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Article overview
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Lattice Codes achieve the Capacity of Gaussian Broadcast Channels with Coded Side Information | | Lakshmi Natarajan
; Yi Hong
; Emanuele Viterbo
; | | Date: |
4 Sep 2015 | | Abstract: | Lattices possess elegant mathematical properties which have been previously
used in the literature to show that structured codes can be efficient in a
variety of communication scenarios, including coding for the additive white
Gaussian noise (AWGN) channel, dirty-paper channel, Wyner-Ziv coding, coding
for relay networks and so forth. Following the approach introduced by Erez and
Zamir, we show that lattice codes are optimal for the family of Gaussian
broadcast channels where the source transmits a set of common messages to all
receivers and each receiver has ’coded side information’, i.e., prior
information in the form of linear combinations of the messages. This channel
model, which is an instance of the Gaussian version of index coding, is
motivated by applications to multi-terminal networks where the nodes may have
access to coded versions of the messages from previous signal hops or through
orthogonal channels. The known results on the capacity of this channel are
based on random Gaussian codebooks. The structured coding scheme proposed in
this paper utilizes Construction A lattices designed over prime finite fields,
and ’algebraic binning’ at the decoders to expurgate the channel code and
obtain good lattice subcodes, for every possible set of linear combinations
available as side information. As a corollary, we show that lattice codes based
on Construction A can achieve the capacity of single-user AWGN channels with
the size ’p’ of the prime field growing as a function of the code length ’n’ as
’n^beta’, for any fixed ’beta>0’, which is the slowest yet reported in the
literature. | | Source: | arXiv, 1509.1332 | | Services: | Forum | Review | PDF | Favorites | |
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