171 research outputs found
Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel
In this paper, we show that Quasi-Cyclic LDPC codes can efficiently
accommodate the hybrid iterative/ML decoding over the binary erasure channel.
We demonstrate that the quasi-cyclic structure of the parity-check matrix can
be advantageously used in order to significantly reduce the complexity of the
ML decoding. This is achieved by a simple row/column permutation that
transforms a QC matrix into a pseudo-band form. Based on this approach, we
propose a class of QC-LDPC codes with almost ideal error correction performance
under the ML decoding, while the required number of row/symbol operations
scales as , where is the number of source symbols.Comment: 6 pages, ISITA1
Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel
International audienceIn this paper, we show that over the binary erasure channel, Quasi-Cyclic LDPC codes can efficiently accommodate the hybrid iterative/ML decoding. We demonstrate that the quasi- cyclic structure of the parity-check matrix can be advantageously used in order to significantly reduce the complexity of the ML decoding. This is achieved by a simple row/column permutation that transforms a QC matrix into a pseudo-band form. Based on this approach, we propose a class of QC-LDPC codes with almost ideal error correction performance under the ML decoding, while the required number of row/symbol operations scales as k √k, where k is the number of source symbols
Distance Properties of Short LDPC Codes and their Impact on the BP, ML and Near-ML Decoding Performance
Parameters of LDPC codes, such as minimum distance, stopping distance,
stopping redundancy, girth of the Tanner graph, and their influence on the
frame error rate performance of the BP, ML and near-ML decoding over a BEC and
an AWGN channel are studied. Both random and structured LDPC codes are
considered. In particular, the BP decoding is applied to the code parity-check
matrices with an increasing number of redundant rows, and the convergence of
the performance to that of the ML decoding is analyzed. A comparison of the
simulated BP, ML, and near-ML performance with the improved theoretical bounds
on the error probability based on the exact weight spectrum coefficients and
the exact stopping size spectrum coefficients is presented. It is observed that
decoding performance very close to the ML decoding performance can be achieved
with a relatively small number of redundant rows for some codes, for both the
BEC and the AWGN channels
On Universal Properties of Capacity-Approaching LDPC Ensembles
This paper is focused on the derivation of some universal properties of
capacity-approaching low-density parity-check (LDPC) code ensembles whose
transmission takes place over memoryless binary-input output-symmetric (MBIOS)
channels. Properties of the degree distributions, graphical complexity and the
number of fundamental cycles in the bipartite graphs are considered via the
derivation of information-theoretic bounds. These bounds are expressed in terms
of the target block/ bit error probability and the gap (in rate) to capacity.
Most of the bounds are general for any decoding algorithm, and some others are
proved under belief propagation (BP) decoding. Proving these bounds under a
certain decoding algorithm, validates them automatically also under any
sub-optimal decoding algorithm. A proper modification of these bounds makes
them universal for the set of all MBIOS channels which exhibit a given
capacity. Bounds on the degree distributions and graphical complexity apply to
finite-length LDPC codes and to the asymptotic case of an infinite block
length. The bounds are compared with capacity-approaching LDPC code ensembles
under BP decoding, and they are shown to be informative and are easy to
calculate. Finally, some interesting open problems are considered.Comment: Published in the IEEE Trans. on Information Theory, vol. 55, no. 7,
pp. 2956 - 2990, July 200
On generalized LDPC codes for ultra reliable communication
Ultra reliable low latency communication (URLLC) is an important feature in
future mobile communication systems, as they will require high data rates, large
system capacity and massive device connectivity [11]. To meet such stringent
requirements, many error-correction codes (ECC)s are being investigated; turbo
codes, low density parity check (LDPC) codes, polar codes and convolutional codes
[70, 92, 38], among many others. In this work, we present generalized low density
parity check (GLDPC) codes as a promising candidate for URLLC.
Our proposal is based on a novel class of GLDPC code ensembles, for which
new analysis tools are proposed. We analyze the trade-o_ between coding rate and
asymptotic performance of a class of GLDPC codes constructed by including a
certain fraction of generalized constraint (GC) nodes in the graph. To incorporate
both bounded distance (BD) and maximum likelihood (ML) decoding at GC nodes
into our analysis without resorting to multi-edge type of degree distribution (DD)s,
we propose the probabilistic peeling decoding (P-PD) algorithm, which models the
decoding step at every GC node as an instance of a Bernoulli random variable with
a successful decoding probability that depends on both the GC block code as well
as its decoding algorithm. The P-PD asymptotic performance over the BEC can
be efficiently predicted using standard techniques for LDPC codes such as Density
evolution (DE) or the differential equation method. We demonstrate that the
simulated P-PD performance accurately predicts the actual performance of the
GLPDC code under ML decoding at GC nodes. We illustrate our analysis for
GLDPC code ensembles with regular and irregular DDs.
This design methodology is applied to construct practical codes for URLLC.
To this end, we incorporate to our analysis the use of quasi-cyclic (QC) structures,
to mitigate the code error floor and facilitate the code very large scale integration
(VLSI) implementation. Furthermore, for the additive white Gaussian noise
(AWGN) channel, we analyze the complexity and performance of the message
passing decoder with various update rules (including standard full-precision sum product and min-sum algorithms) and quantization schemes. The block error rate
(BLER) performance of the proposed GLDPC codes, combined with a complementary
outer code, is shown to outperform a variety of state-of-the-art codes, for
URLLC, including LDPC codes, polar codes, turbo codes and convolutional codes,
at similar complexity rates.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Juan José Murillo Fuentes.- Secretario: Matilde Pilar Sánchez Fernández.- Vocal: Javier Valls Coquilla
- …