HIGH EFFICIENCY GRAY CODES FOR DISK DRIVES
Original Publication Date: 2000-Feb-01
Included in the Prior Art Database: 2003-Jun-12
Described is a method for efficiently encoding the track ID of a disk drive. It requires one flux transition per bit of the track ID, plus one or two flux transitions for parity. It provides the required ability to read the track ID while off-track with at most one error. In this discussion, a bit is referred to as a logical unit of user data. It is encoded in some fashion into flux transitions or their absence, which are the potential changes in state of the magnetization of the disk. If the magnetization changes state, the flux transition is denoted as a 1, and if not, the absence of a flux transition is denoted as a 0. The presence of a flux transition can also be denoted asa+or-, depending on how the magnetization changes. In a disk drive, a track ID is encoded as a gray code because it has the special property that only one bit is different between two consecutive code words. For example, the usual binary code encodes the sequence 0,1,2,3 as 00, 01, 10, 11. Thus both bits change between the code word for 1 and 2. However, a gray code encodement of this sequence is 00, 01, 11, 10, so that only one bit changes from one code word to the next. This is true even when the code wraps (i.e., when written 0,1,2,3,0,1,2....) Because of this property it permits robust decoding of the track ID even when the read head is off track. For example, if the head is between tracks 1 and 2, then it sees part of both code words at the same time. If a binary code is used, it sees part of the 01 encodement for track 0 and part of the 10 encodement for track 1; thus is detects both a 1 and a 0 for both bits, leading to an unpredictable result. If the gray code is used (code words are 01 and 11), the first bit is still unpredictable, but the second bit is detected as a 1. Then no matter how the first bit is decoded, the result will either be 01 (for track 1) or 11 (for track 2), either of which is reasonable.