Design ofNonbinary Quasi-CyclicLDPC Cycle
Rong-Hui PengandRong-Rong Chen Codes · 2007
Inthispaper, we studythedesign ofnonbinary low-density parity-check (LDPC)cycle codesoverGalois field GF(q). First, we construct a special class ofnonbinary LDPC cycle codeswithlowerrorfloors. Ourconstruction utilizes the cycle elimination algorithm toremoveshort cycles inthenormal graphandtoselect nonzero elements intheparity-check matrix toreducethenumberoflow-weight codewords generated by short cycles. Furthermore, weshowthatsimple modifications of suchcodesareparallel sparse encodable (PSE). ThePSEcode, consisting ofaquasi-cyclic (QC)LDPC cycle codeandasimple treecode, hastheattractive feature thatitisnotonlylinearly encodable, butalso allows parallel encoding whichcanreduce the encoding timesignificantly. We provide asystematic comparison betweennonbinary codedsystems andbinary codedsystems. FortheMIMO channel considered, ourresults showthatthe proposed nonbinary system employing thePSEcodeoutperforms notonlythebinary LDPCcodespecified inthe802.16e standard, butalsotheoptimized binary LDPC codeobtained usingthe EXITchartmethods.