The performance of iterative decoding algorithms for multistep majority logic decodable msmld codes of intermediate length is investigated. Firstly, they offer a partial solution to a classical coding theory problem, that of decoder complexity. Belkasmi national institute of computer sciences and systems analysis ensias b. We will then present an iterative majoritylogic decoding imlgd algorithm for nonbinary ldpc codes, followed by an improved imlgd algorithm. Pdf majoritylogic decoding is attractive for three reasons. Further, the decoding complexity of our procedure is compared with that of chens decoding algorithm for various reedmuller codes up to length 210. A novel majority logic coding scheme is proposed which comprises a rststage of linear coding with its ownspreadingfactor, followed by a second stage of majority logic coding with an additional spreading factor. 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. Pdf majority logic decoding of euclidean geometry low. For these codes to be applicable in wireless environment, their performance on fading channels must be examined.
Low power error correcting codes using majority logic decoding. Parity check egldpc codes are one step majority logic decodable. The rst linear stage can be simply an augmentation of parity. In this paper, a new lowcomplexity gradientdescent based iterative majoritylogic decoder gdmlgd is proposed for decoding onestep majoritylogic decodable osmld codes. Index terms majority logic decoding, reedmuller codes, information positions, realtime and embedded systems. Its performance is suboptimum since each of its decoding decision is based only on one output constraint length of received bits. It is shown that it is easy to adapt such a technique to handle the case where the decoder is given an ordered list of two or more prospective candidates for each inner code symbol. A new iterative threshold decoding algorithm for one step majority logic decodable block codes m.
We show that for reversible erasure protocols, information erasure in single units is more ef. Gradientdescent decoding of onestep majoritylogic decodable. We investigate the performance of majority logic decoding in both reversible and finitetime information erasure processes performed on macroscopic bits that contain n microscopic binary units. The main goal of the study is to modify majority logic decoding using sumproduct or minsum decoding algorithms at the highestorder information bits in rm codes. They are simple to implement and have modular encoder and decoder. Vhdl design and fpga implementation of a fully parallel. A method was recently proposed in to accelerate a serial implementation of majority logic decoding of dsldpc codes. Introduction majority logic decoding is a simple procedure. But, the major difference is that instead of decoding all. The reason for using ml decoding is that it is very simple to implement and very practical and has low complexity.
Keywords one step majority logic decodable codes, osmld, iterative threshold decoding, parallel concatenated block. Mostly memory applications require low latency encoders and decoders. Analytical performance of onestep majority logic decoding of regular ldpc codes rathnakumar radhakrishnan. Department of electrical and computer engineering university of arizona, tucson, az85705 email. A fault secure memory system can be implemented by using majority logic decoder. This video will make you understand the design process of any combinational circuit. Majority logic like decoding is an outer concatenated code decoding technique using the structure of a binary majority logic code.
H is an n, n k which generate the dual code,denoted by cd. First, a constant stateenergy protocol of the microscopic unit is considered. But, the major difference is that instead of decoding all codeword bits simultaneously, the. If there are no errors, the decoding can be stopped without completing the rest of the iterations. Numerical results show that compared with the traditional majority logic decoding algorithm, the modified majority logic decoding method proposed in this study can reduce the bit. Thermodynamics of majoritylogic decoding in information erasure. Reduction of decoding time in majority logic decoder for. Semiconductor memory is a storage element which stores binary or 1. Abstract we examine harddecision decoding algorithms for qary ldpc codes. Majority logic decoding of convolutional codes, proposed by massey 308, is a suboptimum but simple decoding scheme that allows a highspeed implementation.
Thermodynamics of majoritylogic decoding in information erasure article pdf available in entropy 2. However, they require a large decoding time that impacts memory performance. Abstractin a recent paper, a method was proposed to accelerate the majority logic decoding of difference set low density parity check codes. Index termsmajoritylogic decoding, reedmuller codes, information positions, realtime and embedded systems. Interpretation of majoritylogic decoding algorithms as a. Majority logic decoding mld, modified majority logic decoding mmld, modified majority logic decoding with control mmldc,multiple cell upsetmcu,difference set low density parity check dsldpc. For any code vin cand w in cd, the inner product of vand wis zero. Among those are some euclidean geometry low density parity check egldpc codes which were used in, and difference set low density parity check dsldpc codes. An algebraic approach called majoritylogic or threshold decoding can also be applied to convolutional codes 1,9. Type i majority logic decoder plain majority logic decoder the majority logic decoder is a simple and powerful d e c o d e r, ca p ab le of correc ti ng multiple random bit flips depending on of parity check equations. So the proposed method has reduced a decoding time by detecting whether a word has errors in the first iteration of majority logic. Efficient majority logic fault detection with egldpc. The memory access time as well as area of utilization and the decoding time is reducing using majority logic decoder.
The commonsymbol decoding problem is that of estimating the symbol in the common position. In euclidean geometry lowdensity paritycheck egldpc codes there. Onestep majority logic decoding is one of the simplest algorithms for decoding cyclic block codes. Decoding of ldpc codes with the osmlgdalgorithm was presented in 5. Since most w ords in a memory w ill be er r or fr ee, the av erage decoding time is gr eatly r ed uced.
Pdf on a class of onestep majoritylogic decodable cyclic codes. The main goal of the study is to modify majoritylogic decoding using sumproduct or minsum decoding algorithms at the highestorder information bits in rm codes. It consists of cyclic shift register, xor matrix, majority gate and. Majority logic decoding of euclidean geometry low density parity check egldpc codes. We give a formulation of the decoding problem of binary osmld codes, as a maximization problem of a derivable objective function. This study investigates the decoding algorithms of binary reedmuller rm codes. Then we shall return to our original goal of constructing explicit codes with constant relative distance and rate. Capability to correct large number of errors majority logic decodable codes is suitable for memory applications.
Physics videos by eugene khutoryansky 357,421 views. The parallel encoders and decoders have been implemented to overcome the drawback of majority logic decoder in which it. Majoritylogiclike vector symbol decoding with alternative. Its performance is suboptimum since each of its decoding decision is based. Towards this, we will convert reed solomon codes in to binary codes. Secondly, a majoritylogic decoder inherently corrects many more random error. However, it is an effective decoding scheme for very few codes. Analytical performance of onestep majority logic decoding of regular ldpc codes. Majority logic decodable codes are suitable for memory applications due to their capability to correct a large number of errors. The discretization then yields a list of symbols for every sample of each gene.
Reduced latency majority logic decoding for error detection. This paper formulates conditions under which this decoding is possible and presents a simple algorithm that accomplishes the same. Iterative decoding of multistep majority logic decodable codes. Majority logic decoding for certain schubert codes using. Thermodynamics of majoritylogic decoding in information. A new iterative threshold decoding algorithm for one step.
We then show how iplgd can be improved by tweaking it into what we call the generalized. While we show that for reversible erasure protocols singleunit transformations are more efficient than majority logic decoding, the latter is found to offer several benefits for finitetime erasure. In a, code, if r1 0 1 1 0, then it would be decoded as,, so r1 1 1 1 1 hence the transmitted message bit was 1. Ingole, sameena zafar published on 20140718 download full article with reference data and citations. Analytical performance of onestep majority logic decoding of.
Based on a co mbinatorial representation of fault con. Channel coding theory one step majority logic decoding consider c as an n, k cyclic code with parity check matrix h. Numerical results show that compared with the traditional majoritylogic decoding algorithm, the modified majoritylogic. Including packages complete source code complete documentation complete presentation slides flow diagram database file screenshots execution procedure readme file addons. Majority logic decoding mld solutions 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 main advantages of random errorcorrecting majoritylogic codes and majoritylogic decoding in general are well known and twofold. We interpret the decoding of each received symbol in terms of.
Introduction majoritylogic decoding is a simple procedure. In the last lecture, we studied the reedmuller code,rm2t,vand saw the majority logic decoder for such codes, in todays lecture, we will start off with a formal statement of the algorithm and then prove its correctness. Majority logic decoding under datadependent logic gate failures srdan brkic, student member, ieee, predrag ivanis. In majority logic decoderdetector the majority logic decoder itself act as a fault detector. Some new results on majoritylogic codes for correction of. Iterative threshold decoding of majority logic decodable. Rudoph 1967 introduced onestep majority logic decoding for linear codes derived from combinatorial designs. Simulation and synthesis of majority logic decoder.
Efficient majority logic fault detection with egldpc codes for memory applications written by mrunali n. In general, the decoding algorithm of mldd is still same as that of majority logic decoder. Lahmer high school of technologies km5, route gouray b. This is beneficial because majority logic decoding can be implemented serially with simple hardware but decoding time is large, in memory application memory access time increases because of this. These ldpc codes can be simply decoded with majoritylogic algorithms, instead of the bp algorithm which requires more. In this section, we present the osmlgdalgorithm for ldpc codes from a new point of view. Jul 27, 2014 including packages complete source code complete documentation complete presentation slides flow diagram database file screenshots execution procedure readme file addons. In one of our recent works 1, we considered a taylorkuznetsov lowdensity parity check ldpc coded memory system 2, 3 with a onestep majority logic decoder. Majoritylogic decoding differs from viterbi and sequential.
This has renewed interest in majority logic decoders. This doubly coded data is recovered by a majority logic based decoding. Majority logic coding and its multinomial representation. This algorithm is a boolean function in its own right, the majority function. Majoritylogic decoding of convolutional codes, proposed by massey 308, is a suboptimum but simple decoding scheme that allows a highspeed implementation. They are devised based on the orthogonal concepts of twostep majoritylogic decoding tsmlgd8. Essentialcodingtheory venkatesanguruswami atri rudra1 madhu sudan march15, 2019 1department of computer science and engineering, university at buffalo, suny. Majoritylogic decoding of convolutional codes, proposed by massey, is a suboptimum but simple decoding scheme that allows a highspeed implementation. A majority logic decoder made of unreliable logic gates, whose failures are tran sient and data dependent, is a nalyzed.
We investigate the performance of majoritylogic decoding in both reversible and finitetime information erasure processes performed on macroscopic bits that contain n microscopic binary units. Er r or detection in majority logic decoding of euclidean. Majority logic decoding looks as the symbols for every sample and selects the symbol that appears in a majority of samples. Iterative pluralitylogic and generalized algorithm b. Analytical performance of onestep majority logic decoding. 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. Distributed decoding of cyclic block codes using a. We note that for each coordinate of a received word the decoder uses those r parity check equations that contain that coordinate plus one additional equation. In error detection and correction, majority logic decoding is a method to decode repetition.
Majoritylogiclike decoding is an outer concatenated code decoding technique using the structure of a binary majority logic code. The onestep majority logic decoding algorithm is briefly explained below. In this paper, we propose an unified interpretation of the existing majoritylogic decoding mlgd algorithms in the literature, as a gradientdescent optimization process. These twostep iterative decoding algorithms tsidas can be generalized to multistep to decode more majoritylogic decodable cyclic codes.
Detection of soft errors in majority logic decoding of. The existent plain majority logic decoder have the method of working in which from the received codeword itself the correct values of each bit under decoding can directly found out. Onestep majoritylogic decoding with subspace designs. However, they require a large decoding time that impacts memory applications. Efficient majority logic fault detection in memory.
Onestep majoritylogic decoding with subspace designs deepai. This is equivalent to onestep majority logic decoding when each of the constituent codes is a simple parity check. A class of cyclic eg codes in this section, we present a simple. First the entire data block is loaded into the registers. Department of electrical and computer engineering university of arizona, tucson, az85705.
Low power error correcting codes using majority logic. Pdf majority logic decoding under datadependent logic. This majoripy,logic decoding scheme is also applicable to a large class of cyclic ancodes generatea by the primitive cyclotomic factors. General terms information theory and coding, signal processing.
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