Eight-to-Fourteen Modulation
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Eight-to-Fourteen Modulation (EFM) is an encoding technique used by CDs and MiniDiscs. EFM belongs to the class of DC-free Run Length Limited (RLL) codes because it ensures that a) the spectrum (power density function) of the encoded sequence vanishes at the low-frequency end and b) both the minimum and maximum number of consecutive bits of the same kind are within specified bounds.
In optical recording systems, servo systems accurately follow the track in three dimensions, radial, focus, and rotational speed. Everyday handling damage, such as dust, fingerprints, and tiny scratches, not only affects retrieved data, but also disrupts the servo functions. In worst cases, the servos may skip tracks or get stuck. Specific sequences of pits and lands are particularly susceptible to disc defects, and disc playability can be improved if such sequences are barred from recording. EFM, which is highly resilient to disc handling, solves the engineering requirements in a very efficient manner.
Under EFM rules, the data to be stored is first broken into 8-bit blocks (bytes). Each 8-bit block is translated into a corresponding 14-bit codeword using a lookup table. The 14-bit words are chosen such that binary ones are always separated by a minimum of two and a maximum of ten binary zeroes. This is because a binary one is stored on the disc as a change from a land to a pit or a pit to a land, while a binary zero is indicated by no change. Because EFM ensures there are at least two zeroes between every two ones, it also ensures that every pit and land is at least three clock cycles long. This reduces the demands on the optical pickup used in the playback mechanism. The ten consecutive-zero maximum ensures worst-case clock recovery in the player. EFM requires 3 merging bits between adjacent 14-bit codewords to ensure that consecutive codewords can be cascaded without violating the specified minimum and maximum runlength constraint. The three merging bits are also used to shape the spectrum of the encoded sequence. Thus, in the final analysis, 17 bits of disk space are needed to encode 8 bits of data.
EFMPlus is the channel code used in DVDs and SACDs. The EFMPlus encoder is based on a deterministic finite state machine having four states, which translates 8-bit input words into 16-bit codewords. The binary sequence generated by the finite state machine encoder has at least two and at most ten zeros between consecutive ones, which is the same as in classic EFM. There are no packing (merging) bits as in classic EFM. This effectively reduces storage requirements by one channel bit per user byte, increasing storage capacity by 17/16 = 7%. Decoding of EFMPlus-generated sequences is accomplished by a sliding-block decoder of length two, that is, two consecutive codewords are required to uniquely reconstitute the sequence of input words.
EFM and EFMPlus were both invented by Kees A. Schouhamer Immink.
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