13,454 research outputs found
Symbol level decoding of Reed-Solomon codes with improved reliability information over fading channels
A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy in the School of Electrical and Information Engineering, 2016Reliable and e cient data transmission have been the subject of current research,
most especially in realistic channels such as the Rayleigh fading channels. The focus
of every new technique is to improve the transmission reliability and to increase
the transmission capacity of the communication links for more information to be
transmitted. Modulation schemes such as M-ary Quadrature Amplitude Modulation
(M-QAM) and Orthogonal Frequency Division Multiplexing (OFDM) were
developed to increase the transmission capacity of communication links without
additional bandwidth expansion, and to reduce the design complexity of communication
systems.
On the contrary, due to the varying nature of communication channels, the message
transmission reliability is subjected to a couple of factors. These factors include the
channel estimation techniques and Forward Error Correction schemes (FEC) used
in improving the message reliability. Innumerable channel estimation techniques
have been proposed independently, and in combination with di erent FEC schemes
in order to improve the message reliability. The emphasis have been to improve
the channel estimation performance, bandwidth and power consumption, and the
implementation time complexity of the estimation techniques. Of particular interest, FEC schemes such as Reed-Solomon (RS) codes, Turbo
codes, Low Density Parity Check (LDPC) codes, Hamming codes, and Permutation
codes, are proposed to improve the message transmission reliability of communication
links. Turbo and LDPC codes have been used extensively to combat
the varying nature of communication channels, most especially in joint iterative
channel estimation and decoding receiver structures. In this thesis, attention is
focused on using RS codes to improve the message reliability of a communication
link because RS codes have good capability of correcting random and burst errors,
and are useful in di erent wireless applications.
This study concentrates on symbol level soft decision decoding of RS codes. In
this regards, a novel symbol level iterative soft decision decoder for RS codes
based on parity-check equations is developed. This Parity-check matrix Transformation
Algorithm (PTA) is based on the soft reliability information derived from
the channel output in order to perform syndrome checks in an iterative process.
Performance analysis verify that this developed PTA outperforms the conventional
RS hard decision decoding algorithms and the symbol level Koetter and Vardy
(KV ) RS soft decision decoding algorithm.
In addition, this thesis develops an improved Distance Metric (DM) method of
deriving reliability information over Rayleigh fading channels for combined demodulation
with symbol level RS soft decision decoding algorithms. The newly
proposed DM method incorporates the channel state information in deriving the
soft reliability information over Rayleigh fading channels. Analysis verify that this
developed metric enhances the performance of symbol level RS soft decision decoders
in comparison with the conventional method. Although, in this thesis, the
performance of the developed DM method of deriving soft reliability information
over Rayleigh fading channels is only veri ed for symbol level RS soft decision
decoders, it is applicable to any symbol level soft decision decoding FEC scheme.
Besides, the performance of the all FEC decoding schemes plummet as a result
of the Rayleigh fading channels. This engender the development of joint iterative channel estimation and decoding receiver structures in order to improve the message
reliability, most especially with Turbo and LDPC codes as the FEC schemes.
As such, this thesis develops the rst joint iterative channel estimation and Reed-
Solomon decoding receiver structure. Essentially, the joint iterative channel estimation
and RS decoding receiver is developed based on the existing symbol level
soft decision KV algorithm. Consequently, the joint iterative channel estimation
and RS decoding receiver is extended to the developed RS parity-check matrix
transformation algorithm. The PTA provides design ease and
exibility, and lesser
computational time complexity in an iterative receiver structure in comparison
with the KV algorithm.
Generally, the ndings of this thesis are relevant in improving the message transmission
reliability of a communication link with RS codes. For instance, it is
pertinent to numerous data transmission technologies such as Digital Audio Broadcasting
(DAB), Digital Video Broadcasting (DVB), Digital Subscriber Line (DSL),
WiMAX, and long distance satellite communications. Equally, the developed, less
computationally intensive, and performance e cient symbol level decoding algorithm
for RS codes can be use in consumer technologies like compact disc and
digital versatile disc.GS201
Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix
An iterative algorithm is presented for soft-input-soft-output (SISO)
decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the
sum product algorithm (SPA) in conjunction with a binary parity check matrix of
the RS code. The novelty is in reducing a submatrix of the binary parity check
matrix that corresponds to less reliable bits to a sparse nature before the SPA
is applied at each iteration. The proposed algorithm can be geometrically
interpreted as a two-stage gradient descent with an adaptive potential
function. This adaptive procedure is crucial to the convergence behavior of the
gradient descent algorithm and, therefore, significantly improves the
performance. Simulation results show that the proposed decoding algorithm and
its variations provide significant gain over hard decision decoding (HDD) and
compare favorably with other popular soft decision decoding methods.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on
Information Theor
Turbo Decoding and Detection for Wireless Applications
A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannon’s visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannon’s capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted
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 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
Iterative Decoding and Turbo Equalization: The Z-Crease Phenomenon
Iterative probabilistic inference, popularly dubbed the soft-iterative
paradigm, has found great use in a wide range of communication applications,
including turbo decoding and turbo equalization. The classic approach of
analyzing the iterative approach inevitably use the statistical and
information-theoretical tools that bear ensemble-average flavors. This paper
consider the per-block error rate performance, and analyzes it using nonlinear
dynamical theory. By modeling the iterative processor as a nonlinear dynamical
system, we report a universal "Z-crease phenomenon:" the zig-zag or up-and-down
fluctuation -- rather than the monotonic decrease -- of the per-block errors,
as the number of iteration increases. Using the turbo decoder as an example, we
also report several interesting motion phenomenons which were not previously
reported, and which appear to correspond well with the notion of "pseudo
codewords" and "stopping/trapping sets." We further propose a heuristic
stopping criterion to control Z-crease and identify the best iteration. Our
stopping criterion is most useful for controlling the worst-case per-block
errors, and helps to significantly reduce the average-iteration numbers.Comment: 6 page
Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes
In this paper, we present an iterative soft-decision decoding algorithm for
Reed-Solomon codes offering both complexity and performance advantages over
previously known decoding algorithms. Our algorithm is a list decoding
algorithm which combines two powerful soft decision decoding techniques which
were previously regarded in the literature as competitive, namely, the
Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation
based on adaptive parity check matrices, recently proposed by Jiang and
Narayanan. Building on the Jiang-Narayanan algorithm, we present a
belief-propagation based algorithm with a significant reduction in
computational complexity. We introduce the concept of using a
belief-propagation based decoder to enhance the soft-input information prior to
decoding with an algebraic soft-decision decoder. Our algorithm can also be
viewed as an interpolation multiplicity assignment scheme for algebraic
soft-decision decoding of Reed-Solomon codes.Comment: Submitted to IEEE for publication in Jan 200
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