3,218 research outputs found
Analysis and Design of Binary Message-Passing Decoders
Binary message-passing decoders for low-density parity-check (LDPC) codes are
studied by using extrinsic information transfer (EXIT) charts. The channel
delivers hard or soft decisions and the variable node decoder performs all
computations in the L-value domain. A hard decision channel results in the
well-know Gallager B algorithm, and increasing the output alphabet from hard
decisions to two bits yields a gain of more than 1.0 dB in the required signal
to noise ratio when using optimized codes. The code optimization requires
adapting the mixing property of EXIT functions to the case of binary
message-passing decoders. Finally, it is shown that errors on cycles consisting
only of degree two and three variable nodes cannot be corrected and a necessary
and sufficient condition for the existence of a cycle-free subgraph is derived.Comment: 8 pages, 6 figures, submitted to the IEEE Transactions on
Communication
Multilevel Decoders Surpassing Belief Propagation on the Binary Symmetric Channel
In this paper, we propose a new class of quantized message-passing decoders
for LDPC codes over the BSC. The messages take values (or levels) from a finite
set. The update rules do not mimic belief propagation but instead are derived
using the knowledge of trapping sets. We show that the update rules can be
derived to correct certain error patterns that are uncorrectable by algorithms
such as BP and min-sum. In some cases even with a small message set, these
decoders can guarantee correction of a higher number of errors than BP and
min-sum. We provide particularly good 3-bit decoders for 3-left-regular LDPC
codes. They significantly outperform the BP and min-sum decoders, but more
importantly, they achieve this at only a fraction of the complexity of the BP
and min-sum decoders.Comment: 5 pages, in Proc. of 2010 IEEE International Symposium on Information
Theory (ISIT
Binary Message Passing Decoding of Product-like Codes
We propose a novel binary message passing decoding algorithm for product-like
codes based on bounded distance decoding (BDD) of the component codes. The
algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the
channel reliabilities and is therefore soft in nature. However, the messages
exchanged by the component decoders are binary (hard) messages, which
significantly reduces the decoder data flow. The exchanged binary messages are
obtained by combining the channel reliability with the BDD decoder output
reliabilities, properly conveyed by a scaling factor applied to the BDD
decisions. We perform a density evolution analysis for generalized low-density
parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles,
from which the scaling factors of the iBDD-SR for product and staircase codes,
respectively, can be obtained. For the white additive Gaussian noise channel,
we show performance gains up to dB and dB for product and
staircase codes compared to conventional iterative BDD (iBDD) with the same
decoder data flow. Furthermore, we show that iBDD-SR approaches the performance
of ideal iBDD that prevents miscorrections.Comment: Accepted for publication in the IEEE Transactions on Communication
A Novel Stochastic Decoding of LDPC Codes with Quantitative Guarantees
Low-density parity-check codes, a class of capacity-approaching linear codes,
are particularly recognized for their efficient decoding scheme. The decoding
scheme, known as the sum-product, is an iterative algorithm consisting of
passing messages between variable and check nodes of the factor graph. The
sum-product algorithm is fully parallelizable, owing to the fact that all
messages can be update concurrently. However, since it requires extensive
number of highly interconnected wires, the fully-parallel implementation of the
sum-product on chips is exceedingly challenging. Stochastic decoding
algorithms, which exchange binary messages, are of great interest for
mitigating this challenge and have been the focus of extensive research over
the past decade. They significantly reduce the required wiring and
computational complexity of the message-passing algorithm. Even though
stochastic decoders have been shown extremely effective in practice, the
theoretical aspect and understanding of such algorithms remains limited at
large. Our main objective in this paper is to address this issue. We first
propose a novel algorithm referred to as the Markov based stochastic decoding.
Then, we provide concrete quantitative guarantees on its performance for
tree-structured as well as general factor graphs. More specifically, we provide
upper-bounds on the first and second moments of the error, illustrating that
the proposed algorithm is an asymptotically consistent estimate of the
sum-product algorithm. We also validate our theoretical predictions with
experimental results, showing we achieve comparable performance to other
practical stochastic decoders.Comment: This paper has been submitted to IEEE Transactions on Information
Theory on May 24th 201
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