To correct a large no of correction majority logic decodable codes are suitable for memory applications. If the dropped symbols are not check symbols then this cyclic code is also a shortened code. However, a similar method is also possible for the second class of algebraic decoders. Low density parity check codes based on finite geometries. Distributed decoding of cyclic block codes using a. In a recent paper, a method was proposed to accelerate the majority logic decoding of difference set low density parity check codes. Fpga implementation of cyclic code encoder and decoder. Efficient majority logic fault detection in memory. Parity check codes, cyclic codes, hamming codes, golay codes, reedsolomon codes, bch codes, reedmuller codes, low density parity check codes. Ldpc codes are used to correct those problems in a digital circuit.
This decoding algorithm has recently found numerous appli. Design and verification of efficient majority logic fault. 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. However, they require a large decoding time that impacts memory applications. Bit error probability for maximum likelihood decoding of. Efficient fault detection majority logic correction with. The encoding and decoding schemes of cyclic codes and bch codes are. A method was recently proposed in to accelerate a serial implementation of majority logic decoding of dsldpc codes.
Index termsmajoritylogic decoding, reedmuller codes. In this paper a new adaptation of the iterative threshold decoding algorithm is considered, for decoding quasi cyclic one step majority logic codes qcosmld codes of high rates. H is an n, n k which generate the dual code,denoted by cd. Simulation and synthesis of majority logic decoderdetector for egldpc codes j. In other words a cyclic shift in a code word in c results in another code word in c. Pdf majoritylogic decoding is attractive for three reasons. This is a collection of solved exercises and problems of cyclic codes for. Design of majority logic decoder for error detection. I have not gone through and given citations or references for all of the results given here, but the presentation relies heavily on two sources, van. For any code vin cand w in cd, the inner product of vand wis zero. Existing method the majority logic decoding is effective scheme for decoding certain classes of block codes, especially for decoding certain classes of cyclic codes. Codes in this class are twostep majoritylogic decodable and they are also constructed based on. Design and verification of efficient majority logic fault detection and correction for memory applications.
This is equivalent to onestep majority logic decoding when each of the constituent codes is a simple parity check. A subgroup of the lowdensity parity check ldpc codes, which belongs to the family of the ml decodable codes, namely the differenceset cyclic codes dsccs, which is widely used in the japanese teletext system or fm multiplex broadcasting systems. Exhaustive simulation test output shows that the proposed system is able to detect any pattern of up to five bitflips in the first three cycles of the decoding, which improves the performance of the design with respect to the traditional majority logic decoding approach. Majority logic decodable codes derived from finite. For these codes to be applicable in wireless environment, their performance on fading channels must be examined. Again, this method is transparent with respect to algebraic decoding, so that the conventional algebraic decoder corresponding to the code considered can still be used. High performance error detection with different set cyclic.
Pallipatti, dharmapuri, tamilnadu, india1 abstract. A new iterative threshold decoding algorithm for one step. When c is a cyclic code, each ei can be decoded simply by cyclically permuting the received word r into the buffer store. Two iterative decod ing algorithms are devised for this class of cyclic codes and they provide signi.
Construct a generator matrix for this code and decode the received codeword. In this technique majority logic decoder is used as fault detector due to usage of quasi cyclic. One step majority decoder code error detection and. Finite field arithmetic is introduced and basic decoding algorithms, such as. Iterative decoding of multistep majority logic decodable codes. However, instead of using an extension of chase algorithm on bch codes, we will apply an extension of massey algorithm on one step majority logic decodable osmld codes. Onestep majoritylogic decoding with subspace designs. Coding theory lecture notes nathan kaplan and members of the tutorial september 7, 2011 these are the notes for the 2011 summer tutorial on coding theory. On a class of onestep majoritylogic decodable cyclic codes. Reed proposed the majority logic decoding for the rst time. Figure 5 flowchart of majority logic decoding with control logic the ml decoder works with a 15tap shift register, an xor array to calculate the orthogonal parity check sums and a majority logic circuit which will decide whether the current bit under decoding is erroneous and the need for its inversion. In error detection and correction, majority logic decoding is a method to decode repetition codes, based on the assumption that the largest number of.
Whenever a data is read from the memory it is protected by quasi cyclic codes in majority logic decoder and which can able to detect up to five bit flips in three decoding cycles, which is. Simulation and synthesis of majority logic decoder. Vhdl design and fpga implementation of a fully parallel. On a class of majoritylogic decodable cyclic codes ieee xplore. In general, if there are j orthogonal equations in each set at each step of the decoding. It is shown that the reliability performance of reedmuller and other majority logic decodable codes can be substantially improved at the. Maximum likelihood decoding of convolutional codes. Fault secure encoder and decoder for memory applications v. Low power error correcting codes using majority logic. Efficient majority logic fault detection with differenceset codes for. Iterative threshold decoding of high rates quasicyclic osmld codes. However, they require a large decoding time that impacts memory performance. This majoripy,logic decoding scheme is also applicable to a large class of cyclic ancodes generatea by the primitive cyclotomic factors.
The reliability information is obtained through a simple modification of the majority logic decoding rule. The idea behind the method is to use the first iterations of majority logic decoding to detect if the word being decoded contains errors. Our iterative decoding process follows that given by pyndiah in 2. The idea behind the method the method is that, the first iterations of the majority. Jeevitha1 mevlsi design, shreenivasa engineering college, b. Consequently, their encoding can be achieved in linear time and. They are simple to implement and have modular encoder and decoder. The performance of iterative decoding algorithms for multistep majority logic decodable msmld codes of. Msmld codes decoded using bitflipping algorithms can outperform compa. Local listdecoding of reedmuller codes over f 2 original paper by gopalan, klivans, and zuckerman 6, 7. Performance improved architecture of majority logic. Also, the majority of known mld codes are cyclic which are limited in the range of the rates. Hocquenghem bch are not suitable for this task in view of complex decoding algorithm.
The first majority logic decoding was devised by reed for a class of multiple error. Transactions letters modified majority logic decoding of. Euclidean geometry low density parity check egldpc codes are one step majority logic decodable. Two iterative decoding algorithms are devised for this class of cyclic codes and they provide significant coding gain over the twostep majoritylogic decoding of codes in this class. Transactions letters modified majority logic decoding of cyclic codes in hybridarq systems. Design of majority logic decoder for error detection and. When applied to decoding cyclic block codes, this technique yields a decoder structure ideal. On a class of onestep majoritylogic decodable cyclic codes article pdf available in ibm journal of research and development 241. An efficient majority logic fault detection to reduce the. Iterative algorithms for decoding a class of twostep. An efficient majority logic fault detection to reduce the accessing time for memory applications r.
Ldpc codes which were used in, and difference set low density parity check dsldpc codes. Valdemar c da rocha this book serves as an introductory text to algebraic coding theory. Coding theory and applications solved exercises and. For a code with block length n, majority logic decoding using serial implementation requires equal number of iterations, means decoding time is directly proportional to code size, so as the code size grows, so does the decoding time. On decoding using codewords of the dual code arxiv. Codes in this class are twostep majority logic decodable and they are also constructed based on. Channel coding theory one step majority logic decoding consider c as an n, k cyclic code with parity check matrix h.
Head of dept, dept of ece, jbiet hyderabad abstract in this paper, a technique was proposed to protect memory. Iterative threshold decoding of majority logic decodable. In chapter 3, cyclic codes and the important family of bch codes are described. Use these three equations to obtain a majoritylogic decoder for this convolutional code. A majoritylogic decoding scheme is developed for the code constructed. Design of parallel architecture of the siso threshold. Codes in this class are twostep majoritylogic decodable and they are also constructed based on finite geometries. One step majority logic codes consider an n, k linear code c with paritycheck matrix h. Reduction of decoding time in majority logic decoder for. Hence decoding of cyclic codes can be realized this way. Abstractmajority logic decoding mld codes are very powerful thanks to the simplicity of the decoder. Pdf on a class of onestep majoritylogic decodable cyclic codes.
Majority logic decodable codes are suitable for memory applications due to their capability to correct a large number of. Any cyclic code can be converted to quasicyclic codes by dropping every th symbol where is a factor of. Fpga implementation of fast error correction and detection. Simple majority logic code mlc consider a linear cyclic code c n, k with h parity check matrix. It turns out that these codes have the same majority logic decoding capability as the codes from geometric designs, but their majority logic decoding complexity is sometimes drastically improved. The contents are suitable for final year undergraduate and first year graduate courses in electrical and computer engineering, and. This paper presents two iterative decoding algorithms for a class of nonbinary twostep majoritylogic nbtsmlg decodable cyclic codes. Cycliccodes, decoding, encoding, error, fault, majoritylogic, memory. 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. The art of error correcting coding wiley online library. This paper formulates conditions under which this decoding is possible and presents a simple algorithm that accomplishes the same. Tech scholar vlsi system design, aits rajampet, kadapa v.
Encoding and decoding of cyclic codes cyclic codes are an important class of linear block codes in which the cyclic shifting of the message bits results in another code vector, hence the name cyclic code. New infinite class of cyclic codes is studied, which has the interesting property that majority logic decoding can be used in a stepbystep manner as in meggitts. Simulation and synthesis of majority logic decoder detector for egldpc codes j. A partial parallel decoding scheme is also introduced to. Efficient majoritylogic decoding of shortlength reed. Shu lin george markowsky 56 on a class of onestep majoritylogic decodable cyclic codes majority logic decoding is attractive for three reasons. Cyclic block codes have the property of being majority logic ml decodable. An overview of the same is presented in this chapter. Therefore cyclic block codes have been described as. One step majority decoder free download as powerpoint presentation. Reedmuller codes and difference set cyclic codes weldon, 1966 are the most important classes of codes that can be decoded with majority logic.
354 1129 1463 1552 1425 125 538 350 108 1137 224 1490 628 1146 1274 191 799 328 621 238 1552 1103 1180 1546 646 190 1535 1010 770 1230 1397 1524 609 705 963 510 838 479 876 374 152 187 640 926 783 463 473 244 1093