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Multiple error-correction coding for optical matrix-vector multipliers

Ahmet Tankut Caglar

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

Optical matrix-vector multipliers are known to suffer from low computational accuracy which is the major drawback preventing them from becoming a practical force in real world applications. Error-correction coding is one technique proposed to overcome this problem of low level accuracy. In this thesis, the effects of the application of multiple error-correction codes to optical matrix-vector multipliers are studied. For this purpose, many different cases were simulated on a computer. Noting that an optical matrix-vector multiplier performs the product y = Ax, basically four cases were considered; signal independent and signal dependent noise in the matrix A, and signal independent and signal dependent noise in the vector x. Two different error-correcting codes were simulated; one being a binary, multiple error-correcting BCH code and other being a non-binary, multiple error-correcting Reed-Solomon code, which is basically an extension of the binary BCH code. The advantages and disadvantages of switching from binary BCH codes to non-binary Reed-Solomon codes were investigated. Based on the results obtained from the simulations, the conditions under which the use of error-correction coding is feasible in optical matrix-vector multipliers are discussed.

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Optical matrix-vector multipliers are known to suffer from low computational accuracy which is the major drawback preventing them from becoming a practical force in real world applications. Error-correction coding is one technique proposed to overcome this problem of low level accuracy. In this thesis, the effects of the application of multiple error-correction codes to optical matrix-vector multipliers are studied. For this purpose, many different cases were simulated on a computer. Noting that an optical matrix-vector multiplier performs the product y = Ax, basically four cases were considered; signal independent and signal dependent noise in the matrix A, and signal independent and signal dependent noise in the vector x. Two different error-correcting codes were simulated; one being a binary, multiple error-correcting BCH code and other being a non-binary, multiple error-correcting Reed-Solomon code, which is basically an extension of the binary BCH code. The advantages and disadvantages of switching from binary BCH codes to non-binary Reed-Solomon codes were investigated. Based on the results obtained from the simulations, the conditions under which the use of error-correction coding is feasible in optical matrix-vector multipliers are discussed.
Optical algebraic processors can perform complex calculations in parallel and at high speeds. However, they commonly suffer from a low analog accuracy which hinders their widespread application. Error detection and correction codes provide one technique for improving the accuracy of optical algebraic processors. The use of these codes would allow some of the errors that may occur during a computation to be detected and possibly corrected. This paper describes the results of various computer simulations of optical matrix-vector multipliers employing error-correction codes. It discusses the application of convolutional codes to optical matrix-vector multipliers along with several block codes. Both binary and nonbinary codes are considered. The results indicate that a significant improvement in performance can be obtained when compared with processors not employing error-correction codes. Also, the type of noise, whether signal-independent or signal-dependent noise, has a significant effect on the performance of a matrix-vector multiplier employing an error code. The encoding and decoding operations required for the error codes can be performed optically.
Optical algebraic processors can perform complex calculations in parallel and at high speeds. However, they commonly suffer from a low analog accuracy which hinders their widespread application. Error detection and correction codes provide one technique for improving the accuracy of optical algebraic processors. The use of these codes would allow some of the errors that may occur during a computation to be detected and possibly corrected. This paper describes the results of various computer simulations of optical matrix-vector multipliers employing error-correction codes. It discusses the application of convolutional codes to optical matrix-vector multipliers along with several block codes. Both binary and nonbinary codes are not employing error-correction codes. Also, the type of noise, whether signal-independent or signal-dependent, has a significant effect on the performance of a matrix-vector multiplier employing an error code. The encoding and decoding operations required for the error codes can be performed optically.
Optical processors can perform complex calculations in parallel at high speeds. They commonly suffer, however, from low accuracy, which currently hinders their widespread use. Various models for the noise in optical processors have been developed.1 In addition, various techniques have been developed to improve their accuracy. One technique involves the use of error-detection and correction codes to improve the accuracy of optical linear algebra processors.2 This allows some of the errors that occur during computation to be detected and possibly corrected. These codes, developed earlier for data transmission and fault tolerance in electronic processors, can thus be used to improve accuracy. Many of the required encoding and decoding operations can be performed optically. Computer simulations of optical matrix-vector multipliers employing various error codes will be presented. They indicate that a significant improvement in accuracy can be obtained when they are compared with processors not employing error codes.
Many disciplines, such as antenna beam-forming and \nadaptive optics, require the ability to perform high \nspeed matrix operations, which often can be reduced to a \nseries of matrix-vector products. Analog optical matrixvector \nprocessors (OMVP's) take advantage of the high \nspeed and parallelism of optics to rapidly compute \nmatrix-vector products. However, OMVP's suffer from a \nlow accuracy which currently hinders their widespread \napplication. Over the past decade, various techniques \nhave been introduced to achieve high accuracy computation \nwith OMVP's. This dissertation studies the application \nof error-correcting codes (ECC's) and the union of ECC's \nwith digital partitioning to achieve high accuracy computation. \nThe ability of ECC's to improve the performance \nof OMVP's is studied through the use of computer simulations. \nThe effect ECC's have on system throughput is \nalso studied. Digital partitioning is a new technique \nfor achieving high accuracy computations on analog \nOMVP's. One potential drawback of digital partitioning \nis its sensitivity to errors. Error-correcting codes can \nenhance the performance of the digital partitioning algorithm \nby reducing this sensitivity to errors. Computer \nsimulation results are presented showing the benefits of \nusing ECC's with digital partitioning. In addition, an \nanalysis of the time requirements for encoding and decoding \nthe ECC's and the effect on system throughput is \npresented.
This thesis discussess Quantum Error Correction and why it is essential for the development of quantum computation. The introduction will cover the basics of quantum computing and classical error correction. In the second section we will show why Quantum Error Correction is necessary and how different types of error correcting codes help detect and prevent errors. The experiments section will compare the real world performance of diferent types of quantum error correcting codes using a quantum simulator and prevent the results of the experiments. The final section will discuss the conclusions [of] our research.
Quantum communication technologies will play an important role in quantum information processing in the near future as we network devices together. However, their implementation is still a challenging task due to both loss and gate errors. Quantum error-correcting codes are one important technique to address this issue. In particular, the quantum Reed-Solomon codes well suited to communication tasks as photons can naturally carry more than one qubit of information. The high degree of physical resources required, however, makes such a code difficult to use in practice. A recent technique called quantum multiplexing has been shown to reduce resources by using multiple degrees of freedom of a photon. In this work, we propose a method to decompose multicontrolled gates using fewer controlled-x (CX\mathrm{CX}CX) gates via this quantum multiplexing technique. We show that our method can significantly reduce the required number of CX\mathrm{CX}CX gates needed in the encoding circuits for the quantum Reed-Solomon code. Our approach is also applicable to many other quantum error-correcting codes and quantum algorithms, including Grovers and quantum walks.