Arithmetic Decoding Algorithm for Binary Quadratic Residue Codes Using Syndrome-Weight Determination

• Main Authors: Zih-Heng Chen, 陳資衡
• Other Authors: Ming-Haw Jing
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/19388682862799593658

博士 === 義守大學 === 資訊工程學系博士班 === 99 === In communication systems, the data transmitted through a noisy channel might be corrupted so that it must be protected by error-correcting code to guarantee the decoded data same as the original data. If the communication channels have diffident purposes, diffident encoding and decoding schemes are selected. For example, the long code (e.g. LDPC code) is applied to DVB-S, and the short code (e.g. Hamming code) is applied to flash memory. The quadratic residue (QR) codes have the characteristic of relative large minimum distances when the length of codeword is less than 100. The famous (7, 4, 3) Hamming code and (23, 12, 7) Golay code also belong to the QR codes. However, Berlekamp indicated that these QR codes are good codes but are hard to decode. In this dissertation, we develop a novel arithmetic decoding algorithm, called syndrome-weight decoder, for the QR codes. The key idea is to obtain the needed syndromes which are calculated by XOR operations, and then to get the error positions determined by the weights of syndromes. The parallel architecture for (23, 12, 7) decoder has also been designed. Based on Altera Cyclone II FPGA (resp. TSMC 0.18-μm CMOS standard cell library), the area cost and the time delay are reduced by up to 86.4% (resp. 91.8%) and 22.5% (resp. 8.3%), respectively.