配合軟資訊傳遞的和積演算法，因式圖形已經被證實不僅能夠以十分優雅的方法、分散式的解決多維度最佳化的問題，同時亦很可能達到最佳解。最近，在通訊系統上應用因式圖形的一個聞名的例子就是低密度同位檢查碼。低密度同位檢查碼實質上已將通訊頻道的頻道容量推到最高可能達到的Shannon極限。在本論文中，我們應用因式圖形的構想來解決無線環境下的網路問題。我們相信這種做法將代表一個全新的突破，而其影響將十分深遠。

使用者定位、動態頻道指定、和廣播排程問題等等全都是無線網路的問題，雖然此等問題的複雜度繁易不一。但是，到目前為止，大家在處理上述的無線網路問題時，總是採用非最佳化的解決方式。這個現象是由於以下的所有或部分原因所造成：1) 在無線網路中，通常有太多的參數同時需要最佳化。2) 無線網路的參數以各種複雜的方式、整體性的相互影響，因而導致最佳化的困難。3) 如果採取集中式的最佳化處理，中央處理中心必須收集網路中的所有網路參數。這是不切實際的做法。4) 如果採取分散式的最佳化處理，演算法追求的通常只是區域性的最佳化，而不是整體的最佳化。區域性的最佳化的效果，有可能遠遠不及整體的最佳化的效果。

網路問題天生便是分散式的問題。因此，網路問題非常匹配以因式圖形為基礎的演算法之特性。本論文將提出非常多個全新的因式圖形演算法來解決上述的無線網路問題。基本上，這些演算法有能力解出整體的最佳化的結果，同時並兼顧演算法的分散性特性與非常低複雜度的要求。除此之外，這些因式圖形演算法可以被應用在分時多工/分碼多工/正交分頻多工的各種通訊系統中：也就是說，應用在第二代/第三代/第四代的各種系統多工模式。在多階層、不規則形狀的無線網路細胞、傳輸多時率訊息的無線網路下，這些因式圖形演算法的優勢將變得格外明顯。這是因為因式圖形演算法天生就是調適性，可以隨著網路狀況的變化而作出適當的調適。相關於因式圖形演算法的各種表現極限、強韌性、穩定性、最佳化程度、與複雜度也都將在本論文中作有系統的分析。

Factor graphs, together with soft-information-passing sum-product algorithms, are known to be able to elegantly solve complex multi-dimensional optimization problems in a distributed low-complexity manner and are likely to reach an optimal solution. One famous recent application of the factor graph is on the LDPC (Low Density Parity Check) code, which virtually pushes the channel capacity to the Shannon limit. In this thesis, we propose to apply the factor graph ideas to solve network problems in wireless scenarios. We believe this approach is revolutionary and its impact is significant.

Position location, dynamic channel assignment, and broadcast scheduling problem are all wireless network problems with various degrees of complexity. Up to now, people always go for sub-optimal solutions in solving these problems due to (part of) the following reasons: 1) There are way too many parameters to optimize in a wireless network. 2) The network parameters interact among themselves jointly in a very complicated way and difficult to optimize. 3) Collecting all the network parameters from all the network nodes to have a centralized joint process is unpractical. 4) Most distributed approaches proposed in the literature are only locally optimal, sometimes far worse than the globally optimal solution.

Since network problems are by nature distributed, which happens to perfectly suit the characteristics of the factor-graph-based algorithms. Quite a few brand new factor-graph-based algorithms are proposed in this thesis to solve the wireless network problems described above. These algorithms are expected to reach the globally optimal solution while remaining distributed and very low complexity. In addition, these algorithms can be applied to TDMA/CDMA/OFDMA systems, i.e. systems with respectively 2G/3G/4G multiple access schemes. The advantages of these algorithms are especially obvious when dealing with wireless networks with multi-layer irregularly-shaped wireless network cells and with multi-rate data transmission, since these algorithms are naturally adaptive and can dynamically adjust themselves to the variation of the network scenario. Various performance bounds, robustness, stability, optimality and complexity of the proposed factor-graph-based algorithms are also systematically analyzed in this thesis.

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