Eight-to-Fourteen Modulation

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Eight-to-Fourteen Modulation (EFM) is an encoding technique used by CDs and pre-Hi-MD MiniDiscs.

Contents 1 History 2 Technological classification 3 How it works 4 Variations 5 External links

[edit] History

EFM and EFMPlus were both invented by Kees A. Schouhamer Immink.

[edit] Technological classification

EFM belongs to the class of DC-free Run Length Limited (RLL) codes because it ensures that

• the spectrum (power density function) of the encoded sequence vanishes at the low-frequency end and
• 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 some 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. The use of EFM produces a disc that is highly resilient to handling and solves the engineering challenge in a very efficient manner.

[edit] How it works

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 bits are encoded with NRZI encoding, or modulo-2 integration, so that a binary one is stored on the disc as a change from a land (zero) to a pit (one) or a pit (one) to a land (zero), while a binary zero is indicated by no change. A sequence 0011 would be changed into 1101 or its inverse 0010 depending on the previous pit written. If there are 2 zeroes between 2 consecutive ones, then the written sequence will have 3 consecutive zeros (or ones), for example, 010010 will translate into 100011 (or 011100). The EFM sequence 000100010010000100 will translate into 111000011100000111 (or its inverse).

Because EFM ensures there are at least 2 zeroes between every 2 ones, it thus ensures that every pit and land is at least three bit clock cycles long. This property is very useful since it 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 3 merging bits are also used to shape the spectrum of the encoded sequence. Thus, in the final analysis, 17 bits of disc space are needed to encode 8 bits of data.

[edit] Variations

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.

EFMPlus effectively reduces storage requirements by one channel bit per user byte, increasing storage capacity by 17/16 = 6.25%. 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.

[edit] External links

Related websites

• Eight-to-Fourteen Modulation Conversion Table
• ECMA-130 CD-ROM standard, including full EFM description
• ECMA-267 DVD-ROM standard, including full EFMPlus description