Design of LDPC coded Equalization over Partial Response Channel

根據以往對於消除通道的研究結果，使用曲線比對法來設計低密度同位檢查(low-density parity check , LDPC)碼已被應用在一些通訊相關的文獻中。ten Brink 等人發展出了在可相加白色高斯雜訊通道中使用二元相移調變情況下的曲線比對法，並將之延伸至衰竭通道下的多輸入輸出天線傳出系統。所以很自然的，我們可以將這個技巧用於其他的通訊系統，像是應用在符號互相干擾通道下使用整合等化與解碼的渦輪等化系統。在本篇論文中，我們研究於部分響應通道和渦輪等化的系統中，LDPC編碼之設計。如何繪製出結合等化器和變數節點解碼器的外質資訊轉換(extrinsic information transfer , EXIT)曲線，並用其來匹配檢查解碼器的資訊轉換特性將會是這個設計法的基礎。模擬結果證實藉由這個方法設計出來的不規則碼其效能的確較規則LDPC編碼佳，並在相同的疊代數目下能以較低的雜訊比收斂。The curve-fitting techniques to design low-density parity check (LDPC) codes motivated by results for erasure channels have already been applied in the communications literature. In the paper authored by ten Brink, et al, the curve-fitting approach for BPSK on the AWGN channel are developed and extended to MIMO fading channels. It is natural to consider once again applying this methodology in the outer coding of turbo equalization system, which is a joint equalization and decoding process to eliminate intersymbol interference. With the proposed scheme, we show a design of LDPC coded equalization system over partial response channel. The design is based on plotting various extrinsic information transfer (EXIT) curves of combined detector/equalizer and variable-node decoder to match the EXIT characteristics of check-node decoder. Simulation results verify that the performances of designed irregular codes are better than regular LDPC codes and converge at lower SNR with the same number of iteration.1 Introduction 1 2 Reviews on LDPC Codes 3 2.1 Representation of LDPC Codes…………..…………………………………….3 2.2 Encoding Methods……..……………………….………………………………6 2.3 Decoding Methods……………………………..….……………………………7 2.3.1 Gallager’s Hard Decision Decoding……………………………………...7 2.3.2 Sum Product Algorithm…………………..………………………………8 2.4 Some Constructions for Regular LDPC Codes….…………………………….10 2.4.1 Gallager’s Codes………………………….……………………………..10 2.4.2 Makay’s Code...………………………………………………………….11 2.4.3 Finite Geometries LDPC Codes.....……………………………………...12 2.5 Irregular LDPC Codes…………………..……………………………………..17 2.6 Construction of Irregular LDPC Codes Based on Masked EG-Gallager LDPC codes……………………………………………………………………18 3 Turbo Equalization over Partial Response Channels 24 3.1 Turbo Code and Turbo Principle………………………………………………25 3.1.1 Encoder of Turbo code…………………………………………………..25 3.1.2 The Iterative Decoder and BCJR algorithm…………..…………………26 3.2 Turbo Equalization…………………………………………………………….29 3.3 Partial Response Channel……………………………………………………...32 3.4 Simulations of LDPC Coded Turbo Equalization……………………………..34 4 Design of LDPC Codes Based on EXIT Charts 38 4.1 Extrinsic Information Transfer Analysis………………………………………39 4.2 LDPC Code Design for Partial Response Channel....…………………………44 4.2.1 EXIT Curve for the Inner VND……………...………………………….45 4.2.2 EXIT Curve for the Outer CND…………………………………………47 4.2.3 EXIT Curve for Code Mixture…………………………………………..48 4.2.4 EXIT Curve of the Combined MAP Detector and VND…...…………...49 4.2.5 Curve-Fitting and Design Example……………………………………...51 4.2.6 Modified Iteration Scheme...…………………………………………….58 5 Conclusion and Future Work 61 Bibliography 6