In this paper, we describe the trellis coding where quantum computing (QC) is employed to analyze the coding gain and complexity.According to quantum information theory, quantum bits increase the storage capacity as well as speed.High complex trellis based on partial memory code (PUM) is designed and simulated in digital computers.In order to reduce simulation time for trellis decoding, QC is analyzed with PUM coding.From the theoretical analysis, QC in a quantum computer will be the best option because quantum bits can be stored simultaneously in a given moment of time.From this theory, trellis states, paths, metric calculations are stored in lesser time and space than conventional storing procedures.Therefore, QC certainly will improve the trellis coder performance.
Coding theory: Grobner bases, Pade approximation, and decoding of linear codes by J. B. Farr and S. Gao Some computational tools for estimating the parameters of algebraic geometry codes by G. L. Matthews An introduction to algebraic coding theory by H. N. Ward Recent results on
p-ranks and Smith normal forms of some
2−(v,k,λ) designs by Q. Xiang Quantum computing: Quantum walks on graphs and quantum scattering theory by E. Feldman and M. Hillery A continuous variable Shor algorithm by S. J. Lomonaco, Jr. and L. H. Kauffman Entangled states of light by S. J. van Enk Entanglement beyond subsystems by L. Viola, H. Barnum, E. Knill, G. Ortiz, and R. Somma Generalized GHZ states and distributed quantum computing by A. Yimsiriwattana and S. J. Lomonaco, Jr.
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes. Many quantum codes can be described in terms of the stabilizer of the codewords. The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code. The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over GF(4), the finite field with four elements. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault-tolerant quantum computation, instructing us how to perform quantum gates on qubits which are encoded in a quantum error-correcting code. The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary quantum computation provided the error rate per physical gate or time step is below some constant threshold value.