On index coding with side information

Building communication schemes which allow participants to communicate efficiently has always been a challenging yet intriguing problem for communication theorists. Index Coding with Side Information (ICSI) (Birk and Kol (1998)) is a communication scheme dealing with broadcast channels in which receivers have prior side information about the messages to be broadcast. Exploiting the knowledge about the side information, the sender may significantly reduce the number of required transmissions compared with the naive approach. As a consequence, the efficiency of the communication over this type of broadcast channels could be dramatically improved. Apart from being a special case of the well-known (nonmulticast) Network Coding problem (Alhswede et al. (2000), Koetter and Médard (2003)), the ICSI problem has also found various potential applications on its own, such as audioand video-on-demand, daily newspaper delivery, data pushing, and oppoturnistic wireless networks. While most of the known works on ICSI focus on the performances of index codes of various kinds, the security and error correction aspects of those codes have never been examined. Although similar issues have been thoroughly investigated in multicast Network Coding, on the side of non-multicast Network Coding, where ICSI is one example, things are much less understood. In this work, we make an attempt to fill in this gap. We first analyze the block security level of the linear index code based on a

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