An Improved Step-by-Step Decoding Algorithm And Its Application

Reed-Solomon codes have advantage of correcting bursting error and random error together, especially to the former. Because its correcting capability amounts to the utmost correcting capability of block correcting codes, RS codes are widely used in telecom technology and data storage system. But as we know, decoding of RS codes is very complicate. Now many scholars have promoted a lot of efficient decoding algorithm to resolve the problem.After the advantage and disadvantage of many kinds of decoding algorithm of RS codes was analyzed, the Step-by-Step decoding algorithm is used in this paper, according to the environment of Coke Plant. But conventional Step-by-Step decodingalgorithm requires that every symbol of received word r(x) orderly adds to 2m -1nonzero elements of GF( 2) to determine whether the weight of the error pattern has been reduced. If the weight of error pattern is reduced, the error location and the corresponding error value are found. All nonzero elements of GF(2m) must be verified by the conventional Step-by-Step decoding algorithm, which increases the computational complexity of decoding, so the conventional Step-by-Step decoding algorithm can't be adapt to the requirement of rapid decoding.According to the theorem about judging the number of error symbol concluded in this paper, an improved Step-by-Step decoding algorithm is put forward and proved, which based on some relative theorem promoted by T. -C. Chen and Shyue-Win Wei. Compared with the conventional Step-by-Step decoding algorithm, the improved Step-by-Step decoding algorithm can rapidly determine the error location and the corresponding error value. To a (n, k, t) RS code, when v, the number of the errorsymbol in its received words r(x), is equal to t, rn-1 must be an inaccurate symbol if and only if det(Njt+1) = 0 and nonzero element B = det(Njt)/det(Mjt-1) exist. Subsequently a conclusion can be drew that det(Mjv-1)≠ 0 and nonzero elementβ = det(Njv)/det(Mjvt-1) is the error value of the symbol rn-j When this improvedalgorithm found the error location and the corresponding error value, all nonzero element in the field of GF( 2m) need not be verified, but get the error location and the corresponding error value directly according to the calculated value of syndrome matrix.An engineer case is introduced, which is " The Identification of Coke Oven Sequence Number and Distant Transmission of Pushing Coke Information". Advanced technology of wireless data transmission and computer control is adopted to improve pushing coke motor. The data transmitter-receiver is introduced in the engineer case, and the improved Step-by-Step decoding algorithm is put into practice. A reliable and effective communication can be built between pushing coke motor and computer. A good anti-interference is presented. The result of practical control shows that the improved Step-by-Step decoding algorithm can be easily realized, and can reduce computational complexity and simplify the program.