768 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
The q-ary image of some qm-ary cyclic codes: permutation group and soft-decision decoding
Using a particular construction of generator matrices of
the q-ary image of qm-ary cyclic codes, it is proved that some of these codes are invariant under the action of particular permutation groups. The equivalence of such codes with some two-dimensional (2-D) Abelian codes and cyclic codes is deduced from this property. These permutations are also used in the area of the soft-decision decoding of some expanded Reed–Solomon (RS) codes to improve the performance of generalized minimum-distance decoding
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
Self-concatenated code design and its application in power-efficient cooperative communications
In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions
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