近年來噴泉碼被大家廣泛的討論，如同字面意思，只要給定某個編碼機制，編出來的碼就會如噴泉般源源不絕。LT碼為噴泉碼的一種編碼方式，其性能不錯且編碼及解碼的複雜度皆低。然而，當LT碼要在雜訊通道中運作時，因為有符際干擾現象發生，導致錯誤在LT硬式解碼中會更加蔓延。則其原本LT硬式解碼就無法使用，這個問題也無法由增加編碼封包來解決。信心度傳播演算法為為解決此問題的方法，然而，模擬顯示,使用信心度傳播演算法解碼後的位元錯誤率十分高，因此我們需要一些新的方法來降低錯誤率。
在本論文，我們將理德所羅門與LT碼結合，創造出一種嶄新的混合式噴泉碼。當錯誤在理得所羅門碼錯誤更正能力之內，則利用理得所羅門碼優異的解碼性能，將此部分正確訊息源解回，並移除線的連結，如此可大大減少接線數量,降低Tanner graph密度，進而降低複雜度。對數概似值比的計算是此法的重點，我們需要取出資訊源封包跟編碼封包的對數概似值比，才能做硬決策，論文中也推導出軟決策跟硬決策的結合方式，有時候我們有資訊源封包的硬決策值和編碼封包的軟決策值，有時候則是有資訊源封包的軟決策值和編碼封包的硬決策值。在上下傳多次後，有可能對數概似值比大過電腦可運算的範圍，此時利用近似公式去做運算。且若資訊源單純使用LT軟式解碼，有可能做再多次錯誤率依舊居高不下。使用混合式噴泉碼，則在複雜度降低的優點下，有機會達到位元錯誤率降至0。

Fountain codes have been widely discussed recently. The main characteristic is that the number of encoded packets is not fixed before the transmission. LT code is the first practical type of fountain code; it can achieve great performance and reach low coding and encoding complexities. Since LT codes act well on erasure channel, one might consider whether it can be applied on noisy channel. Because the inter-symbol interference (ISI), the packets may be contaminated. The detrimental effect of error propagation in LT hard decoding may occur. Belief propagation algorithm is a solution to avoid situation like this. However, the simulation results of the bit error rate turn out to be quite high. We need to come up with some method to improve the performance. In this thesis, we create a new type of codes called "Hybrid Fountain Codes" by combining Reed-Solomon codes and LT codes.
Under Reed-Solomon codes' correcting ability, errors can be corrected easily and Tanner graph can be updated. By passing information, renewing Tanner graph and removing connections, complexities can be reduced dramatically. The calculation of LLR is an important issue. We have to extract LLR value of both source packets and encoded packets so hard decision can be made. The combination of both hard and soft decision value is also important. Sometimes we have to combine encoded packets' soft decision with source packets' hard decision and vice versa. In this thesis, we derive unified computations for combining hard and soft decisions at the source nodes and encoded nodes. Sometimes the LLR value may be too large to deal with, so the approximate formula is also derived. The main advantage of this scheme is that the bit error rate can approach zero and total iteration times can be lower as compared to LT soft decoding only.

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