Abstract
AbstractA differential coding method regards the transmission line code as a kind of state and assigns the original codeword to each state transition. This method is used widely to regenerate the original codeword as an invariant for the state transition even if there exists state ambiguity during transmission. This paper derives a differential coding theorem as the necessary and sufficient condition for the existence of a differential code on the basis of the mathematical formulation of differential coding problems. According to the theorem, the necessary and sufficient condition for the existence of a differential code is that the set of ambiguity operators should be an irreducible and nonseparable group Gσ, and that a stationary successive operator, which is antihomomorphism on Gσ, should exist. the importance of the theorem is demonstrated through the differential coding for the staggered QAM transmission system, which has been considered difficult to code differentially. Since the theorem is derived under some general conditions, it is applicable to a variety of differential coding problems which may appear in the future.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
