低密度奇偶檢查迴旋碼其遮蔽機制與編碼限制條件放寬之研究

Abstract

低密度奇偶檢查迴旋碼須滿足徵狀形成矩陣之零空間。透過對其徵狀形成矩陣 加上一個條件限制, 我們可以直接利用此徵狀形成矩陣造出其徵狀形成編碼器編碼 器。首尾相連和收尾是兩種用來完成低密度奇偶檢查迴旋碼之編碼的機制。 在本論文中我們介紹三個主題。我們在第一個主題介紹針對首尾相連低密度奇 偶檢查迴旋碼提出的效能改善機制, 透過對其使用遮蔽機制, 我們能夠大幅改善其 效能。接著我們從陷阱碼字的觀點來分析這種效能改善並且提出與遮蔽式首尾相連 低密度奇偶檢查迴旋碼相對應的徵狀形成編碼器。第二個主題將介紹針對收尾低密 度奇偶檢查迴旋碼提出的效能改善機制, 我們分析徵狀形成編碼器的特性後發現其 在編碼過程中有些碼字位元必定為0, 在傳送時這些位元可不被傳送, 因此減少碼率 損失。在最後一個主題我們放寬使用徵狀形成編碼器所需的條件限制, 並說明此限 制並非編碼所必要的, 最後我們提供放寬限制條件後的編碼器造法。

Low density parity check convolutional codes (LDPC-CCs) are usually defined as the null space of their syndrome former matrices. With a certain constraint on the syndrome former matrices, LDPC-CCs can be fast encoded by syndrome former encoders. When encoding, zero padding and tail biting are two often-used schemes for trellis termination.

There are three topics for investigation in this thesis. Two methods used to improve the performance of the terminated LDPC-CCs and tail biting LDPCCCs are introduced in the first two topics. For the tail biting LDPC-CCs, masking technique is used to improve the bit-error-rate (BER) performance. From the viewpoint of trapping sets, the performance improvement is then discussed. The variations on encoder and decoder of the tail biting LDPC-CCs corresponding to the masking technique are also proposed. For the terminated LDPC-CCs, by analyzing the structure of its syndrome former encoder, wesuggest to avoid sending some known bits when codewords are transmitted, thus alleviating the possible rate-loss. Simulation results show that the codes utilizing these two methods have much better performance. In the last topic, we show that syndrome former matrices violating the constraint, which make fast encoding feasible, are not necessarily with poor BER performance. Thus we relax the constraint on syndrome former matrices of LDPC-CCs. Under the relaxed constraint, the encoding method is then presented.