15 research outputs found
Instanton-based Techniques for Analysis and Reduction of Error Floors of LDPC Codes
We describe a family of instanton-based optimization methods developed
recently for the analysis of the error floors of low-density parity-check
(LDPC) codes. Instantons are the most probable configurations of the channel
noise which result in decoding failures. We show that the general idea and the
respective optimization technique are applicable broadly to a variety of
channels, discrete or continuous, and variety of sub-optimal decoders.
Specifically, we consider: iterative belief propagation (BP) decoders, Gallager
type decoders, and linear programming (LP) decoders performing over the
additive white Gaussian noise channel (AWGNC) and the binary symmetric channel
(BSC).
The instanton analysis suggests that the underlying topological structures of
the most probable instanton of the same code but different channels and
decoders are related to each other. Armed with this understanding of the
graphical structure of the instanton and its relation to the decoding failures,
we suggest a method to construct codes whose Tanner graphs are free of these
structures, and thus have less significant error floors.Comment: To appear in IEEE JSAC On Capacity Approaching Codes. 11 Pages and 6
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Polytope of Correct (Linear Programming) Decoding and Low-Weight Pseudo-Codewords
We analyze Linear Programming (LP) decoding of graphical binary codes
operating over soft-output, symmetric and log-concave channels. We show that
the error-surface, separating domain of the correct decoding from domain of the
erroneous decoding, is a polytope. We formulate the problem of finding the
lowest-weight pseudo-codeword as a non-convex optimization (maximization of a
convex function) over a polytope, with the cost function defined by the channel
and the polytope defined by the structure of the code. This formulation
suggests new provably convergent heuristics for finding the lowest weight
pseudo-codewords improving in quality upon previously discussed. The algorithm
performance is tested on the example of the Tanner [155, 64, 20] code over the
Additive White Gaussian Noise (AWGN) channel.Comment: 6 pages, 2 figures, accepted for IEEE ISIT 201
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
New decoding scheme for LDPC codes based on simple product code structure
In this paper, a new decoding scheme for low-density parity-check (LDPC)
codes using the concept of simple product code structure is proposed based on
combining two independently received soft-decision data for the same codeword.
LDPC codes act as horizontal codes of the product codes and simple algebraic
codes are used as vertical codes to help decoding of the LDPC codes. The
decoding capability of the proposed decoding scheme is defined and analyzed
using the paritycheck matrices of vertical codes and especially the
combined-decodability is derived for the case of single parity-check (SPC) and
Hamming codes being used as vertical codes. It is also shown that the proposed
decoding scheme achieves much better error-correcting capability in high signal
to noise ratio (SNR) region with low additional decoding complexity, compared
with a conventional decoding scheme.Comment: This work has been submitted to the IEEE for possible publication.
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