posted on 2015-05-18, 00:00authored byA. Dytso, D. Tuninetti, N. Devroye
In multiuser information theory, it is often assumed
that every node in the network possesses all codebooks used in
the network. This assumption may be impractical in distributed
ad hoc, cognitive, or heterogeneous networks. This paper
considers the two-user interference channel with one oblivious
receiver (IC-OR), i.e., one receiver lacks knowledge of the
interfering cookbook, whereas the other receiver knows both
codebooks. This paper asks whether, and if so how much, the
channel capacity of the IC-OR is reduced compared with that of
the classical IC where both receivers know all codebooks. A novel
outer bound is derived and shown to be achievable to within
a gap for the class of injective semideterministic IC-ORs; the
gap is shown to be zero for injective fully deterministic IC-ORs.
An exact capacity result is shown for the general memoryless
IC-OR when the nonoblivious receiver experiences very strong
interference. For the linear deterministic IC-OR that models the
Gaussian noise channel at high SNR, nonindependent identically
distributed. Bernoulli(1/2) input bits are shown to achieve
points not achievable by i.i.d. Bernoulli(1/2) input bits used in
the same achievability scheme. For the real-valued Gaussian
IC-OR, the gap is shown to be at most 1/2 bit per channel use,
even though the set of optimal input distributions for the derived
outer bound could not be determined. Toward understanding the
Gaussian IC-OR, an achievability strategy is evaluated in which
the input alphabets at the nonoblivious transmitter are a mixture
of discrete and Gaussian random variables, where the cardinality
of the discrete part is appropriately chosen as a function of
the channel parameters. Surprisingly, as the oblivious receiver
intuitively should not be able to jointly decode the intended
and interfering messages (whose codebook is unavailable), it is
shown that with this choice of input, the capacity region of the
symmetric Gaussian IC-OR is to within 1/2 log (12πe) ≈ 3.34 bits
(per channel use per user) of an outer bound for the classical
Gaussian IC with full codebook knowledge at both receivers.
Funding
The work of the authors was partially funded by NSF under award number
1017436. The contents of this article are solely the responsibility of the authors
and do not necessarily represent the official views of the NSF.
History
Publisher Statement
This is a non-final version of an article published in final form in Dytso, A., Tuninetti, D. and Devroye, N. On the two-user interference channel with lack of knowledge of the interference codebook at one receiver. Ieee Transactions on Information Theory. 2015. 61(3): 1257-1276. DOI: 10.1109/TIT.2015.2388481.