Coding for Relay Networks and Effective Secrecy for Wire-tap Channels

This thesis addresses two problems of network information theory: coding for relay networks and (accurate) approximations of distributions based on unnormalized informational divergence with applications to network security. For the former problem, we first consider short message noisy network coding (SNNC). SNNC differs from long message noisy network coding (LNNC) in that one transmits many short messages in blocks rather than using one long message with repetitive encoding. Several properties of SNNC are developed. First, SNNC with backward decoding achieves the same rates as SNNC with offset encoding and sliding window decoding for memoryless networks where each node transmits a multicast message. The rates are the same as LNNC with joint decoding. Second, SNNC enables early decoding if the channel quality happens to be good. This leads to mixed strategies that unify the advantages of decode-forward and noisy network coding. Third, the best decoders sometimes treat other nodes’ signals as noise and an iterative method is given to find the set of nodes that a given node should treat as noise sources. We next consider the multiple access relay channel (MARC) with relay-source feedback. We propose a new decode-forward (DF) coding scheme that enables the cooperation between the sources and the relay to achieve rate regions that include the capacity region of the MARC without feedback. For the latter problem, we show that the minimum rate needed to accurately approximate a product distribution based on an unnormalized informational divergence is a mutual information. This result subsumes results of Wyner on common information and Han-Verdú on resolvability. The result also extends to cases where the source distribution is unknown but the entropy is known. We then apply this result to network security where an effective security measure is defined that includes both strong secrecy and stealth communication. Effective secrecy ensures that a message cannot be deciphered and that the presence of meaningful communication is hidden. To measure stealth we use resolvability and relate this to binary hypothesis testing. Results are developed for wire-tap channels and broadcast channels with confidential messages.