
(AWGN) channel
Characterization and Efficient Search of Non-Elementary Trapping Sets of LDPC Codes with Applications to Stopping Sets
In this paper, we propose a characterization for non-elementary trapping sets
(NETSs) of low-density parity-check (LDPC) codes. The characterization is based
on viewing a NETS as a hierarchy of embedded graphs starting from an ETS. The
characterization corresponds to an efficient search algorithm that under
certain conditions is exhaustive. As an application of the proposed
characterization/search, we obtain lower and upper bounds on the stopping
distance of LDPC codes.
We examine a large number of regular and irregular LDPC codes, and
demonstrate the efficiency and versatility of our technique in finding lower
and upper bounds on, and in many cases the exact value of, . Finding
, or establishing search-based lower or upper bounds, for many of the
examined codes are out of the reach of any existing algorithm
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