Research On The Root-LDPC Construction Algorithms For Block Fading Channels

With the development of the mobile communication age, people require the wireless communication system to be more and more reliable and effective. Interference is a fundamental nature of wireless communication systems with multiple transmissions, mobilie and multiple frequencies. To deal with the different interference, the communication systems must adopt advanced error correction coding techniques to achieve improved reliability and throughput. For different wireless fading channel, the design of optimal error correcting code is an important research problem. The block fading channel is a channel model which is particularly relevant in wireless communications situations involving slow time frequency hopping system. Supposing the base station and mobile station almost have no relative move, the channel fading remains constant for some time. The channel is memory when the channel varies slowly compared to the symbol duration. Low Density Parity Check codes (LDPC) have achieved performance close to the channel capacity in memoryless ergodic channels. However, Classical capacity-achieving graph codes can not approach the outage limit and perform well over block fading channels. Thus specifically designing codes for block fading channels become a hot issue.The issue overviews the block fading channel coding and introduce the development history, research significance and status. The block fading channel model is elaborated. Two main parameters characterize the error rate performace on block fading channel:the diversity order and the coding gain. The outage probability defines the information theoretical limit on such non-ergodic wireless channels and can not be surpassed by the word error probability of any coding scheme. Root Check LDPC (Root-LDPC) can sufficient to achieve the outage probability limit over block fading channels. According to the basic principles of Root-LDPC codes, the check matrix plays a crucial role in the encoding process or the decoding process. A good Root-LDPC code must has the good performance and need less decoding time. Therefore, constructing a Root-LDPC code with the good performance and the low encoding/decoding complexity has been a deserving study.This issue focuses on two main constructing algorithms of parity check matrix: Progressive Edge-Growth (PEG) algorithm and Quasi-cycle (QC) algorithm based on the Root-LDPC. PEG algorithm progresses on an edge-by-edge basic. Edge placements are such that when a cycle is created, that cycle is of maximum possible length. But the PEG algorithm does not considerate the connectivity of the cycles. We use the ACE metric to modify the traditional PEG algorithm to ensure having better performance.The new algorithm is named MPEG algorithm. However, essentially MPEG algorithm is one of the greedy algorithms which have the high complexity. Meanwhile the QC algorithm has low complexity because of its quasi cycle feature. The paper combines the MPEG algorithm and QC algorithm, which guarantees not only the performance but also the quasi cycle feature. The novel algorithm reaches a tradeoff between the code performance and the encoding/decoding complexity, so that it is more suitable for the practical application. Simulation results demonstrate that the combination algorithm can achieve full diversity and better code performance, suitable to different fading blocks. For medium to high SNR, the average required number of iterations can be decreased.