全光都會網狀/環狀骨幹及其互聯之光纖及無線擷取網路整合技術---子計畫四：高速移動與高速傳輸擷取網路的結合通道估量、等化與錯誤更正之最佳整合系統設計、分析與實作

Abstract

在本計畫中，我們將針對未知通道參數的慢速與快速時變多路徑衰減通道，研究 並設計結合通道參數估量、等化與錯誤更正的非線性通道碼的系統化建碼規則，與其 相對之最大概度解碼演算法。經由過去的研究努力，我們發現在慢速時變多路徑衰減 通道上，效能好的非線性通道碼，都會符合一個共通的數學性質，運用這個數學性質， 我們找到並初步證明非線性通道碼的系統化的碼樹建碼規則。在我們的規則下所建立 的碼表，與由史崔克蘭等研究者電腦搜尋之最佳碼幾乎沒有效能上的分別；同時經由 數學推導，我們也得出可適用於非線性通道樹碼的循序解碼法的最大概度自我疊代解 碼量度公式。這樣一來，大大的提升了結合通道參數估量、等化與錯誤更正的非線性 通道碼的實用性，同時在高速移動載具下進行高速傳輸的目標，應可以藉由非線性通 道碼的引入而達成。 本計畫將分三年從三方面著手。第一年將著重於系統理論架構的延伸與確立，將 同樣的分析技巧，推廣至在通道參數在一個解碼區塊會有數次改變之快速時變系統。 第二年在第一年所建立的系統架構下，將非線性通道碼的循序解碼法的最大概度自我 疊代解碼量度公式，延伸至維特比解碼法，以進一步降低解碼複雜度。第三年將設計 可適用於快速時變或是以多種不同速率改變通道參數的碼表建立規則，並配合第二年 之解碼法，進行長碼長的整體系統模擬。

In this project, the principle and practice of non-linear error correcting codes, jointly considering channel estimation and equalization, for slowly and fast multi-path fading channels will be developed, along with their corresponding maximum-likelihood decoding algorithms. After two years of working on this subject, we have found a common mathematical property that all good (non-linear) codes have to satisfy for fading channels. Based on this property, we can construct codes by rules, not by computer searches, which have comparable performance to the computer-searched optimal code by Skoglund. Moreover, a maximum-likelihood recursive decoding metric formula for sequential decoding algorithms for our codes has been established. Our achievement made feasible the combining-estimation-and-equalization codes over the fading channels. As a result, reaching high transmission rate in a highly mobile environment may become an achievable goal by the introduction of our codes. The tasks that are going to perform in this project can be chronologically divided as follows. In the first year, we will focus on the underlying principle behind the considered system. Efforts will be mostly on the extension of the established result in slowly fading channels to fast fading ones, in which the channel parameters may have several unaware changes within one decoding block. In the second year, attempts will be made to extend the maximum-likelihood recursive decoding metric for sequential decoding algorithms to Viterbi-like decoding so that the decoding complexity can be further reduced. In the third year, the code construction rules for fast time-varying channels will be researched and designed. Complete system simulations based on the constructed codes and the proposed decoding algorithms will also be performed.