1 research outputs found
A unified graphical approach to random coding for multi-terminal networks
A unified approach to the derivation of rate regions for single-hop
memoryless networks is presented. A general transmission scheme for any
memoryless, single-hop, k-user channel with or without common information, is
defined through two steps. The first step is user virtualization: each user is
divided into multiple virtual sub-users according to a chosen rate-splitting
strategy which preserves the rates of the original messages. This results in an
enhanced channel with a possibly larger number of users for which more coding
possibilities are available. Moreover, user virtualization provides a simple
mechanism to encode common messages to any subset of users. Following user
virtualization, the message of each user in the enhanced model is coded using a
chosen combination of coded time-sharing, superposition coding and joint
binning. A graph is used to represent the chosen coding strategies: nodes in
the graph represent codewords while edges represent coding operations. This
graph is used to construct a graphical Markov model which illustrates the
statistical dependency among codewords that can be introduced by the
superposition coding or joint binning. Using this statistical representation of
the overall codebook distribution, the error probability of the code is shown
to vanish via a unified analysis. The rate bounds that define the achievable
rate region are obtained by linking the error analysis to the properties of the
graphical Markov model. This proposed framework makes it possible to
numerically obtain an achievable rate region by specifying a user
virtualization strategy and describing a set of coding operations. The largest
achievable rate region can be obtained by considering all the possible
rate-splitting strategies and taking the union over all the possible ways to
superimpose or bin codewords