A Fixed-Length Source Coding Theorem on Quasi-Probability Space

The existing source coding theorems are established on probability meas-ure space or Sugeno measure space. It is difficult to deal with the source coding problems on quasi-probability space which is an extension of probability measure space and Sugeno measure space. In order to overcome the limitation, fixed-length source coding problems on quasi-probability space are discussed. Based on the definition and properties of information entropy on quasi-probability space, an asymptotic equipartition property of discrete memoryless information source on quasi-probability space is proved. Then, a fixed-length source coding theorem for discrete memoryless information source on quasi-probability space is provided.