應用於短長度LT編碼之連線分佈改進

Abstract

適用於無線網路的影像傳輸是目前的一個熱門研究主題，如何解決在無線網路環境下通道品質的不穩定所帶來的影響是目前最主要的議題。LT編碼(LT codes)是一種湧泉碼(fountain codes)，並且在這個議題上有非常好的表現。LT編碼可以有效的減少雜訊所帶來的影響，但是在影像傳輸的應用上，長度較長的編碼相較於短長度的編碼會需要較長的緩衝時間。因此，在這篇論凜我們選擇使用短長度的LT編碼當作研究主題，並且改善其連線分佈進而增進編碼的效能。 在這篇論文裡，我們主要的做法是增加僅連線到一個的碼字(codeword)數量，並且提出一個新的編碼方式-不重複編碼，來減少這些碼字間的重覆情形。整個修正的演算法可以分成兩大迴圈。第一個迴圈主要是增加僅連線到一個的碼字數量，並減少其他的碼字，以增加碼字的有效使用率，並且增加整體的解碼率。但是因為之前的修正降低了整體資訊的涵蓋率，所以第二個部分主要就是要改進這方面的問題。最後的模擬結果顯示，我們的修正方式可以有效的增加整體的解碼率，並且可以有效的增加整體的解碼成功率。

Wireless video communication has become the most exciting research area recently. The main challenge is that the wireless channel quality varies greatly over time compared with wired network. Luby Transform (LT) codes, one kind of rateless codes, have good performance in this issue. For video streaming applications, although LT codes can reduce the effect of noise, more buffer time is needed with larger block length than those with short block length. Therefore, we choose short length LT codes, k = 1000, as the main target and modify degree distributions to enhance decoding performance in this thesis. The main idea of the modification is increasing the number of degree-1 codewords to prevent early decoding termination and using a new algorithm named Non-Repeat Encoding to avoid generating redundant degree-1 codewords. The whole modification can be separated into two iterative loops. At the first loop, it starts from slightly increasing the proportion of degree-1 codewords and scaling down the proportion of other codewords. Since it will result in more redundant codewords which have no contribution in decoding information symbol, the following step at the first loop is to modify degree distribution by reducing the number of low-degree codewords, except for degree-1, to enhance codeword utilization. In the end of the first loop, two criterions are developed to decide whether the loop terminates or not. One criterion is to ensure that the proportion of degree-1 codewords is lower than the upper-bound, which can be calculated by setting the highest possible channel erasure rate; the other is to check whether the symbol loss rate is lower than that of the previous step. Note that the first loop decreases average degree of codewords will cause lower probability of covering all information symbols. As a result, we raise the highest degree iteratively to compensate the full coverage probability at the second loop. As compared with conventional LT codes, simulation results show that our scheme can reduce symbol loss rate at least 2 orders from ε = 0.1 to ε= 0.3, where ε denotes the overhead of LT codes. Meanwhile, it can also achieve almost 40% improvement at successful decoding rate when ε= 0.1.