International Journal of Recent Technology and Engineering (IJRTE)
Hamming Code Converter using Reversible Toffoli Netlist
Dept. of Computer Science and Engineering, Techno International Batanagar, Kolkata, West Bengal 700141, India,, Diganta Sengupta, Mahamuda Sultana, Dept. of Information Technology, Techno International New Town, Kolkata, West Bengal 700150, India,, Atal Chaudhuri
Technological advancements in the last two decades have witnessed a plethora of emerging technologies gaining global research attention. One of them is reversible logic due to its capability to arrest tremendous amount of heat generated in modern digital conversions at the architecture level. With CMOS reaching near capping of threshold parameters, researchers are imperatively exploring the reversible domain for possible alternatives. Telecommunication is one area which expects appreciable share of digital resources. This communication proposes the reversible version of Hamming Code converter, decoder, and Corrector unit. Hamming codes form one of the perfect codes attaining the Hamming Bound. The designs have been implemented using Toffoli Netlist. A state-of-the-art four variable reversible gate in literature has been used to design the high level schematic for part of the proposals. The authors provide the results in terms of primitive Quantum Metrics.
Technological advancements in the last two decades have witnessed a plethora of emerging technologies gaining global research attention. One of them is reversible logic due to its capability to arrest tremendous amount of heat generated in modern digital conversions at the architecture level. With CMOS reaching near capping of threshold parameters, researchers are imperatively exploring the reversible domain for possible alternatives. Telecommunication is one area which expects appreciable share of digital resources. This communication proposes the reversible version of Hamming Code converter, decoder, and Corrector unit. Hamming codes form one of the perfect codes attaining the Hamming Bound. The designs have been implemented using Toffoli Netlist. A state-of-the-art four variable reversible gate in literature has been used to design the high level schematic for part of the proposals. The authors provide the results in terms of primitive Quantum Metrics.
Summary form only given, as follows. With the increasing emphasis on low-power design and quantum computation, research activities in the area of reversible logic synthesis and testing have gained momentum over the last couple of decades. It is expected that reversible logic will provide us with a viable alternative to building ultra-low power circuits and systems in not too distant future. In the classical works for synthesis of reversible circuits, gate libraries comprising of standard reversible gates like NOT, CNOT, TOFFOLI, FREDKIN, etc. are considered. To evaluate the goodness of a synthesized netlist, various metrics such as gate count, quantum cost, and equivalent transistor cost have been considered by various researchers. The synthesis approaches that have been reported can be broadly categorized into three groups: (a) exact synthesis approaches which try to obtain optimal reversible gate netlists, but can be used for small circuits only, (b) heuristic based approaches which try to utilize some domain knowledge intelligently to reduce the complexity of search, and can be used for somewhat larger circuits, and (c) synthesis approaches that rely on higher level functional representations like binary decision diagram (BDD) or exclusive sum-ofproducts (ESOP). The last approach is scalable to larger circuits (with 200 inputs or more), however, the synthesized netlist is not optimal and various rule-based heuristic approaches have been proposed to minimize the cost. There have been works also that report techniques for implementing sequential circuits with reversible properties, which will be useful for building complex systems containing finite-state machines. There are various transformations that are carried out as part of cryptographic algorithms that are inherently reversible in nature. For instance, any block cipher that uses a key K to transform a plaintext P into a ciphertext C during encryption must be reversible, because decryption will be doing just the reverse (C to P). Also, in standard symmetric block ciphers like DES or AES, there is a combinational block called substitution box or S-box which is also reversible in nature. In AES, the S-box has 8 inputs and 8 outputs, and implements a one-to-one onto mapping. The same reversibility requirements hold for stream ciphers and public-key ciphers like RSA. Although not much work has been carried out in the area of reversible implementations of cryptographic algorithms, this can be a very good area for future research. Similar considerations hold for various coding and decoding techniques used in communication, which are also inherently reversible in nature. Some examples of such coding/decoding are Manchester, Differential Manchester, Bipolar AMI, 4B/5B, 8B/10B, Hamming error correcting code, etc. All these techniques can potentially be implemented using reversible logic circuits. Specific case studies of some of the areas as mentioned will be reported, with synthesis results.
Throughout the last decade, reversible logic has been an emerging research topic. Over the years, a considerable number of application specific new reversible gates with varied characteristics have been proposed. Barring few, most of the gates lack fundamental quantum mapping in contemporary literature. This paper takes into account the four variable reversible gates those have been proposed and provides the Toffoli mapping using positive control lines. The authors optimize the designs using negative control lines wherever possible. The quantum cost, quantum gate count and two-qubit gate count required to implement those reversible gates have been provided which will set a benchmark for optimized gate choice for complex Boolean realizations. The authors also provide Hamming Distance based Complexity analysis.
Abstract — Reversible logic is one of the most vital issue at present time and it has different areas for its application, those are low power CMOS, quantum computing, nanotechnology, cryptography, optical computing, DNA computing, digital signal processing (DSP), quantum dot cellular automata, communication, computer graphics. It is not possible to realize quantum computing without implementation of reversible logic. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs. This paper provides the basic reversible logic gates, which in designing of more complex system having reversible circuits as a primitive component and which can execute more complicated operations using quantum computers. The reversible circuits form the basic building block of quantum computers as all quantum operations are reversible. This paper presents the data relating to the primitive reversible gates which are available in literature and helps researches in designing higher complex computing circuits using reversible gates.
Reversible logic, also known as information lossless logic, is a promising technology that allows embedded data within circuits to be retrieved in case of failure.This study explores the use of reversible gates, such as Feynman gates, Toffoli gates, Fredkin gates, Peres gates, Double Feynman gates, NFT gates, DKG gates, and DFT gates, to construct logic circuits.These reversible logic gates can be effectively used for the implementation of any higher logic circuits-based applications.In the proposed paper the Arithmetic logic unit based on reversible logic hates is implemented in Verilog as well as IBM quantum software.The major applications of reversible logic gates include quantum computing, low power circuits, nano and CMOS technologies, photonics.In the last part of the paper the circuits implemented using Verilog and IBM quantum a chip level design using Cadance layout is implemented.
Quantum computing is one of the emerging fields of technology that has been a guiding light for low power VLSI, low power CMOS design, optical information computing, DNAcomputing, Bio-informatics and Nano-technology .A quantum circuit is a model for quantum computation in which a computation is performed by a sequence of quantum gates, which are reversible transformation on a quantum mechanical analog of an n bit register, referred to as an n-qubit.Code converters are required day in and day out.In this paper, a reversible 5421 to binary code converter is implemented.
Recent applications of quantum computing is the design and evaluations on the reversible logic technology. The digital systems widely utilize the code conversion technology in enhancing the data security and also minimize the required hardware. This nano-metric technology is high prolific in digital systems as it minimize the power consumption in logic circuits. This paper proposes the reversible logic design for such a code conversion including the binary to gray code, gray to binary code, BCD to excess 3 codes, excess 3 to BCD code.