9 research outputs found
Design and Analysis of Nonbinary LDPC Codes for Arbitrary Discrete-Memoryless Channels
We present an analysis, under iterative decoding, of coset LDPC codes over
GF(q), designed for use over arbitrary discrete-memoryless channels
(particularly nonbinary and asymmetric channels). We use a random-coset
analysis to produce an effect that is similar to output-symmetry with binary
channels. We show that the random selection of the nonzero elements of the
GF(q) parity-check matrix induces a permutation-invariance property on the
densities of the decoder messages, which simplifies their analysis and
approximation. We generalize several properties, including symmetry and
stability from the analysis of binary LDPC codes. We show that under a Gaussian
approximation, the entire q-1 dimensional distribution of the vector messages
is described by a single scalar parameter (like the distributions of binary
LDPC messages). We apply this property to develop EXIT charts for our codes. We
use appropriately designed signal constellations to obtain substantial shaping
gains. Simulation results indicate that our codes outperform multilevel codes
at short block lengths. We also present simulation results for the AWGN
channel, including results within 0.56 dB of the unconstrained Shannon limit
(i.e. not restricted to any signal constellation) at a spectral efficiency of 6
bits/s/Hz.Comment: To appear, IEEE Transactions on Information Theory, (submitted
October 2004, revised and accepted for publication, November 2005). The
material in this paper was presented in part at the 41st Allerton Conference
on Communications, Control and Computing, October 2003 and at the 2005 IEEE
International Symposium on Information Theor
Efficient implementation of linear programming decoding
While linear programming (LP) decoding provides more flexibility for
finite-length performance analysis than iterative message-passing (IMP)
decoding, it is computationally more complex to implement in its original form,
due to both the large size of the relaxed LP problem, and the inefficiency of
using general-purpose LP solvers. This paper explores ideas for fast LP
decoding of low-density parity-check (LDPC) codes. We first prove, by modifying
the previously reported Adaptive LP decoding scheme to allow removal of
unnecessary constraints, that LP decoding can be performed by solving a number
of LP problems that contain at most one linear constraint derived from each of
the parity-check constraints. By exploiting this property, we study a sparse
interior-point implementation for solving this sequence of linear programs.
Since the most complex part of each iteration of the interior-point algorithm
is the solution of a (usually ill-conditioned) system of linear equations for
finding the step direction, we propose a preconditioning algorithm to
facilitate iterative solution of such systems. The proposed preconditioning
algorithm is similar to the encoding procedure of LDPC codes, and we
demonstrate its effectiveness via both analytical methods and computer
simulation results.Comment: 44 pages, submitted to IEEE Transactions on Information Theory, Dec.
200
Analysis of error floors of non-binary LDPC codes over MBIOS channel
Communications (ICC), 2011 IEEE International Conference, Kyoto, 5-9 June 201