1,514 research outputs found
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
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 0.29 dB and 0.31 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
On Low-Complexity Decoding of Product Codes for High-Throughput Fiber-Optic Systems
We study low-complexity iterative decoding algorithms for product codes. We revisit two algorithms recently proposed by the authors based on bounded distance decoding (BDD) of the component codes that improve the performance of conventional iterative BDD (iBDD). We then propose a novel decoding algorithm that is based on generalized minimum distance decoding of the component codes. The proposed algorithm closes over 50% of the performance gap between iBDD and turbo product decoding (TPD) based on the Chase-Pyndiah algorithm at a bit error rate of 10^-5. Moreover, the algorithm only leads to a limited increase in complexity with respect to iBDD and has significantly lower complexity than TPD. The studied algorithms are particularly interesting for high-throughput fiberoptic communications
Novel High-Throughput Decoding Algorithms for Product and Staircase Codes based on Error-and-Erasure Decoding
Product codes (PCs) and staircase codes (SCCs) are conventionally decoded
based on bounded distance decoding (BDD) of the component codes and iterating
between row and column decoders. The performance of iterative BDD (iBDD) can be
improved using soft-aided (hybrid) algorithms. Among these, iBDD with combined
reliability (iBDD-CR) has been recently proposed for PCs, yielding sizeable
performance gains at the expense of a minor increase in complexity compared to
iBDD. In this paper, we first extend iBDD-CR to SCCs. We then propose two novel
decoding algorithms for PCs and SCCs which improve upon iBDD-CR. The new
algorithms use an extra decoding attempt based on error and erasure decoding of
the component codes. The proposed algorithms require only the exchange of hard
messages between component decoders, making them an attractive solution for
ultra high-throughput fiber-optic systems. Simulation results show that our
algorithms based on two decoding attempts achieve gains of up to dB for
both PCs and SCCs. This corresponds to a optical reach enhancement over
iBDD with bit-interleaved coded modulation using quadrature amplitude
modulation
Improved Soft-aided Decoding of Product Codes with Dynamic Reliability Scores
Products codes (PCs) are conventionally decoded with efficient iterative
bounded-distance decoding (iBDD) based on hard-decision channel outputs which
entails a performance loss compared to a soft-decision decoder. Recently,
several hybrid algorithms have been proposed aimed to improve the performance
of iBDD decoders via the aid of a certain amount of soft information while
keeping the decoding complexity similarly low as in iBDD. We propose a novel
hybrid low-complexity decoder for PCs based on error-and-erasure (EaE) decoding
and dynamic reliability scores (DRSs). This decoder is based on a novel EaE
component code decoder, which is able to decode beyond the designed distance of
the component code but suffers from an increased miscorrection probability. The
DRSs, reflecting the reliability of a codeword bit, are used to detect and
avoid miscorrections. Simulation results show that this policy can reduce the
miscorrection rate significantly and improves the decoding performance. The
decoder requires only ternary message passing and a slight increase of
computational complexity compared to iBDD, which makes it suitable for
high-speed communication systems. Coding gains of up to 1.2 dB compared to the
conventional iBDD decoder are observed.Comment: Submitted to IEE
Decomposition Methods for Large Scale LP Decoding
When binary linear error-correcting codes are used over symmetric channels, a
relaxed version of the maximum likelihood decoding problem can be stated as a
linear program (LP). This LP decoder can be used to decode error-correcting
codes at bit-error-rates comparable to state-of-the-art belief propagation (BP)
decoders, but with significantly stronger theoretical guarantees. However, LP
decoding when implemented with standard LP solvers does not easily scale to the
block lengths of modern error correcting codes. In this paper we draw on
decomposition methods from optimization theory, specifically the Alternating
Directions Method of Multipliers (ADMM), to develop efficient distributed
algorithms for LP decoding.
The key enabling technical result is a "two-slice" characterization of the
geometry of the parity polytope, which is the convex hull of all codewords of a
single parity check code. This new characterization simplifies the
representation of points in the polytope. Using this simplification, we develop
an efficient algorithm for Euclidean norm projection onto the parity polytope.
This projection is required by ADMM and allows us to use LP decoding, with all
its theoretical guarantees, to decode large-scale error correcting codes
efficiently.
We present numerical results for LDPC codes of lengths more than 1000. The
waterfall region of LP decoding is seen to initiate at a slightly higher
signal-to-noise ratio than for sum-product BP, however an error floor is not
observed for LP decoding, which is not the case for BP. Our implementation of
LP decoding using ADMM executes as fast as our baseline sum-product BP decoder,
is fully parallelizable, and can be seen to implement a type of message-passing
with a particularly simple schedule.Comment: 35 pages, 11 figures. An early version of this work appeared at the
49th Annual Allerton Conference, September 2011. This version to appear in
IEEE Transactions on Information Theor
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