830 research outputs found
Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding
We propose a binary message passing decoding algorithm for product codes
based on generalized minimum distance decoding (GMDD) of the component codes,
where the last stage of the GMDD makes a decision based on the Hamming distance
metric. The proposed algorithm closes half of the gap between conventional
iterative bounded distance decoding (iBDD) and turbo product decoding based on
the Chase--Pyndiah algorithm, at the expense of some increase in complexity.
Furthermore, the proposed algorithm entails only a limited increase in data
flow compared to iBDD.Comment: Invited paper to the 53rd Annual Conference on Information Sciences
and Systems (CISS), Baltimore, MD, March 2019. arXiv admin note: text overlap
with arXiv:1806.1090
Approaching Capacity at High-Rates with Iterative Hard-Decision Decoding
A variety of low-density parity-check (LDPC) ensembles have now been observed
to approach capacity with message-passing decoding. However, all of them use
soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of
their component codes. In this paper, we show that one can approach capacity at
high rates using iterative hard-decision decoding (HDD) of generalized product
codes. Specifically, a class of spatially-coupled GLDPC codes with BCH
component codes is considered, and it is observed that, in the high-rate
regime, they can approach capacity under the proposed iterative HDD. These
codes can be seen as generalized product codes and are closely related to
braided block codes. An iterative HDD algorithm is proposed that enables one to
analyze the performance of these codes via density evolution (DE).Comment: 22 pages, this version accepted to the IEEE Transactions on
Information Theor
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
On the Complexity of Exact Maximum-Likelihood Decoding for Asymptotically Good Low Density Parity Check Codes: A New Perspective
The problem of exact maximum-likelihood (ML) decoding of general linear codes is well-known to be NP-hard. In this paper, we show that exact ML decoding of a class of asymptotically good low density parity check codes â expander codes â over binary symmetric channels (BSCs) is possible with an average-case polynomial complexity. This offers a new way of looking at the complexity issue of exact ML decoding for communication systems where the randomness in channel plays a fundamental central role. More precisely, for any bit-flipping probability p in a nontrivial range, there exists a rate region of non-zero support and a family of asymptotically good codes which achieve error probability exponentially decaying in coding length n while admitting exact ML decoding in average-case polynomial time. As p approaches zero, this rate region approaches the Shannon channel capacity region. Similar results can be extended to AWGN channels, suggesting it may be feasible to eliminate the error floor phenomenon associated with belief-propagation decoding of LDPC codes in the high SNR regime. The derivations are based on a hierarchy of ML certificate decoding algorithms adaptive to the channel realization. In this process, we propose an efficient O(n^2) new ML certificate algorithm based on the max-flow algorithm. Moreover, exact ML decoding of the considered class of codes constructed from LDPC codes with regular left degree, of which the considered expander codes are a special case, remains NP-hard; thus giving an interesting contrast between the worst-case and average-case complexities
Short Block-length Codes for Ultra-Reliable Low-Latency Communications
This paper reviews the state of the art channel coding techniques for
ultra-reliable low latency communication (URLLC). The stringent requirements of
URLLC services, such as ultra-high reliability and low latency, have made it
the most challenging feature of the fifth generation (5G) mobile systems. The
problem is even more challenging for the services beyond the 5G promise, such
as tele-surgery and factory automation, which require latencies less than 1ms
and failure rate as low as . The very low latency requirements of
URLLC do not allow traditional approaches such as re-transmission to be used to
increase the reliability. On the other hand, to guarantee the delay
requirements, the block length needs to be small, so conventional channel
codes, originally designed and optimised for moderate-to-long block-lengths,
show notable deficiencies for short blocks. This paper provides an overview on
channel coding techniques for short block lengths and compares them in terms of
performance and complexity. Several important research directions are
identified and discussed in more detail with several possible solutions.Comment: Accepted for publication in IEEE Communications Magazin
LDPC Codes Which Can Correct Three Errors Under Iterative Decoding
In this paper, we provide necessary and sufficient conditions for a
column-weight-three LDPC code to correct three errors when decoded using
Gallager A algorithm. We then provide a construction technique which results in
a code satisfying the above conditions. We also provide numerical assessment of
code performance via simulation results.Comment: 5 pages, 3 figures, submitted to IEEE Information Theory Workshop
(ITW), 200
Energy-Efficient Soft-Assisted Product Decoders
We implement a 1-Tb/s 0.63-pJ/bit soft-assisted product decoder in a 28-nm
technology. The decoder uses one bit of soft information to improve its net
coding gain by 0.2 dB, reaching 10.3-10.4 dB, which is similar to that of more
complex hard-decision staircase decoders
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