Thus we in this paper make use of the effective psdrm expressions. Reedmuller code 64 shades of grey pt2 computerphile. The reedmuller rm canonical expansion of a variable. Mvl, the binary fprm expansion has been extended to represent multiple. Data encryption and decryption using reedmuller techniques. The algorithm is based on the dual property and the gray code strategy. There is few methods for calculation of coefficients in these expressions. In boolean logic, a reed muller or davio expansion is a decomposition of a boolean function. We will restrict our investigation to the binary case. A direct algorithm for calculating reed muller coefficients under each fixed polarity is derived. Pseudo reedmuller psdrm expression is a more generalized class of reedmuller expression and requires less or at most equal number of.
Fprm expansion utilizes a much smaller number of product terms than. However, he provided no proof that this technique produced the correct fprm expansion. Bidirectional conversion algorithms between sop and andxor also between pos and. It differs to traditional genetic algorithm, in which the proposed ga forms an intermediate population by using 23. Reedmuller expansions are advantageous for many important boolean functions in terms of area, speed and testability point of view 10. Optimisation of mixed polarity reedmuller functions meng yang state key lab of asic and system, fudan university, shanghai, china.
A power efficient design of reversible ram using pseudo reed. The result of arithmetic operations is represented. Tree restructuring approach to mapping problem in cellulararchitecture fpgas author. The motivation for incorporating reed muller into the introductory course on logic design are as follows. Pdf this article provides a novel technique of x mod p realization.
For the love of physics walter lewin may 16, 2011 duration. This paper proposes a technique for arithmetic operations representation based on reed muller expansions of symmetric boolean functions sbfs. This equation is written in a way that it resembles a taylor expansion of about. It carries out symbolic simplification, and works from the bottom of a binary variable decision tree to the top, with variable choice determined using a genetic algorithm. Positive polarity reedmuller pprm expression and fixed polarity reedmuller fprm expression based circuits. Shared reedmuller decision diagram based thermalaware. Vlsi design of power efficient reversible lfsr using pseudo. By using this technique there is more optimization as well as improvement in other factors such as number of gates, memory usage, garbage output. Vlsi design of power efficient reversible lfsr using. Pdf fast synthesis for ternary reedmuller expansion. Other compression methods used in this scheme include minterm coding, coordinate data coding, generalized kvariable mixedpolarity reedmuller expansion and the reference row technique. Fast tabular technique for fixedpolarity reed muller logic with inherent parallel processes.
A study of arithmetic circuits and the effect of utilising. Pdf reedmuller realization of x mod p researchgate. A heuristic method for the determination of optimum or nearoptimum fixed polarity reedmuller fprm representation of multiple output, completely specified boolean systems is presented. The technique is based on the definition and use of a transfer. Shared reedmuller decision diagram based thermalaware and. Direct reedmuller transform of digital logic netlists. Yang, fast tabular technique for fixedpolarity reedmuller. Gorodecky united institute of informatics problems of nas of belarus minsk, belarus danila. This technique is used to find the best polarity of fpdrm among the 2n fixed polarities. 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. A new technique using the reedmuller transform has been applied for image data bandwidth compression. Pdf an application specific integrated circuit for optimization of. Efficient calculation of fixedpolarity polynomial expressions for.
Reedmuller codes reedmuller codes are among the oldest known codes and have found widespread applications. Techniques for dual forms of reedmuller expansion conversion. Reed muller expansion an expression which can represent any boolean function as a modulo2 sum of products, is known as the complimentfree ringsum or reed muller expression rme. The pprm expansion is an esop expression which uses. Reedmuller logic is an algebraic technique for logic circuit design based on and and exclusive or modulo 2 arithmetic operations. If we apply pd expansion on all variables of an nvariable boolean function f x 1.
The second algorithm is used to compute all the coefficients of the fixed polarity dual reed muller fpdrm with polarity p from any polarity q. Reedmuller treebased minimisation of fixed polarity reed. Reed, and is more general when applied to other finite geometry codes. On applications of the reed muller expansion in circuit design u. The reedmuller rm tree representation forms the conceptual framework for the method, which involves manipulations of arrays of cubes.
Hamed hassani, and rudiger urbanke abstractwe explore the relationship between polar and rm codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Dual forms of reed muller dfrm are implemented in orxnor forms, which are based on the features of coincidence operation. Matrix algorithms for reed muller, arithmetic and walsh spectrum computing have been mapped to parallelpipelining. Function synthesis algorithm of rtdbased universal. The motivation for incorporating reedmuller into the introductory course on logic design are as follows. The most popular minimisation subminimisation criterion of the reedmuller form is obtained by the exhaustive search of all the polarity vectors. A power efficient design of reversible ram using pseudo. Tr ee restructuring approach to mapping problem in cellulararchitecture fpgas n.
Deriving the reedmuller code, used by mariner 9 to send back pictures from mars. In this paper, threevariable threshold functions are divided into four categories. This paper presents a nonexhaustive method for reedmuller expansions. In this paper, we define a tabular technique tt for calculation of fixedpolarity polynomial expressions for mv functions as a generalization of the corresponding methods for fixedpolarity reed muller fprm expressions for switching functions. Decision diagram dd technique for reedmuller, arithmetic and walsh spectrum computing introduced in 11. Implementation of reed muller expansion technique using mach. Deriving a fixed polarity polynomial expansion given a boolean function is a. Then we have for the reed muller or positive davio expansion. This algorithm has not only a simple procedure but also much lower computational cost than the stepbystep flow graph algorithm with the polarities in. Techniques for dual forms of reed muller expansion conversion. The standard decoding algorithm for reedmuller codes uses majoritylogic decoding which in turn requires harddecision demodulation. Pdf reedmuller representation in arithmetic operations.
The most popular minimisation subminimisation criterion of the reed muller form is obtained by the exhaustive search of all the polarity vectors. Fast tabular technique for fixedpolarity reedmuller logic with inherent parallel processes. These codes were initially given as binary codes, but modern generalizations to qary codes exist. Tayfehrezaie institute for studies in theoretical physics and mathematics ipm p. Repeated application of the reedmuller expansion results in an xor polynomial in. Map folding and transformation techniques are proposed for the conversion between boolean and dfrm expansions. It outlines the background for rmbdd expanded with respect to one variable and the new 2vrmbdd when the expansion is with. The approach is competitive with the known realizations on the speed processing. Design of reversible mac unit, shift and add multiplier. Fprm expansion utilizes a much smaller number of product terms than the original reed muller form with high testability. Rosenstiel editors wsi932 ubtib hannover 89 111 721 911. Reedmuller treebased minimisation of fixed polarity.
An algorithm called xorga is presented which minimises boolean multioutput logic functions as multilevel andexor networks of twoinput logic gates. Positive davio expansion and variable x 2 uses the an exact minimization of. Introduction to readmuller logic computer action team. Dual forms of reedmuller dfrm are implemented in orxnor forms, which are based on the features of coincidence operation. Direct reed muller transform of digital logic netlists mitchell a. Consequently, a logic function in reed muller expansion with less products can often generate a more economical circuit. The resonant tunneling device rtd has attracted much attention because of its unique negative differential resistance characteristic and its functional versatility and is more suitable for implementing the threshold logic gate. Reedmuller expansions in multiplevalued logic sys tems, 22nd ismvl.
This paper proposes a technique for arithmetic operations representation based on reedmuller expansions of symmetric boolean functions sbfs. Teaching reedmuller techniques in introductory classes on. Khan 6 proposed mapping of fixed polarity x2 x2 reedmuller coefficients from. Polarity reedmuller pprm and fixed polarity reedmuller fprm based reversible circuit synthesis was adopted. Reedmuller psdrm expression is a more generalized class of reedmuller expression and requires less or at most equal number of product terms than fprm expression. Some results may be feasible for commercial products. The multiplication and accumulation mac are the important operations. Thornton and jennifer dworak southern methodist university dallas, texas, usa abstract a method for computing the reedmuller spectrum of a digital logic circuit based on the circuit topology is developed. These decision diagrams are called functional bdds fbdds. Design of reversible mac unit, shift and add multiplier using. Reedmuller expansion an expression which can represent any boolean function as a modulo2 sum of products, is known as the complimentfree ringsum or reedmuller expression rme.
Reed muller code 16, 11, hamming code 7, 4 and hybrid technique combination of signal scrambling and signal distortion proposed by us are used as proposed coding techniques, the simulation results shows that performance of hybrid technique, reduces papr significantly as compared to conventional and modified selective. Professor brailsford shows how it can be coded recursively. Generalised kvariablemixedpolarity reedmuller expansions. Similar to binary decision diagrams bdds, where nodes represent shannon expansion with respect to the. Two algorithms are presented, the first is a technique to determine good, though not necessarily optimum, fixed polarity reedmuller expansions of completely.
There is another reed muller canoni cal expansion known as the generalised reed muller grm expansion which consists of a total of 2 alter native forms 3, 5, 8, 10, 11, 22, 24, 251. The technique is derived from a generalization of the corre sponding methods for. School of engineering napier university edinburgh eh10 5dt scotland, uk abstract this paper proposes a variation of decision diagram, the 2vrmbdd. Map folding and transformation techniques are proposed for the. The representation in which a variable can have either positive or negative polarity throughout the function is known as fixed polarity reed muller fprm form as given by davio and deschamps. On applications of the reedmuller expansion in circuit design u. Direct reedmuller transform of digital logic netlists mitchell a. This paper presents a nonexhaustive method for reed muller expansions. Box 193955746, tehran, iran abstract in this paper, we discuss reedmuller codes using a settheoretic approach. In certain applications, andxor reed muller, and orlxnor dual form of reed muller logic have shown some attractive advantages over the standard sum of products sop and product of sums pos. This technique is used to find the best polarity of fpdrm among the 211 fixed polarities.
Chong et al a new construction of 16qam golay complementary sequences 2955 for any generalized boolean function in variables, we can identify a valued vector of length in which where is the binary expansion of, i. Consequently, a logic function in reedmuller expansion with less products can often generate a more economical circuit. Then we shall return to our original goal of constructing explicit codes with constant relative distance and rate. Combinational logic synthesis based on the dual form of. However, map techniques can only be used for up to 6 variables. Implementation of reed muller expansion technique using. It is possible to design synchronous sequential circuits directly from reversible gates using pseudo reed muller expressions representing the state transition and the output functions of the circuit. Data encryption and decryption using reedmuller techniques upputuri neelima1, fazal noorbasha2 1, 2 department of ece, kl university green fields,vaddeswaram, guntur 522502, a. We apply to the minterm expansion the two identities x d 1. Feb 28, 2014 for the love of physics walter lewin may 16, 2011 duration.
This article provides a novel technique of x mod p realization. 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. Fprmbased reversible circuit synthesis method is more ef. Reed muller codes reed muller codes are among the oldest known codes and have found widespread applications. They were discovered by muller and provided with a decoding algorithm by reed in 1954. This representation is unique and sometimes also called reedmuller. Similar to binary decision diagrams bdds, where nodes represent shannon expansion with respect to the according variable, we can define a decision diagram based on the reedmuller expansion. Other compression methods used in this scheme include minterm coding, coordinate data coding, generalized kvariable mixedpolarity reed muller expansion and the reference row technique. An efficient method of computing generalized reedmuller expansion from the binary decision diagram. Combinational logic synthesis based on the dual form of reed. It is based on the reedmuller polynomial expansion. The representation in which a variable can have either positive or negative polarity throughout the function is known as fixed polarity reedmuller fprm form as given by davio and deschamps.
Computer vision, graphics, and image processing 42, 4861 1988 reed muller transform image coding b. Representation of boolean quantum circuits as reedmuller. A new algorithm is presented that allows us to obtain the mixed polarity reedmuller expansion of boolean functions. On applications of the reedmuller expansion in circuit design. Fast computing of the positive polarity reed muller transform over. A new algorithm is presented that allows us to obtain the mixed polarity reed muller expansion of boolean functions. A new construction of 16qam golay complementary sequences. There is another reedmuller canoni cal expansion known as the generalised reedmuller grm expansion which consists of a total of 2 alter. The main reason is that reedmuller techniques are more complicated than sopbased techniques. Digital circuit testing and testability is an easy to use introduction to the practices and techniques in this field.
There is a similar decomposition corresponding to an expansion about negative davio. We provide such a proof, thus establishing the validity of the transeunt triangle technique. Tree restructuring approach to mapping problem in cellular. By combining global searching ability of genetic algorithm and local searching ability of simulated annealing, the proposed ga method could achieve fast convergence. A variablelength chromosome evolutionary algorithm for. Workshop on applications of the reedmuller expansion in circuit design,sept. Pai department of computer science, arizona state university, tempe, arizona 85287 received october 10, 1986. The advantage of the approach concludes in the capability to realize x mod p for an arbitrary p. The same expansion must be used for the same variable s a a pd 1 b pd 1 b nd 1. Towards this, we will convert reed solomon codes in to binary codes.
The universal logic gate has become an important unit circuit of digital circuit design because of its powerful logic function, while the threshold logic gate is a. Apr 07, 2017 deriving the reedmuller code, used by mariner 9 to send back pictures from mars. Vlsi design of power efficient reversible lfsr using pseudo reedmuller expressions shibinu a. Thornton and jennifer dworak southern methodist university dallas, texas, usa abstract a method for computing the reed muller spectrum of a digital logic circuit based on the circuit topology is developed. Fast mixed linearly independent arithmetic logic transforms. Since the algorithm is multilevel in nature, it delivers more compact. Reedmuller code 16, 11, hamming code 7, 4 and hybrid technique. Technique of spectral transforms of boolean and multiplevalued functions was developed in 27, 25, 26. Optimisation of mixed polarity reedmuller functions.
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