  In this paper, the Gaussian many-to-one X channel, which is a special case of
general multiuser X channel, is studied. In the Gaussian many-to-one X channel,
communication links exist between all transmitters and one of the receivers,
along with a communication link between each transmitter and its corresponding
receiver. As per the X channel assumption, transmission of messages is allowed
on all the links of the channel. This communication model is different from the
corresponding many-to-one interference channel (IC). Transmission strategies
which involve using Gaussian codebooks and treating interference from a subset
of transmitters as noise are formulated for the above channel. Sum-rate is used
as the criterion of optimality for evaluating the strategies. Initially, a $3
\times 3$ many-to-one X channel is considered and three transmission strategies
are analyzed. The first two strategies are shown to achieve sum-rate capacity
under certain channel conditions. For the third strategy, a sum-rate outer
bound is derived and the gap between the outer bound and the achieved rate is
characterized. These results are later extended to the $K \times K$ case. Next,
a region in which the many-to-one X channel can be operated as a many-to-one IC
without loss of sum-rate is identified. Further, in the above region, it is
shown that using Gaussian codebooks and treating interference as noise achieves
a rate point that is within $K/2 -1$ bits from the sum-rate capacity.
Subsequently, some implications of the above results to the Gaussian
many-to-one IC are discussed. Transmission strategies for the many-to-one IC
are formulated and channel conditions under which the strategies achieve
sum-rate capacity are obtained. A region where the sum-rate capacity can be
characterized to within $K/2-1$ bits is also identified.
