On the decoding of the (24, 12, 8) Golay code
On the decoding of the (24, 12, 8) Golay code
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关于 (24, 12, 8) Golay 码的解码
DOI：
10.1016/j.ins.2010.08.015
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
T. Truong
中科院分区：
文献类型：
--
作者：
Tsung;Hsin;Hung;T. Truong
提出了一种改进的伴随式移位寄存器译码算法--伴随式加权译码算法，用于（24，12，8）Golay码的三种可能错误的译码和四种错误的检测。该方法也可推广到其它两种短码的译码，如（15，5，7）循环码和（31，16，7）二次剩余码。该译码算法利用循环码的性质、伴随式的权值以及伴随式译码器中的缩减查找表（Reduced Size Lookup Table，RISK）来减少伴随式及其对应陪集首的数目。这种方法导致查找表的存储器需求的显著减少，从而产生更快的解码算法。仿真结果表明，该算法的译码速度比代数译码算法快约3.6倍。
An improved syndrome shift-register decoding algorithm, called the syndrome-weight decoding algorithm, is proposed for decoding three possible errors and detecting four errors in the (24,12,8) Golay code. This method can also be extended to decode two other short codes, such as the (15,5,7) cyclic code and the (31,16,7) quadratic residue (QR) code. The proposed decoding algorithm makes use of the properties of cyclic codes, the weight of syndrome, and the syndrome decoder with a reduced-size lookup table (RSLT) in order to reduce the number of syndromes and their corresponding coset leaders. This approach results in a significant reduction in the memory requirement for the lookup table, thereby yielding a faster decoding algorithm. Simulation results show that the decoding speed of the proposed algorithm is approximately 3.6 times faster than that of the algebraic decoding algorithm.