Research Of Generalized LDPC Code Technology

Low density parity check code (LDPC Codes) is a kind of linear block code,like the Turbo code, it has excellent error correction performance which is veryclose to the Shannon limit. LDPC becomes a strong competitor for channelcoding scheme in modern communication systems, has already been applied inthe actual system, such as WiFi, WiMax and so on. Generalized low densityparity check code (GLDPC Codes) is the concept extension of LDPC code; it isconstructed by replacing each single parity check in Gallager’s LDPC codeswith the parity check matrix of a small linear block code called the constituentcode. GLDPC code has some advantages beyond the traditional LDPC code. Itserror floor is very low. It is agile to choose its component code, so it supportsmultiple code rates and multiple code lengths more easily. Its decodingperformance is still very good when its code rate is low. Its hard decisiondecoding performance is extremely good, so it is suitable for high speedtransmission system. GLDPC code has a good application prospect in the opticalfiber transmission, satellite laser communication and storage system, someliteratures show that it has been used in100Gb/s optical fiber system.Consideration of its application prospect and less research paper for it, theresearch of GLDPC code has very important significance.This article studysGLDPC code’s key technologys, such as construction, encoding and decodingand so on.In respect of the construction, with the absorption of the idea for traditionalconstruction, the improved PEG algorithm is proposed to construct code. Because GLDPC’s minum hanming distance grows with mother matrix’s girthexponentially and PEG algorithm will gain as large girth code as possible, thecode contructed has good performance and low error floor. The new method ispracticable according to the results of simulation with Comparision of2traditional pseudo random construction methods, Boutros’s method andLentmaier’s method.This paper introduces three code structures which have efficient encodingalgorithm. The first structure is based on matrix decomposition algorithm, itsquick encoding algorithm absorbs the idea of the RU decomposition algorithmand takes use the special matrix structure of GLDPC code, but it is moreefficient than RU algorithm. Then, inspired by the fast coding structurecombined with QC and RA for the traditional LDPC code standard, the paperextends the idea of RA and QC structure to GLDPC code, and proposes astructure combined with QC and RA which is suitable for fast coding. Itsstructure is like RA structure, so it can use encoding algorithm based on iterativedecoding and is very fast for encoding. It has the QC structure and so supportsparallel decoding, whose throughput is higher respectly, and its girth is larger, itserror floor is lower. From the simulation results, the BER of the proposedstructure code is only less than traditional pseudo random construction codeswithin0.3dB.In respect of the decoding, this paper’s researches focus on the hard decisionalgorithm and its hardware implementation, while soft decision algorithm isbased on the information propagation algorithm and it is almost the same withLDPC code’s soft decoding algorithm except calculation of its extra information,which needs a SISO decoder for component code decoding, but not minum summethod, because check nodes is component code rather than SPC. There is lot ofresearch of the SISO decoding algoritm for linear block code. The hardwareimplementation of soft decoding algorithm is very hard, so it is not suitable forhigh speed transmission system. There are many hard decision algorithms forGLDPC, which are most based on the bit flip algorithm. The non-vote bits fliphard decision algorithms only take use of the component code’s error correction, while weighted bits flip vote (WBFV) algorithm further utilizing thecharacteristic that the error bit position can be determined by the componentcode for its bit flip strategy, so it gains a better decoding performance. WBFValgorithm is hard for hardware implementation, because there is a need of themaximum value finding module for its bit flip strategy which needs to find themaxium voting pair value from all bits. Supposed that the code length is N, andthen if the max finding is serially processed, it takes N cycles to get the result,while parallelly finding needs Nlog(N) comparators. So this paper puts forwardan improvement algorithm that it replaces maximum voting finding method witha group voting rule suitable for hardware implementation. The paper simulatesthe improved algorithm with GLDPC of different code length, differentcomponent code and different bit node degree. The simulation results show thatthe improved algorithm performance is almost the same with the originalalgorithm, but it speeds up the iterative convergence greatly, especially when bitnode degree is big, its effect is very apparent and iterations decrease to5fromoriginal25to gain the BER for10-5. Finally, the paper proposes a hardwaredesign for the improved algorithm, which is a full parallel solution and has avery high throughput.