| 摘要 |
An error correction system includes an encoder that uses a modified Reed-Solomon code to encode w-bit data symbols over GF(2w+i) and form a preliminary code with d-1 (w+i+1)-bit redundancy symbols. The preliminary code word is modified as necessary to set for each symbol a selected i bits to the same value as a corresponding i+1st bit. The preliminary code word also includes R pseudo redundancy symbols that are required for decoding the modified code word. The i+1 bits are then truncated from each of the code word symbols, to form a code word with w-bit symbols. The Galois Field GF(2w+i) is selected such that the elements of the field can be represented by (w+i+1)-bit symbols that are determined by a polynomial h(x) modulo an irreducible polynomial p(x), which is p(x)=xw+i+xw+i-1+ . . . +x1+x0, with the polynomial h(x) representing a primitive element. The encoder uses the lower weight representations of the (w+i+1)-bit symbols and performs multiplication and raising the symbols to powers of 2i as combinations of cyclic shifts and permutations that are readily performed in hardware. A decoder decodes the code word as (w+i+1)-bit symbols to take advantage of the simplified multiplication and exponentiation operations. |
