本論文中，我們基於因式圖模型搭配了和積演算法、最大乘積演算法來建立低複雜度、高通道容量及高傳輸率的資源分配演算法
發展出適用於MIMO系統接收端天線選擇、MIMO系統使用者天線選定以及天使用者子頻段分配等資源分配問題。

對於MIMO多使用者傳送端天線選定問題中我們利用因式圖模型以及搭配最大乘積演算法，提出相對於Hungarian演算法較快速的多使用者傳送端天線選定演算法。
並且考慮當使用者人數K>M的情況下，我們利用已知的通道資訊以及每位使用者與傳輸天線之間的關係建立因式圖模型。以及利用最大乘積演算法作為
軟式資訊交換的核心運算。如此一來，不但大幅的減少了不必要的加法或乘法運算量而且可以對於每個使用者與每根傳送天線之間能有更週全的考量。

另外，對於正交分頻多工超寬頻無線通訊系統中多使用者子頻段的分配問題，我們利用因式圖模型搭配加權和積演算法來對於Greedy演算法提出
能分配出較高整體平均傳輸率的使用者子頻段分配演算法。我們使用軟式資訊及以使用者所要求的傳輸率為基礎，於使用者因式點(Agent node)上
使用了對於軟式資訊加權的權重，因此有助於對所有使用者與子頻段之間能做更細部的調整。

最後，經由實驗結果可以發現我們所提出的天線選定演算法可以比Hungarian演算法擁有更高的通道容量以及較少的計算時間(約30%)。
更進一步，我們同時考慮並整合公平性與天線選定演算法後仍可以比傳統的Hungarian演算法與公平性演算法分開處理的作法，同樣有較高的通道容量
以及較少的運算時間。我們所提出的子頻段分配演算法與Greedy演算法比較之下，我們所提出的多使用者子頻段分配演算法的確可以將整體平均傳輸速率提昇30Mbps
之多。

In the thesis, we make use of the factor graph to develop some low complexity, yet high resource algorithm for resofurce allocation problems in wireless communications.
First, we develop two new algorithms based on the factor graph model along with max-product algorithm.
We use the original channel state information as our soft information, and then use the max-product algorithm to exchange the soft-information in between.
The algorithms considered collect and pass the maximum soft information to the desire variable node without extra computations,
thus calling for lower complexity than the existing approach such as the Hungarian algorithms.

Second, we consider the sub-band allocation problem in MB-OFDM UWB systems.
For the new factor graph based approach along with the sum-product algorithm is addressed.
By passing the soft information among the variable nodes and the agent nodes, An ingeneous choice of the weights are also imposed in the soft
information exchange process to enhance the possbility of choosing appropriate subbands.

Conducted simulations show that our proposed multi-user antenna assignment algorithm can attain higher channel capacity with lower computational
time compared with previous works.
Likewize the new multi-user MB-OFDM chanel allocation algorithm can reach the higher average transmission rate than the classical Greedy algorithm.

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