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Register a new userBroadcast Function Computation with Complementary Side Information
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Added by
Jithin Ravi
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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We consider the function computation problem in a three node network with one encoder and two decoders. The encoder has access to two correlated sources $X$ and $Y$. The encoder encodes $X^n$ and $Y^n$ into a message which is given to two decoders. Decoder 1 and decoder 2 have access to $X$ and $Y$ respectively, and they want to compute two functions $f(X,Y)$ and $g(X,Y)$ respectively using the encoded message and their respective side information. We want to find the optimum (minimum) encoding rate under the zero error and $epsilon$-error (i.e. vanishing error) criteria. For the special case of this problem with $f(X,Y) = Y$ and $g(X,Y) = X$, we show that the $epsilon$-error optimum rate is also achievable with zero error. This result extends to a more general `complementary delivery index coding problem with arbitrary number of messages and decoders. For other functions, we show that the cut-set bound is achievable under $epsilon$-error if $X$ and $Y$ are binary, or if the functions are from a special class of `compatible functions which includes the case $f=g$.
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This paper simplifies an existing coding scheme for the two-receiver discrete memoryless broadcast channel with complementary receiver side information where there is a passive eavesdropper and individual secrecy is required. The existing coding scheme is simplified in two steps by replacing Wyner secrecy coding with Carleial-Hellman secrecy coding. The resulting simplified scheme is free from redundant message splits and random components. Not least, the simplified scheme retains the existing achievable individual secrecy rate region. Finally, its construction simplicity helps us gain additional insight on the integration of secrecy techniques into error-correcting coding schemes.
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This paper investigates the capacity regions of two-receiver broadcast channels where each receiver (i) has both common and private-message requests, and (ii) knows part of the private message requested by the other receiver as side information. We first propose a transmission scheme and derive an inner bound for the two-receiver memoryless broadcast channel. We next prove that this inner bound is tight for the deterministic channel and the more capable channel, thereby establishing their capacity regions. We show that this inner bound is also tight for all classes of two-receiver broadcast channels whose capacity regions were known prior to this work. Our proposed scheme is consequently a unified capacity-achieving scheme for these classes of broadcast channels.
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This paper investigates the capacity region of the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) may know some of the messages requested by other receivers as side information. We first classify all 64 possible side information configurations into eight groups, each consisting of eight members. We next construct transmission schemes, and derive new inner and outer bounds for the groups. This establishes the capacity region for 52 out of 64 possible side information configurations. For six groups (i.e., groups 1, 2, 3, 5, 6, and 8 in our terminology), we establish the capacity region for all their members, and show that it tightens both the best known inner and outer bounds. For group 4, our inner and outer bounds tighten the best known inner bound and/or outer bound for all the group members. Moreover, our bounds coincide at certain regions, which can be characterized by two thresholds. For group 7, our inner and outer bounds coincide for four members, thereby establishing the capacity region. For the remaining four members, our bounds tighten both the best known inner and outer bounds.
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