Apparatus for modulating data having a basic data length of m bits, to a variable-length code (d, k; m, n; r) having a basic code length of n bits. A sync signal is added to a received train of codes after a minimum run. The sync signal has a pattern that is repeated twice continuously. The minimum run is repeated no more than six times; and the sync signal exhibits seven types of sync signal IDs, with any adjacent two bits of a sync signal ID being spaced apart by a distance of 2.