7 research outputs found
On the Capacity of Abelian Group Codes Over Discrete Memoryless Channels
For most discrete memoryless channels, there does not exist a linear code for
the channel which uses all of the channel's input symbols. Therefore, linearity
of the code for such channels is a very restrictive condition and there should
be a loosening of the algebraic structure of the code to a degree that the code
can admit any channel input alphabet. For any channel input alphabet size,
there always exists an Abelian group structure defined on the alphabet. We
investigate the capacity of Abelian group codes over discrete memoryless
channels and provide lower and upper bounds on the capacity
Multilevel Polarization of Polar Codes Over Arbitrary Discrete Memoryless Channels
It is shown that polar codes achieve the symmetric capacity of discrete
memoryless channels with arbitrary input alphabet sizes. It is shown that in
general, channel polarization happens in several, rather than only two levels
so that the synthesized channels are either useless, perfect or "partially
perfect". Any subset of the channel input alphabet which is closed under
addition, induces a coset partition of the alphabet through its shifts. For any
such partition of the input alphabet, there exists a corresponding partially
perfect channel whose outputs uniquely determine the coset to which the channel
input belongs. By a slight modification of the encoding and decoding rules, it
is shown that perfect transmission of certain information symbols over
partially perfect channels is possible. Our result is general regarding both
the cardinality and the algebraic structure of the channel input alphabet; i.e
we show that for any channel input alphabet size and any Abelian group
structure on the alphabet, polar codes are optimal. It is also shown through an
example that polar codes when considered as group/coset codes, do not achieve
the capacity achievable using coset codes over arbitrary channels
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
On the capacity of abelian group codes over discrete memoryless channels
Abstract—For most discrete memoryless channels, there does not exist a linear code which uses all of the channel’s input symbols. Therefore, linearity of the code for such channels is a very restrictive condition and there should be a loosening of the algebraic structure of the code to a degree that the code can admit any channel input alphabet. For any channel input alphabet size, there always exists an Abelian group structure defined on the alphabet. We investigate the capacity of Abelian group codes over discrete memoryless channels and provide lower and upper bounds on the capacity. I
Group, Lattice and Polar Codes for Multi-terminal Communications.
We study the performance of algebraic codes for multi-terminal communications.
This thesis consists of three parts: In the rst part, we analyze the performance of
group codes for communications systems. We observe that although group codes are
not optimal for point-to-point scenarios, they can improve the achievable rate region
for several multi-terminal communications settings such as the Distributed Source
Coding and Interference Channels. The gains in the rates are particularly signicant
when the structure of the source/channel is matched to the structure of the underlying
group. In the second part, we study the continuous alphabet version of group/linear
codes, namely lattice codes. We show that similarly to group codes, lattice codes
can improve the achievable rate region for multi-terminal problems. In the third part
of the thesis, we present coding schemes based on polar codes to practically achieve
the performance limits derived in the two earlier parts. We also present polar coding
schemes to achieve the known achievable rate regions for multi-terminal communications
problems such as the Distributed Source Coding, the Multiple Description
Coding, Broadcast Channels, Interference Channels and Multiple Access Channels.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108876/1/ariaghs_1.pd