Note on unique decipherability

We consider an alphabet of a letters, used under the restrictions: 1) messages uniquely decipherable into words by use of one of the letters as a space mark, and 2) words limited to a maximum length of
L
letters. Although imposing these constraints simultaneously may cause a large reduction in the channel capacity of the alphabet, neither by itself causes any reduction. Accordingly, in the absence of constraints other than 1), an inequality of McMillan pertaining to uniquely decipherable messages can be made to be an equality. Defining "semi-optimal" transmission by the condition that the mean transmission time per word is minimized for a given entropy per word, we find the attainable rate of information transmission under semi-optimal conditions. Transmission at full channel capacity is a special case of semi-optimal transmission. Some generalizations and analogies to statistical mechanics are discussed.