Retransmission is a widely adopted and effective approach for ensuring the reliability of communication links for applications of wireless packet-oriented data networks. In an automatic retransmission request (ARQ) scheme, frame errors are examined at the receiver by using error detecting codes, e.g., cyclic redundancy check (CRC). If a received packet passes the CRC, the receiver sends an acknowledgement (ACK) of successful transmission to the receiver. Otherwise, the receiver sends back a negative acknowledgement (NACK) to request retransmission. The user data and its CRC bits may be additionally protected by an error correcting code which increases the probability of successful transmission. These schemes, when combining powerful channel coding with retransmission protocols to enhance reliability, are called hybrid ARQ (HARQ). Among currently available HARQ schemes, the most elementary form is the repetition-coding-based HARQ which combines several noisy observations of the same packet by using a suitable diversity technique at the receiver, such as maximumratio, equal-gain, or selection combining. A more powerful HARQ scheme is the so-called incremental redundancyHARQ,which achieves higher efficiency by adapting its error correcting code redundancy to fluctuating channel conditions. In an incremental redundancy scheme as depicted in Fig. 5.1, the message is encoded at the transmitter by a "mother" code. Initially, only a selected number of coded symbols are transmitted (transmission # 1 in the figure). The selected number of coded symbols form a codeword of a punctured code. Decoding of this punctured code is attempted at the receiver. If a retransmission is requested, additional redundancy symbols are sent under possibly different channel conditions (depicted as taller boxes in transmission # 2 in the figure). Decoding is again attempted at the receiver, where the new parity bits are combined with the previously received bits. This procedure is repeated until either the receiver decodes successfully or all parity bits of the mother code are transmitted. Confidentiality is a further basic requirement for secure communication over wireless networks. The broadcast nature of the wireless medium gives rise to a number of security issues. In particular, wireless transmission is very susceptible to eavesdropping since anyone within the communication range can listen to the traffic and possibly extract information. Traditionally, confidentiality has been provided by using cryptographic methods, which rely heavily on secret keys. However, the distribution and maintenance of secret keys are still open issues for large wireless networks. Fortunately, confidential communication is possible without sharing a secret key between legitimate users. This was shown by Wyner in his seminal paper . In the discrete memoryless wire-tap channel model he proposed, the communication between two legitimate users is eavesdropped upon via a degraded channel (the eavesdropper channel). The level of ignorance of the eavesdropper with respect to the confidential message is measured by the equivocation rate. Perfect secrecy requires that the equivocation rate should be asymptotically equal to the message entropy rate. Wyner showed that perfect secrecy can be achieved via a stochastic code, referred to as the Wyner secrecy code in this work. A general review of the recent research advances in information theoretic security can be found in . In this chapter, we investigate secure packet communication based on HARQ schemes. The challenge of this problem is twofold: first, the encoder at the transmitter needs to provide sufficient redundancy for the legitimate receiver to decode its message successfully; on the other hand, too much redundancy (or insufficient randomness) may help adversarial eavesdropping. As an example, retransmission is an effectiveway to enhance reliability but, nevertheless, it may also compromise confidentiality. These considerations motivate the joint consideration of channel coding, secrecy coding and retransmission protocols.
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