15 research outputs found
Locally Decodable Index Codes
An index code for broadcast channel with receiver side information is locally
decodable if each receiver can decode its demand by observing only a subset of
the transmitted codeword symbols instead of the entire codeword. Local
decodability in index coding is known to reduce receiver complexity, improve
user privacy and decrease decoding error probability in wireless fading
channels. Conventional index coding solutions assume that the receivers observe
the entire codeword, and as a result, for these codes the number of codeword
symbols queried by a user per decoded message symbol, which we refer to as
locality, could be large. In this paper, we pose the index coding problem as
that of minimizing the broadcast rate for a given value of locality (or vice
versa) and designing codes that achieve the optimal trade-off between locality
and rate. We identify the optimal broadcast rate corresponding to the minimum
possible value of locality for all single unicast problems. We present new
structural properties of index codes which allow us to characterize the optimal
trade-off achieved by: vector linear codes when the side information graph is a
directed cycle; and scalar linear codes when the minrank of the side
information graph is one less than the order of the problem. We also identify
the optimal trade-off among all codes, including non-linear codes, when the
side information graph is a directed 3-cycle. Finally, we present techniques to
design locally decodable index codes for arbitrary single unicast problems and
arbitrary values of locality.Comment: Accepted for publication in the IEEE Transactions on Information
Theory. Parts of this manuscript were presented at IEEE ISIT 2018 and IEEE
ISIT 2019. This arXiv manuscript subsumes the contents of arXiv:1801.03895
and arXiv:1901.0590
Locally Decodable Index Codes
An index code for broadcast channel with receiver side information is locally decodable if each receiver can decode its demand by observing only a subset of the transmitted codeword symbols instead of the entire codeword. Local decodability in index coding is known to reduce receiver complexity, improve user privacy and decrease decoding error probability in wireless fading channels. Conventional index coding solutions assume that the receivers observe the entire codeword, and as a result, for these codes the number of codeword symbols queried by a user per decoded message symbol, which we refer to as locality, could be large. In this paper, we pose the index coding problem as that of minimizing the broadcast rate for a given value of locality (or vice versa) and designing codes that achieve the optimal trade-off between locality and rate. We identify the optimal broadcast rate corresponding to the minimum possible value of locality for all single unicast problems. We present new structural properties of index codes which allow us to characterize the optimal trade-off achieved by: vector linear codes when the side information graph is a directed cycle; and scalar linear codes when the minrank of the side information graph is one less than the order of the problem. We also identify the optimal trade-off among all codes, including non-linear codes, when the side information graph is a directed 3-cycle. Finally, we present techniques to design locally decodable index codes for arbitrary single unicast problems and arbitrary values of locality