Decoder for decoding a two-stage encoded code

Abstract

A decoder for decoding a code C which is two-stage encoded by a C.sub.1 code ((N, K, D) Q dimensional code) and a C.sub.2 code ((n, k, d) q dimensional code), which includes: a C.sub.1 decoder including an error correction means for conducting an error correction of the errors below the number [(D-1)/2] to output the decoded word, and a weight generator which generates wj (j=1, 2, . . . , n) when i (i=0 to [(D-1)/2 ]) errors are corrected and an error detection (correction disability) is judged; a C.sub.2 decoder for decoding the C.sub.2 code including a forfeiture error correction means for judging the position j of the wj among the weight vector w in the received word r which is obtained in accordance with the decoded word output from the C.sub.1 decoder, and conducting a forfeiture error decoding. A weighted distance calculating means for calculating the weighted distance .rho..sup.(k) between the decoded word r.sup.(k) and the received word r when a decoded word in each of K=0, 1, . . . , [(D-1)/2] is obtained; the C.sub.2 decoder also including a comparator for comparing the weighted distance .rho..sup.(k) and the integer .tau., outputs the decoded word r.sup.(k) as a correct decoded word when the .rho..sup.(k) is smaller than or equal to .tau., and the correction disability signal when the .rho..sup.(k) is larger than .tau. or no decoded word is obtained by the forfeiture error correction means.