Some theorems on noiseless coding

For a generalized random variable X, a measure L¯X of average code length is defined. Using L¯X, some coding theorems for discrete noiseless channels are proved. Some new concepts like strongly decipherable codes, absolutely strongly optimal codes, etc. are also proposed. It is asserted that if the celebrated noiseless coding theorem of Shannon (for complete random variables) is to be extended properly for generalized random variables, then the coding must be done in a strongly decipherable way