New Soft Set Based Class of Linear Algebraic Codes

Algebraic Coding Theory and Applications, 1979

2006

Title of dissertation: PERFORMANCE ANALYSIS OF ALGEBRAIC SOFT-DECISION DECODING OF REED-SOLOMON CODES Andrew Duggan, Masters of Science, 2006 Thesis directed by: Professor Alexander Barg Department of Electrical and Computer Engineering We investigate the decoding region for Algebraic Soft-Decision Decoding (ASD) of Reed-Solomon codes in a discrete, memoryless, additive-noise channel. An expression is derived for the error radius within which the soft-decision decoder produces a list that contains the transmitted codeword. The error radius for ASD is shown to be larger than that of Guruswami-Sudan hard-decision decoding for a subset of low-rate codes. We then present an upper bound for ASD’s probability of error, where an error is defined as the event that the decoder selects an erroneous codeword from its list. This new definition gives a more accurate bound on the probability of error of ASD. We also derive an estimate of the error-correction radius under multivariate interpolatio...

IEEE Journal on Selected Areas in Communications, 2006

In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon (RS) 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 RS codes.

Journal of Symbolic …, 2010

2011

Algebraic Codes For Error Correction In Digital Communication Systems

2008

International Journal of Intelligent Engineering and Systems, 2019

Digital transmission systems carry information from the source to the receiver using a physical medium such as cable, fiber optic or even propagation on a radio channel which isn't entirely reliable and causes the change of data originally emitted. Today the use of error correcting codes for protection and correction becomes an integral part in the design of communication systems and computers. In this work, we present a new interesting way to accelerate the decoding process of linear codes. The proposed method called Soft Decision Decoder by Hash Techniques (SDHT) is based on syndrome-decoding algorithm and hash techniques. The use of this latest allows reducing considerably the search time of all possible error patterns of weights less than a fixed threshold. SDHT is applicable on many linear codes and exploit the polynomial form to reduce again the run time decoding for cyclic codes. SDHT is successfully applied to decode some Bose Ray-Chaudhuri and Hocquenghem (BCH), Quadratic Residue (QR) and Extended Quadratic Residue (EQR) codes. The simulation results show that the proposed SDHT yield to good error correcting performances with reduced complexity. The comparison between SDHT and many competitors shows that it gives better performances in terms of correction rate. The experimental study of the decoding steps for the BCH(63,45,7) code shows that the time search of the most likely error pattern is reduced at about 26214153% comparing to an exhaustive search of all possible error patterns of weights less than or equal to 4. This study proves the huge success of the proposed SDHT decoder.

IEEE Communications Letters, 2005

In this paper, we describe two novel modifications of an algorithm for deriving sparse parity-check matrix representations of classical binary and non-binary algebraic codes. The proposed sparse representations are obtained by introducing a small number of auxiliary variables and check-equations that lead to Tanner graphs without four-cycles. When used with iterative decoding, the developed code representations show significant gain in performance when compared to other known description techniques.

Computer Modeling and Intelligent Systems

Methods of soft decoding of cascade code constructions based on the schemes-products of linear block codes (Turbo Product Codes) are considered. An approach is being developed based on the iterative exchange of soft solutions between block codes constituting a cascade design. It is shown that a sequential execution of procedures for the formation of ordered subsets of test equations and the logarithms estimation of a likelihood ratio allows decoding of turbo-productive codes according to the criterion of minimizing the erroneous reception of code symbols.