8 research outputs found
On the Capacity of the Finite Field Counterparts of Wireless Interference Networks
This work explores how degrees of freedom (DoF) results from wireless
networks can be translated into capacity results for their finite field
counterparts that arise in network coding applications. The main insight is
that scalar (SISO) finite field channels over are analogous
to n x n vector (MIMO) channels in the wireless setting, but with an important
distinction -- there is additional structure due to finite field arithmetic
which enforces commutativity of matrix multiplication and limits the channel
diversity to n, making these channels similar to diagonal channels in the
wireless setting. Within the limits imposed by the channel structure, the DoF
optimal precoding solutions for wireless networks can be translated into
capacity optimal solutions for their finite field counterparts. This is shown
through the study of the 2-user X channel and the 3-user interference channel.
Besides bringing the insights from wireless networks into network coding
applications, the study of finite field networks over also
touches upon important open problems in wireless networks (finite SNR, finite
diversity scenarios) through interesting parallels between p and SNR, and n and
diversity.Comment: Full version of paper accepted for presentation at ISIT 201
Achievable rate region for three user discrete broadcast channel based on coset codes
We present an achievable rate region for the general three user discrete
memoryless broadcast channel, based on nested coset codes. We characterize
3-to-1 discrete broadcast channels, a class of broadcast channels for which the
best known coding technique\footnote{We henceforth refer to this as Marton's
coding for three user discrete broadcast channel.}, which is obtained by a
natural generalization of that proposed by Marton for the general two user
discrete broadcast channel, is strictly sub-optimal. In particular, we identify
a novel 3-to-1 discrete broadcast channel for which Marton's coding is
\textit{analytically} proved to be strictly suboptimal. We present achievable
rate regions for the general 3-to-1 discrete broadcast channels, based on
nested coset codes, that strictly enlarge Marton's rate region for the
aforementioned channel. We generalize this to present achievable rate region
for the general three user discrete broadcast channel. Combining together
Marton's coding and that proposed herein, we propose the best known coding
technique, for a general three user discrete broadcast channel.Comment: A non-additive 3-user discrete broadcast channel is identified for
which achievable rate region based on coset codes is analytically proven to
be strictly larger than that achievable using unstructured iid codes. This
version is submitted to IEEE Transactions on Information Theor
Recommended from our members
On the capacity of the finite field counterparts of wireless interference networks
This paper explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over \(\mathbb p are analogous to n × n vector (MIMO) channels in the wireless setting, but with an important distinction - there is additional structure due to finite field arithmetic, which enforces commutativity of matrix multiplication and limits the channel diversity to n, making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity or linear capacity optimal solutions for their finite field counterparts. This is shown through the study of capacity of the 2-user X channel and linear capacity of the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over p also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between p and SNR, and n and diversity. © 2014 IEEE. n
Recommended from our members
On the capacity of the finite field counterparts of wireless interference networks
This paper explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over \(\mathbb pn are analogous to n × n vector (MIMO) channels in the wireless setting, but with an important distinction - there is additional structure due to finite field arithmetic, which enforces commutativity of matrix multiplication and limits the channel diversity to n, making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity or linear capacity optimal solutions for their finite field counterparts. This is shown through the study of capacity of the 2-user X channel and linear capacity of the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over pn also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between p and SNR, and n and diversity. © 2014 IEEE