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ceived is called decoding.Intuitively, as more redundant information is added, the probability of error in decoding n could approach to 0, in turn, the transmission eciency would decrease. So, it is very important to know the minimum redundant in-formation that realizes error-free communication to design a communication system. Based on such motivation, Shannon showed that the decoding error probability n can be decreased arbitrarily by extending n if encoding rate RB = k/n that is a ratio of code word size n to message size k, is smaller than channel capacity C that is dened for each transmission channel. is theory is called channel coding theorem which is the most fundamental problem in information theory.In order to evaluate channel capacity C concretely, here we dene some probabilities in a communication system. Alice can select and transmit bit x based on independent and identical probability )(xPX . Also, the probability of occurrence of error in the channel can be modeled with conditional probability (transition probability) where Bob can obtain symbol y when symbol x is input, WB (y | x). Here, we assume a stationary and memoryless communica-tion channel. Under such precondition, mutual information I (X;Y) is calculated from the following equation, which expresses the amount of transmissible information between Alice and Bob.xyxBXBBXxyWxPxyWxyWxPYXI'2)'|()'()|(log)|()();( .e input probability )(xPX can be optimized so that Alice can transmit as much information as possible to Bob. As a result, the channel capacity C is derived as follows.);(max)(YXICxPX .2.2Wiretap channel codingUnlike the channel coding explained in the previous section, wiretap channel coding concerns the situation in which communication between Alice and Bob using a main channel is wiretapped by Eve using a wiretapper channel as shown in Fig. 1. However, in such a case, the purpose of Alice and Bob is to transmit information without not only decoding error but also leakage to Eve, that is, to communicate in a highly reliable and information theo-retically secure way.Intuitively, security seems to be ensured if Eve uses channel code that fails in error correction. Here, we assume a schematic example where when Alice transmits a message of 3 bits in size, Bob can receive the message without error and Eve receives a correct message or a bit sequence with one-bit error in 1/2 probability for each case. In other words, when Alice transmits a message of 000, Eve would receive one bit sequence from four bit sequences, 000, 100, 010, and 001, in 1/4 probability. In this case, Eve cannot identify the message that Alice sent, but it should be noted that she can narrow down the possibilities. For example, if Eve received a bit sequence of 001, she can guess that Alice sent one from 001, 101, 011, or 000. is means that one bit of the information of the message has been leaked because the number of candidates of the correct message decreased from eight to four. So, it is not considered to be information-theoretically secure anymore.When Alice and Bob want to communicate in an in-formation theoretically secure way, they want to prevent even such one-bit leakage. e possible sequences gener-ated at Eve when Alice transmits a message are listed in Table 1 for comparison. en, it is clear that all the se-quences possibly generated at Eve cover all the sequences expressed by 3 bits for both 000 and 111. en, Alice combines two messages that meet such condition and as-signs 2-bit message for each pair. is is a secret message that enables information theoretically secure transmission. In the case of sending a certain secret message, one of the 3-bit messages corresponding to the secret message is randomly selected and transmitted. As Bob can receive the Alice(Sender)Main ch.Wiretapper ch.Bob(Receiver)Eve(Wiretapper)FiF1　Schematic view of wiretap channel encodingTabT13 Bit messages and generated bit sequences possible at Eve and 2-bit secret messagesMessagesThe possible sequences generated at Eve2-bit secret messages000000, 100, 010, 00100111111, 011, 101, 110100100, 000, 110, 10110011011, 111, 001, 010010010, 110, 000, 01101101101, 001, 111, 100001001, 101, 011, 00011110110, 010, 100, 111333-3 Channel Estimation Experiment for Physical Layer Cryptography in Free-space Optical Communication