Design of majority logic decoder for error detection. Majoritylogicdecodable cyclic arithmeticmodular an. In this brief, the application of a similar technique to a class of euclidean geometry low density parity check egldpc codes that are one step majority logic decodable. Vhdl design and fpga implementation of a fully parallel. Osmld codes but they use an approximation of hartmannrudolph algorithm. These codes have also been extended to address postmanufacturing. Pdf on a class of onestep majoritylogic decodable cyclic codes. On a class of onestep majoritylogic decodable cyclic codes article pdf available in ibm journal of research and development 241. Thus these codes are attractive for errorcontrol systems. H is an n, n k which generate the dual code,denoted by cd. Pdf iterative decoding of multiplestep majority logic. In this paper, we will focus on one specific type of ldpc codes, namely the differenceset cyclic codes dsccs, which is widely used in the. Therefore, they provide an intermediate solution between ols and non osmld codes in terms of decoding delay and number of parity check bits. Some new results on majoritylogic codes for correction of.
A bound is established for the maximum minimum distance which can be decoded using weighted majority logic. Efficient majority logic fault detectorcorrector using. In this paper, a new lowcomplexity gradientdescent based iterative majority logic decoder gdmlgd is proposed for decoding onestep majority logic decodable osmld codes. Weaknesses of margulis and ramanujanmargulis lowdensity. A locally decodable code ldc is an errorcorrecting code that allows a single bit of the original message to be decoded with high probability by only examining or querying a small number of bits of a possibly corrupted codeword. On a class of majoritylogic decodable cyclic codes ieee xplore. A new class of majoritylogic decodable codes derived. Capability to correct large number of errors majority logic decodable codes is suitable for memory applications. The performance of iterative decoding algorithms for multistep majority logic decodable msmld codes of intermediate length is investigated.
Majority logic decodable codes are suitable for memory applications due to their capability to correct a large number of errors. However, the code length and code dimension of finite geometry codes are rather. Simulation and synthesis of majority logic decoderdetector for egldpc codes j. Majority logic decoder is mainly based on number of parity check equations which are orthogonal to each other so that for each iteration, each codeword bit participates in only one parity check equation, except the very first bit which contributes to all equations. The proposed tbo codes have been implemented for some block sizes and compared to both ols and bch codes to illustrate the trade off in delay and memory overhead. Codes in this class are twostep majoritylogic decodable and they are also constructed based on.
The r esults obtained sh ow that the method is also eff ect iv e f or eg ld pc codes. The majority logic secret writing is used here, since it will correct associate degree outsize type of errors. On a class of onestep majoritylogic decodable cyclic codes. Analytical performance of onestep majority logic decoding of. The polarity designs, introduced in 9, are combinatorial 2designs having the same parameters as a projective geometry design pgs2s,q formed by the s subspaces of pg2s,q, s. To avoid the degrading effect of these 4cycles in performance, twostep iterative decoding algorithms are devised. Anouar yatribi phd student error correcting codes and. Construction and iterative threshold decoding for low rates quasicyclic one step majority logic decodable codes abstract. Pdf majoritylogic decoding is attractive for three reasons.
If there are no errors, the decoding can be stopped without completing the rest of the iterations. These decoding schemes are parallel to the classical majority logic decoding schemes and thus can be easi. The cyclic shift register is primarily stored with. Efficient majority logic fault detection with differenceset codes for. Class of majoritylogicdecodable codes with a minimum. The idea behind the method the method is that, the first iterations of the majority logic decoding is to detect if the word being decoded contains errors. This paper investigates the construction and iterative threshold decoding of low rate quasicyclic one step majority logic codes based on combinatorial designs. For these codes to be applicable in wireless environment, their performance on fading channels must be examined. The memory access time as well as area of utilization and the decoding time is reducing using majority logic decoder. The proposed faultdetection method uses differenceset cyclic codes instead of several other block codes such as bch code, hamming code, rs. A new iterative threshold decoding algorithm for one step. Firstly, they offer a partial solution to a classical coding theory problem, that of decoder complexity. In this paper, we investigate the performance achieved by the bp algorithm for decoding onestep majority logic decodable osmld codes.
In the proposed algorithm, a hardinhardout decoder is combined with a harddecision signal detector in an iterative manner. Iterative decoding of multiplestep majority logic decodable. Codes of this class can be decoded in a stepbystep manner, usingmajority logic. In this paper we study a class of onestep majoritylogic decodable cyclic codes. Error identification to translate majority logic design by. Pdf a new iterative threshold decoding algorithm for one. In what follows we often refer to locally decodable codes of the rst generation as reedmuller rm. One step majority logic codes consider an n, k linear code c with paritycheck matrix h. A particularly interesting question is the possibility of decoding arithmetic codes by majority logic.
Majority logic decodable codes derived from finite inversive. Liniterative decoding of onestep majority logic decodable codes based on belief propagation ieee transactions on communications, 48 2000, pp. Analysis of one step majority logic decoders constructed from. Information and control 18, 319325 1971 majority logic decodable codes derived from finite inversive planes philippe delsarte mble research laboratory, brussels, belgium a new class is defined of geometric codes that are majority logic decodable up to their minimum distance. Channel coding theory one step majority logic decoding consider c as an n, k cyclic code with parity check matrix h. One step majority decoder free download as powerpoint presentation. Low power error correcting codes using majority logic decoding. Among the majoritylogic decodable codes, the onestep decodable codes can be most easily implemented. A sub group of the lowdensity parity check ldpc codes, which be longs to the family of the ml decodable codes, has been re searched in 911. Performance improved architecture of majority logic decoder. Two iterative decod ing algorithms are devised for this class of cyclic codes and they provide signi. This is sometimes referred to as a cods unbounded performance. One step majority logic decoding can be implemented serially with.
However the computation time of the proposed algorithm is very low. Its performance is suboptimum since each of its decoding decision is based only on one output constraint length of received bits. Tech scholar vlsi system design, aits rajampet, kadapa v. Iterative threshold decoding of majority logic decodable.
Ieee transactions on communications 2007 55 6 1099 1102. Based on constant weight codes, a new construction for classes of majority logic decodable codes with even minimum distances and their implementation are presented. Hong decodification algorithm is also applicable to these codes, but achieves quite higher. A subgroup of the lowdensity parity check ldpc codes, which belongs to the family of the ml decodable codes, has been researched in. Efficient fault detection majority logic correction with. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Onestep majoritylogic decoding with subspace designs deepai. Iterative decoding of onestep majority logic deductible codes based on belief propagation abstract. The decoder is easily realizable in hardware and requires that the dual code has to contain the blocks of so called geometric designs as codewords. In a memory, this would increase the access time which is an important system parameter. Simple majority logic code mlc consider a linear cyclic code c n, k with h parity check matrix. Most majority logic decodable codes found so far are cyclic codes, an algebraic approach can also be taken to the decoding of convolutional codes, the first majority logic decoding algorithms for. This property could be useful, say, in a context where information is being transmitted over a noisy channel, and only a small subset of the data is required at a. Parity check egldpc codes are one step majority logic decodable.
First, we briefly describe the codes in a simple manner. Some previously known codes fall in this class, and thus admit simpler. These architectures are hard decision decoder architecture hard in hard out hiho, the siho threshold decoding soft in hard out and the siso threshold decoding soft in soft out. Rudoph 1967 introduced onestep majority logic decoding for linear codes derived from combinatorial designs. We investigate the performance of iterative decoding algorithms for multistep majority logic decodable msmld codes of intermediate length. Onestep majority logic decodable code listed as osmld.
Introduction low density parity check codes 3 are block codes with paritycheck matrices contains a very small number of nonzero entries. We introduce a new bitflipping algorithm that is able to decode these codes nearly as well as a maximumlikelihood decoder on. Serial onestep majority logic decoder for the 15,7 eglpdc code. One step majority logic decoding can be implemented serially with very simple circuitry, but requires long decoding times. Construction and iterative threshold decoding for low. Orthogonal latin square ols codes 6 are a class of majority logic decodable codes which offer very low latency decoding based on a majority vote. In general, for a code with block length n majority logic decoding requires n iterations so that as the code size grows. Iterative decoding of multiplestep majority logic decodable codes article pdf available in ieee transactions on communications 556. Iterative decoding of multistep majority logic decodable codes. However, they require a large decoding time that impacts memory performance. They are simple to implement and have modular encoder and decoder.
However, they require a large decoding time that impacts memory applications. Majority logic decoding of convolutional codes, proposed by massey 308, is a suboptimum but simple decoding scheme that allows a highspeed implementation. Further work on this topic was then presented in this paper. Decoding for arithmetic codes by matching the orbits or permuting the residues associated with the codes is straightfor. Low power error correcting codes using majority logic. We also demonstrate how a long r,talrc can be constructed from a short onestep majority logic decodable code using multilevel tensor product structure. The second advantage of majority logic codes is with regard to their performance when more random errors occur than the code can guarantee to decode. In euclidean geometry lowdensity paritycheck egldpc codes there. They are devised based on the orthogonal concepts of twostep majority logic decoding tsmlgd8. Generalized minimum distance decoding on majority logic. In a binary alphabet made of, if a, repetition code is used, then each input bit is mapped to the code word as a string of replicated input bits. We give a formulation of the decoding problem of binary osmld codes, as a maximization problem of a derivable objective function.
Simulation and synthesis of majority logic decoderdetector. Majority logic decodable codes derived from finite. Ex tens iv e simulation r esults are giv en to accurately estimate the pr obability of. One step majority decoder code error detection and correction. Codes with a minimum distance of four are better than shivas codes, some codes are optimal or with the same parameters as the best known codes.
New construction for classes of majority logic decodable. General terms information theory and coding, signal processing. A new construction of majority logic decodable quasicyclic codes is presented. The ideas behind the rst generation of locally decodable codes go back to classical codes 73, 95, named after their discoverers, reed and muller. Design of majority logic decoder for error detection and. For any code vin cand w in cd, the inner product of vand wis zero. Previously, the belief propagation bp algorithm has received a lot of attention in the coding community, mostly due to its nearoptimum decoding for lowdensity parity check ldpc codes and its connection to turbo decoding. Iterative decoding of onestep majority logic deductible. Er r or detection in majority logic decoding of euclidean.
Efficient fault detection majority logic correction with in. Majority logic ml decodable qc codes are found with the aid of cyclic di. The performance of iterative decoding algorithm for onestep majority logic decodable osmld codes is investigated. The results obtained show that the method is also effective for egldpc codes. The main advantages of random errorcorrecting majority logic codes and majority logic decoding in general are well known and twofold. Majority logic decoding of euclidean geometry low density. They have been successfully used in caches to enable reliable operation 7. Iterative threshold decoding of product and parallel concatenated block codes based on one step majority logic decodable osmld codes has proven to perform remarkably well on awgn channels.
New construction of majority logic decodable quasicyclic codes. Simulation and synthesis of majority logic decoder. Onestep majority logic decodable code how is onestep majority logic decodable code abbreviated. The decoding complexity of these codes has been further reduced by a recently developed scheme chen, 1972. Gradientdescent decoding of onestep majoritylogic decodable codes. Generalized minimum distance decoding schemes are found for majority logic decodable codes. Albeit the majority secret writing consumes longer, it will be overcome by the projected. The tanner graphs of codes in this class have many 4cycles. Fpga implementation of hiho and siho decoders for dsc codes.
Iterative threshold decoding of product codes constructed. As an example, an infinite family of quasicyclic codes with a minimum distance of four is constructed, and comparisons are made to show that they are better than selforthogonal quasicyclic codes and shiva codes. In this study, the authors present a lowcomplexity iterative joint detectiondecoding algorithm for majoritylogic decodable nonbinary lowdensity paritycheck ldpc coded modulation systems. Efficient majority logic fault detection in memory. The circuit implementing a serial onestep majority logic decoder 6,12 for 15, 7, 5 egldpc code is shown in fig. In this paper, we will focus on one specific type of ldpc codes, n amely the differenceset cyclic codes dsccs, which is wid ely used in the japanese teletext. Head of dept, dept of ece, jbiet hyderabad abstract in this paper, a technique was proposed to protect memory. To avoid a high decoding complexity, the use of one step majority logic decodable codes was first proposed in for memory applications. A new class of majoritylogic decodable codes derived from. If q 2, any polarity 2design is extendable to a 3design having the same parameters and 2rank as an. The viterbigmlgd algorithm works in an iterative manner by exchanging harddecisions between the viterbi detector and the generalized majority logic decoder gmlgd. In this work, we propose a design and fpga field programmab le gate a rrays imp lementation of three parallel architectures for majority logic decoder of low co mplexity for high data rate applications. If q p is a prime, a polarity design has also the same p rank as pgs2s,p. In this brief, we study the application of a similar technique to a class of euclidean geometry low density parity check egldpc codes that are one step majority logic decodable.
A subgroup of the lowdensity parity check ldpc codes, which belongs to the family of the ml decodable codes, has been researched in 911. These codes are constructed with two type of difference family. Class of one step majority logic decodable codes let c be a n, k cyclic code generated by g x, where n 2m 1. Gradientdescent decoding of onestep majoritylogic decodable. Reduction of decoding time in majority logic decoder for. Muller discovered the codes 74 in the 1950s, and reed proposed the majority logic decoding 83. Among the majority logic decodable codes, the onestep decodable codes can be most easily implemented.
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