廣義擴展視窗噴泉碼之有限長度分析

Abstract

噴泉碼 (fountain codes) 適合用在二進抹去通道 (binary erasure channel) 上的資料傳輸。當這種噴泉碼用於現場直播的即時傳輸應用時，由於有限的傳輸頻寬以及傳輸時間上的限制，往往會因為資料處理上的便利，而將串流媒體分割成許多小資料區塊，並依序對每一小資料區塊獨立進行編碼及解碼。但是，使用小塊的資料區塊做編碼及解碼會導致編碼的效率降低。因此，在此論文中我們介紹了一種方法來提高編碼效率，即利用逐漸加大的資料區塊做編碼及解碼。我們所採用的方法可以視為是更為一般化的擴展視窗噴泉碼 [6]。除此之外，我們還推導出了廣義擴展視窗噴泉碼的錯誤率分析，此分析是利用狀態產生函數 (state generating function) 所推導出來的。此狀態產生函數可以幫助廣義擴展噴泉碼的分析及設計，並可以做為一個效能評估的工具。

Fountain codes are suitable for data transmission over binary erasure channels. When such codes are applied in live broadcast applications, due to the limited bandwidth and delay constraints, it is often convenient to treat the input media stream as a concatenation of short data blocks and to encode each block individually. However, the use of a small block size may result in poor coding efficiency. In this thesis, we introduce an approach to enhance the coding efficiency by encoding over progressively more source bits. Our approach can be considered as a generalization of the expanding window fountain code concept. In addition, we provide an error analysis based on state generating functions. The state generating function is useful both as a performance evaluation tool and as a design criterion for the generalized expanding window codes.