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Abstract:
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The primary challenge in communication over wireless networks, unlike wireline
networks, is the existence of interference and channel variations (fading). Having
more users at higher data rates means that current point-to-point networks will not
scale. To engineer a scalable network, we introduce a new paradigm that exploits
different network characteristics. We show that cooperation between users in the net-
work, network coding, not only reduces existing (destructive) interferences from other
users but it can also generate constructive interference, transforming the destructive
interference into useful information.
In this thesis, we explore the problem of source and channel coding over wireless
networks, ranging from information theoretical analysis to code design and practical
implementation issues. We show that significant gains in throughput can be achieved
through network coding. Despite the importance of the problem and the work done
on wireless networks, little is known about network coding and the effective use of the relaying function and cooperative strategy at the intermediate nodes. A notable
example is the lack of an optimal coding scheme over the relay channel, the simplest
form of a network, which has remained an outstanding open question for the last
three decades.
We propose new approaches to network coding that improve upon the best known
coding schemes by many decibels. Specifically, we develop two main coding tech-
niques, one for the multi-state relay channel and the other for the multiple access
with generalized feedback (MAC-GF). We show that by using the new coding tech-
niques, higher transmission rates than those previously known are achievable. The
first technique achieves the ultimate transmission rate (capacity) for both half-duplex
and the original relay channel under certain conditions. These improved capacity re-
sults for the relay channel are the only known results since Cover's in 1979 and El
Gamal's in 1982. The second coding technique improves the best known achievable
transmission rate for the MAC-GF by Willems in 1983. This latter result also im-
proves the achievable transmission rate for the Gaussian relay channel over all other
known schemes for some channel conditions.
We also present a practical code design technique for the relay channel. The
design gains more than 4dB over direct transmission and closes the gap to the relay
channel Shannon limit to less than 1dB with a code length of only 2 x 10^4 bits. The
new coding techniques and transmission strategies developed in this thesis provide
important steps toward overcoming the challenges of wireless network coding. |
