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Ganesh Rao (in his book “Signals and Systems: Theory and Applications”) looks at the transmission of messages between at least two nodes in the network. The problem of transmitting a message from the source node to the receiver node, which is the primary concern in the study of communication networks, is called the transmission problem. In most cases, we are interested in the optimization of the transmission for a given message. On the other hand, in some special cases, the information of the message itself is of significance. For example, the lengths of some messages must be controlled in the case of routing in the Internet. If the communication medium is a radio channel, such an optimization can be achieved by introducing the concepts of the code and the codebook. The code is a mathematical object in the space of messages used for transmission of a given message and codebook is a collection of codes for a given message.
One of the first books that dealt with the problem of coding for a radio channel is Minsky's book “A Mathematical Theory of Communications” (1967). The problem with this book is that Minsky has not dealt with the optimization of the transmission for a given message and the inherent constraint of the transmission medium. In addition, he assumes that the channel is free of noise. This is in sharp contrast to the performance theory developed by Shannon (see Shannon's work in the chapter titled “Communication Theory and Information Theory”).
Minsky's book “A Mathematical Theory of Communications” is a rare book that deals with the problem of coding for a radio channel, in a mathematically correct manner, under the constraint of a fixed cost for the transfer. The work of R. Gallager (1952) is a good text book for the theory of coding for a fixed channel cost. The last sentence of the book states that the author does not deal with the problem of coding for a codebook of more than one codeword. However, the author does deal with that of a codebook of more than two codewords (see sec. II.6). The work of C. E. Shannon (1949) is a good book for transmitting a message at a given average cost.
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