近幾年來，隨著網路的發展，資料的廣播也受到相當程度的重視，多方的相關研究也群雄並起，其中之一的湧泉碼(Fountain codes)，編碼方式就如同名字一樣，像湧泉般不間斷的釋放出碼字，即是一種單一發送端，對多方接受端的編碼機制。發送端會不斷的編碼，接受端根據本身不同的通道狀態，接受到不同的碼字。因為，發送端是根據一定的資料進行編碼，因此接受端，在傳輸的過程中，若因通道的干擾而產生碼字的遺失，還是可以透過，其他接受到的碼字，而恢復原始的資料。在許多不同形式的湧泉碼中，其中最先被實踐的LT碼(LT codes)和生長碼(Growth codes)。
最近受到更多注意在無碼率編碼特徵是接收到相當數量編碼過的的碼字，所有的原始資訊有相當高的機率被解碼恢復。與LT碼不同的是生長碼能夠在不同階段接收到新編碼過的碼字後即時解碼，如此可以漸漸的恢復原始資訊。
這是生長碼在網路應用需要的好處，例如:圖片能夠逐漸的顯示。在這篇論文中，我們將生長碼應用在多播式通訊中。為了能提升傳輸速度，簡單在接收端根據不同的目的選擇使用不同的位元回應自動要求重傳演算法，包括首先到達回應，最後到達回應和多數決到達回應。在多使用者環境下考慮通道為獨立通道與相關通道，與原始不使用自動要求重傳演算法的生長碼比較，比較結果顯示改進方案會有效地減少碼字傳送量。

Luby Transform (LT) codes and Growth codes are fountains codes which receivemore attention recently in their rateless encoding characteristic. Once an enough amount of encoded symbols are correctly received, all information
symbols could be recovered with high probability. Different from the characteristic of LT codes which promptly recover most information symbols in the latter receiving stages, Growth codes gradually recover them in every receiving
stage. This is a desirable advantage of Growth codes for some internet applications such as picture showing. In this thesis, we consider applying Growth codes for multicast communication. In order to speed up the transmissions
and therefore the reception and decoding processes, simple Automatic Repeat reQuest (ARQ) algorithms using 1-bit acknowledgment, ACK at first arrival, ACK at last arrival and ACK at majority arrival are proposed for various
purposes. Both independent and dependent erasure channels are considered. Compared to the original scheme without using ARQ, the simulation results show that the proposed schemes with the superiorities of effectively reducing
the encoding overheads.

[1] Songqing Zhao, Daniela Tuninetti, Rashid Ansari, and Dan Schonfeld,”Mutiple Description Coding Over Correlated Multipath Erasure channels,”March 31 2008-April 4 2008 Page(s):2153 - 2156 Digital Object Identifier 10.1109/ICASSP.2008.4518069

[2] Dimakis, A.G.; Jiajun Wang; Ramchandran, K.; ”Unequal Growth Codes: Intermediate Performance and Unequal Error Protection for Video Streaming,” 1-3 Oct. 2007 Page(s):107 - 110 Digital Object Identifier
10.1109/MMSP.2007.4412829

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