The concept of homogeneous interpolation problem (HIP) over fields is introduced.It is discovered that solving HIP over finite fields is equivalent to decoding Reed-Solomon (RS) codes.The Welch-Berlekamp algorithm of ...The concept of homogeneous interpolation problem (HIP) over fields is introduced.It is discovered that solving HIP over finite fields is equivalent to decoding Reed-Solomon (RS) codes.The Welch-Berlekamp algorithm of decoding RS codes is derived;besides,by introducing the concept of incomplete locator of error patterns,the algorithm called incomplete iterative decoding is established.展开更多
In consideration of decoding cydic codes, a general formula for error pattern prediction is obtained. It extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm, so that the limitation from BCH b...In consideration of decoding cydic codes, a general formula for error pattern prediction is obtained. It extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm, so that the limitation from BCH bound is broken, and the algorithm turns into a universal one which meets the actual minimum distance as well as complete decoding beyond the minimum distance in the case of decoding BCH codes and general cydic codes.展开更多
As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid wi...As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘The concept of homogeneous interpolation problem (HIP) over fields is introduced.It is discovered that solving HIP over finite fields is equivalent to decoding Reed-Solomon (RS) codes.The Welch-Berlekamp algorithm of decoding RS codes is derived;besides,by introducing the concept of incomplete locator of error patterns,the algorithm called incomplete iterative decoding is established.
基金the National Natural Science Foundation of China, the Military Science Foundation of the Electronic Industrial Ministry of China and Frderung der Wissenschaft Foundation of Austria
文摘In consideration of decoding cydic codes, a general formula for error pattern prediction is obtained. It extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm, so that the limitation from BCH bound is broken, and the algorithm turns into a universal one which meets the actual minimum distance as well as complete decoding beyond the minimum distance in the case of decoding BCH codes and general cydic codes.
基金the National Natural Science Foundation of China and the Military Science Foundation in Ministry of Electronic Industry of China.
文摘As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH
