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Eight-to-fourteen modulation
Eight-to-fourteen modulation
Eight-to-fourteen modulation
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Eight-to-fourteen modulation (EFM) is a data encoding technique – formally, a line code – used by compact discs (CD), laserdiscs (LD) and pre-Hi-MD MiniDiscs. EFMPlus is a related code, used in DVDs and Super Audio CDs (SACDs).

EFM and EFMPlus were both invented by Kees A. Schouhamer Immink. According to European Patent Office former President Benoît Battistelli, "Immink's invention of EFM made a decisive contribution to the digital revolution."[1]

Technological classification

[edit]

EFM[2] belongs to the class of DC-free run-length limited (RLL) codes; these have the following two properties:

  • 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.[3][4]

In optical recording systems, servo mechanisms 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.

How it works

[edit]

Under EFM rules, the data to be stored is first broken into eight-bit blocks (bytes). Each eight-bit block is translated into a corresponding fourteen-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 zeros. 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 to a pit or a pit to a land, 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 two consecutive zeros between two ones, then the written sequence will have three 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 that there are at least two zeros between every two ones, it is guaranteed 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 three merging bits between adjacent fourteen-bit codewords. Although they are not needed for decoding, they ensure that consecutive codewords can be concatenated without violating the specified minimum and maximum runlength constraint. They are also selected to maintain DC balance of the encoded sequence. Thus, in the final analysis, seventeen bits of disc space are needed to encode eight bits of data.[5]

EFMPlus

[edit]

EFMPlus[6][7] is the channel code used in DVDs and SACDs.

The EFMPlus encoder is based on a deterministic finite automaton having four states, which translates eight-bit input words into sixteen-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 1/16 = 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.

References

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[edit]
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Eight-to-fourteen modulation

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Eight-to-fourteen modulation (EFM) is a block coding technique that maps groups of eight data bits into fourteen channel bits for reliable storage and retrieval of digital signals on optical media, such as compact discs (CDs). Developed as part of the System, EFM ensures a run-length limited (RLL) code with parameters (d,k) = (2,10), meaning no fewer than two and no more than ten consecutive zeros appear between consecutive ones in the channel bit stream. This constraint facilitates precise during readout and maintains sufficient transitions for tracking of the disc's spiral groove. In operation, EFM employs a predefined to convert each 8-bit input symbol into one of 256 possible 14-bit codewords, all of which inherently satisfy the minimum run-length limit of two zeros while avoiding runs longer than ten within the block itself. To connect adjacent codewords without violating the overall run-length constraints, three merging bits chosen from the patterns 000, 001, 010, or 100 are inserted between each pair of 14-bit blocks, allowing optimization for low-frequency suppression. These merging bits also help achieve DC-free encoding by minimizing the low-frequency content in the spectrum, which is crucial for stable optical detection and reducing baseline wander in the readout signal. The primary purposes of EFM include enhancing against defects like scratches and fingerprints on the disc surface, while supporting high-density recording to fit over one hour of 16-bit, two-channel audio on a 12 cm disc. By providing consistent pit and edge , it ensures reliable servo tracking and focus control in the optical pickup . EFM integrates seamlessly with the Cross-Interleaved Reed-Solomon Code (CIRC) for error correction, contributing to the system's overall robustness. EFM was jointly developed by and in the late 1970s and early 1980s, with key contributions from engineer Kornelis Schouhamer Immink, and formalized in the Red Book standard published in 1980 by and , and later as the international standard IEC 60908 in 1987. Initially designed for audio CDs, the modulation scheme was later adapted for data storage in CD-ROMs and (which use the same EFM), and influenced variants like EFMPlus in DVD formats, influencing technology for decades.

Introduction

Definition and Purpose

Eight-to-fourteen modulation (EFM) is a that maps each 8-bit input data byte to one of 256 predefined 14-bit codewords using a , designed specifically for optical systems. This encoding ensures that the resulting channel bits adhere to strict run-length limited (RLL) constraints, classified as RLL(2,10), where there are at least two consecutive zeros between any two ones to minimize in optical readout and no more than ten consecutive zeros to facilitate through self-clocking properties. The code also incorporates additional DC control mechanisms to maintain a low digital sum variation (DSV), reducing low-frequency components that could interfere with servo tracking and reliable signal detection. The primary purposes of EFM are to enable high-density recording while ensuring robust in the presence of optical channel imperfections. By enforcing the minimum run-length of two zeros between ones, EFM guarantees that pits and lands on the disc are at least three channel bit periods long, which helps suppress and timing during playback. The maximum run-length constraint of ten zeros provides frequent transitions for phase-locked loop-based , allowing the receiver to regenerate the bit clock without external references. Furthermore, the DC balance achieved through careful codeword selection and merging bits minimizes baseline wander, enhancing the for error-free decoding. EFM's overall coding efficiency is characterized by a rate of 8/17, accounting for the 14-bit codewords plus three additional merge bits inserted between symbols to resolve run-length violations at block boundaries and further optimize DC balance. This rate, approximately 0.4706, approaches the theoretical capacity of the RLL(2,10) constraint while incorporating the overhead for DC control, making it suitable for achieving reliable data rates in constrained optical channels.

Historical Development

Eight-to-fourteen modulation (EFM) was developed in the late 1970s at Research Laboratories in , , as a critical component of the (CD) specification, in collaboration with Corporation. The effort began amid ' broader research into , building on earlier technologies, and aimed to create a durable medium superior to analog vinyl records. Key to this development was engineer Kees A. Schouhamer Immink, who invented the EFM encoding scheme to enable high-density data storage while ensuring resilience against errors from disc imperfections and handling. The timeline of EFM's creation aligned closely with the CD's standardization process. and formalized their joint task force in 1979 to unify standards, with Immink contributing the initial EFM proposal that year during intensive meetings in and . By May 1980, under a tight deadline from 's leadership, the modulation system was finalized and incorporated into the Red Book, the official CD Digital Audio (CD-DA) specification published that year. Further testing and refinement followed, culminating in the commercial launch of the first CD players in 1982, marking EFM's debut in consumer products. EFM's design was driven by the need to support a 44.1 kHz sampling rate for audio on 120 mm discs rotating at a constant linear of 1.2 m/s, achieving approximately 74 minutes of playback capacity. This required an audio data rate of 1.4112 Mbps to accommodate the encoded audio stream while fitting within the physical constraints of optical readout. Early challenges centered on balancing this high data rate with run-length limited pit and land lengths—typically to 11T, where T is the channel bit period—to ensure reliable tracking and manufacturability, avoiding overly sparse or dense patterns that could disrupt servo systems.

Core Encoding Process

Basic 8-to-14 Bit Conversion

The basic 8-to-14 bit conversion in eight-to-fourteen modulation (EFM) transforms each 8-bit input byte into a 14-bit channel symbol through a fixed lookup table comprising 256 entries, corresponding to all possible byte values from 00000000 to 11111111 in binary. This table maps each input to a specific 14-bit codeword drawn from the 16384 possible 14-bit sequences (2^{14}), with selections limited to those that individually adhere to run-length limited (RLL(2,10)) constraints: no fewer than two consecutive zeros and no more than ten consecutive zeros between any two ones, ensuring consistent pit and land lengths on the disc for reliable optical readout. The codewords in this lookup table were algorithmically selected during the design of EFM to minimize the average digital sum variation (DSV)—the cumulative difference between the number of ones and zeros in the encoded stream—thereby suppressing low-frequency components and promoting DC-free signaling, while allowing subsequent merge bits to further optimize balance across symbol boundaries. For each 8-bit input, multiple RLL(2,10)-compliant 14-bit candidates exist, but the table assigns a single codeword per entry chosen for its compatibility with inter-symbol merging and overall spectral performance. A representative example is the mapping for the input byte 0x00 (binary 00000000), which converts to the 14-bit codeword 01001000100000; this codeword features three , with inter-one run lengths of two zeros (between the first and second one) and three zeros (between the second and third one), fully compliant with RLL(2,10). The resulting channel symbols maintain a rate of 8/14 ≈ 0.571, providing a increase over the while preserving timing recovery through enforced transitions. Within the encoding pipeline, this EFM conversion occurs after the Cross-Interleaved Reed-Solomon Code (CIRC) has been applied for on of audio or bytes, but before NRZI encoding to define the transitions for pits and lands on the disc. This positioning ensures that EFM symbols benefit from CIRC's burst-error handling while contributing to the physical layer's run-length and DC-balance requirements.

Run-Length Limited Constraints

Eight-to-fourteen modulation (EFM) employs run-length limited (RLL) constraints to shape the channel bitstream for reliable recovery in systems, specifically adhering to the RLL(2,10) code. In this scheme, the d = 2 ensures a minimum of two consecutive zeros between any two ones in the 14-bit codeword, corresponding to at least three channel bits between transitions. The k = 10 limits the maximum to ten consecutive zeros between ones, or eleven channel bits between transitions. These constraints control the lengths of runs of zeros in the (NRZ) representation of the codewords, preventing invalid patterns that could degrade . The RLL(2,10) constraints serve critical purposes in optical media like compact discs. The d = 2 minimum run length avoids excessively short pits or lands, which could merge due to limits or manufacturing tolerances, thereby reducing (ISI) and enabling distinct during readout. Conversely, the k = 10 maximum run length ensures frequent enough transitions to facilitate clock extraction from the , while preventing overly long runs that might cause timing or loss of in the (PLL) used for bit timing recovery. This balance optimizes the spectral content of the recorded signal, concentrating energy in mid-frequency bands suitable for the optical channel's . In the physical recording, each '1' in the channel bitstream triggers a transition between pit and land (or vice versa) in non-return-to-zero inverted (NRZI) format, while '0's maintain the current state without transition. The RLL constraints thus directly dictate pit and lengths, measured in multiples of the channel bit period T (3T minimum to 11T maximum). Without merging bits, the nominal modulation rate is 8/14 ≈ 0.571 bits per channel bit; however, the addition of three merging bits between symbols to preserve RLL across boundaries reduces the effective rate to 8/17 ≈ 0.471. The statistical properties of EFM codewords, governed by the lookup table and RLL enforcement, provide sufficient transitions per symbol under uniform input data distribution to support robust self-clocking without excessive high-frequency content. This transition density ensures the read signal maintains adequate timing information across varying data patterns, contributing to the overall reliability of in the optical system.

Channel Coding Enhancements

Merge Bits for Balance

In eight-to-fourteen modulation (EFM), three additional merge bits, denoted as m1, m2, and m3, are appended between adjacent 14-bit symbols to connect them seamlessly while enforcing global DC balance. These merge bits are selected from eight possible combinations (000 through 111), allowing flexibility in linking symbols without violating the run-length limited (RLL) constraints of the individual symbols. The primary role of these bits is to minimize the digital sum value (DSV), defined as the running sum of the channel bits where each '1' contributes +1 and each '0' contributes -1, thereby suppressing low-frequency components in the signal spectrum that could impair pit tracking in optical media. By keeping the absolute DSV low—ideally below 4 blocks (where a block refers to a 17-bit unit of symbol plus merges)—the merge bits ensure stable and reliable . The selection for merge bits operates sequentially for each pair of consecutive EFM symbols, evaluating all valid combinations to identify the one that results in the smallest absolute DSV after incorporation, while simultaneously preserving the minimum pit length of (transition units, corresponding to three channel bits). Only combinations that prevent run lengths shorter than or longer than 11T across symbol boundaries are considered, ensuring compliance with the (d=2, k=10) RLL inherent to EFM symbols. For instance, if the trailing bits of one symbol end with multiple zeros and the leading bits of the next begin similarly, merge options like 000 or 001 might be restricted to avoid excessive run lengths. This process is repeated across the entire frame, with the cumulative DSV tracked from the start to dynamically adjust for balance, prioritizing options that drive the DSV closest to zero. A complete EFM frame processes 24 bytes of audio data (corresponding to 12 stereo 16-bit samples), plus 1 byte for subcode, 4 bytes for Q-parity, and 4 bytes for P-parity, yielding 33 total 8-bit symbols that are each converted to 14 channel bits. With three merge bits added (33 sets, including after the sync pattern), the EFM portion totals 33 × 17 = 561 bits. This is preceded by a 27-bit synchronization pattern (24-bit core + 3 initial merges), resulting in 588 channel bits per frame. Following merge bit insertion, the full channel bit stream undergoes encoding prior to modulation onto the disc. In NRZ-I, a '1' bit triggers a level transition (from pit to or vice versa), while a '0' bit maintains the current level, facilitating edge-based detection during readout and further aiding without additional circuitry. This encoding complements the DC-balanced properties achieved by the merge bits, ensuring the overall signal remains suitable for the optical channel.

Synchronization and Framing

In eight-to-fourteen modulation (EFM), is achieved through a unique 24-channel-bit pattern inserted at the beginning of each frame, extended to 27 channel bits with 3 merging bits to ensure compliance with run-length limited (RLL) constraints while maintaining uniqueness. This sync pattern, binary sequence 100000000001000000000010, is designed to violate typical symbol combinations by incorporating an 11T run , which cannot occur in standard EFM-encoded due to the (2,10) RLL code limiting runs to 3-11T but restricting specific long-run placements across symbol boundaries. The overall frame structure comprises 588 channel bits, consisting of a 27-bit sync pattern (24-bit core + 3 merging bits) followed by 33 EFM —24 for main data, 1 for subcode, 4 for Q-parity, and 4 for P-parity—each encoded as 14 channel bits, with 3 merging bits per symbol (totaling 33 sets of merging bits). This arrangement yields 27 + 33 × 17 = 588 channel bits, ensuring seamless stream continuity. These 98-frame blocks form a complete sector, providing periodic alignment for subcode extraction and timing references. Clock recovery in EFM relies on the frequent transitions inherent to the RLL(2,10) constraints, where channel bit changes occur every 3 to 11T periods, enabling a (PLL) to synchronize to the 4.3218 MHz channel without additional clock bits. The sync pattern's distinctive transitions further aid initial lock-in, while subcode symbols every 98 offer coarse timing updates to maintain long-term stability during constant linear velocity playback. Frame synchronization integrates with error detection by using sync pattern detection to delineate frames; loss of sync, due to media defects or noise, triggers PLL re-acquisition and frame resynchronization, limiting propagation to complement the Cross-Interleaved Reed-Solomon Code (CIRC) error correction, which operates on 8-bit symbols and flags uncorrectable errors if sync misalignment persists.

Applications and Implementations

Use in Compact Discs

In (CD-DA) systems, the encoding pipeline transforms raw pulse-code modulated (PCM) audio into physical pits and lands on the disc surface. Stereo PCM audio, sampled at 44.1 kHz with 16-bit resolution per channel, generates a raw of 1.411 Mbps. This is first processed through Cross-Interleaved Reed-Solomon Coding (CIRC) for , incorporating parity bits and interleaving to yield a formatted rate of 2.034 Mbps. EFM modulation then maps each 8-bit to a 14-bit channel codeword, appending 3 merging bits for DC balance and run-length control, resulting in a channel bit stream at 4.3218 Mbps. The EFM output undergoes Inverted (NRZ-I) encoding, where bit transitions denote logical '1's, before being converted to a bipolar radiofrequency (RF) signal for laser etching. This RF-modulated signal dictates the physical pattern: sequences of pits and lands, with minimum lengths of 3T and maximum of 11T, to represent the channel bits on the polycarbonate substrate. The efficiency of EFM, constrained by its (2,10) run-length limited code, significantly impacts storage capacity by enabling dense packing while maintaining reliable optical readout. On a standard 120 mm disc with a spiral track length of approximately 5.38 km and track pitch of 1.6 µm, this modulation supports 74 to 80 minutes of uninterrupted audio playback, accommodating up to 783 MB of total data equivalent when factoring in overheads. Physically, each EFM channel bit corresponds to a time unit T of 231.4 ns, translating to spatial lengths at the constant linear velocity (CLV) of 1.2 m/s used during playback: pits and lands range from 0.833 µm (3T minimum) to 3.054 µm (11T maximum), with typical depths of 0.1 µm and widths of 0.5–0.7 µm. These dimensions ensure sufficient contrast for detection via reflection differences between pits and lands. EFM's integration into CD technology was formalized in the Red Book standard (IEC 60908), jointly published by Philips and Sony in 1980, which mandates EFM for the modulation layer in CD-DA to achieve the specified audio fidelity and error resilience. This specification was extended to data storage in the Yellow Book standard for CD-ROM, released by the same developers in 1983, retaining EFM for compatibility in the physical and channel coding layers.

Adoption in Other Optical Media

Eight-to-fourteen modulation (EFM) found application in Laserdisc (LD) formats during the 1980s, where it encoded digital audio tracks in later constant angular velocity (CAV) and constant linear velocity (CLV) models. These tracks, which coexisted with analog video signals, utilized EFM to deliver uncompressed pulse-code modulation (PCM) audio at a 44.1 kHz sampling rate and 16 bits per channel, achieving a channel bit rate of approximately 4.32 Mbps for the audio data stream. This implementation leveraged EFM's run-length limited constraints to enhance error resilience against disc imperfections, while operating at lower effective data densities compared to full audio-only media due to the hybrid analog-digital structure. Sony's pre-Hi-MD , launched in 1992 and produced through 2004, incorporated EFM for storing ATRAC-compressed audio on 68 mm magneto-optical discs protected by a cartridge. The format supported up to 74 minutes of recording or 148 minutes of monaural recording per 74-minute disc, with an underlying capacity of about 140 MB when used in mode. EFM, combined with an adapted Interleaved Reed-Solomon Code (ACIRC), ensured robust error correction tailored to the compressed audio stream and magneto-optical recording process. Adaptations of EFM in these media maintained the core 8-to-14 bit conversion and merging bits for DC balance but were optimized for differing physical constraints, such as 's constant linear velocity of 1.2 to 1.4 m/s and narrower track pitch of 1.6 µm to accommodate the compact disc size while preserving playback speeds around 400 to 900 rpm. Both and phased out in the post-2000s amid the rise of players and flash-based storage, though legacy hardware continues to provide playback support for existing libraries.

Variants and Evolutions

EFMPlus Modifications

EFMPlus represents an optimized evolution of the original Eight-to-Fourteen Modulation (EFM) scheme, specifically tailored for higher storage densities in optical media while maintaining compatibility with run-length limited (RLL) constraints for reliable . Developed by Kees A. Schouhamer Immink at in collaboration with during the 1995 formulation of the Multimedia Compact Disc (MMCD) proposal—which formed the basis for the DVD standard—EFMPlus employs an 8-to-16 bit mapping with a code rate of 8/16 to encode data symbols. A 4-state selects codewords from a main table or substitution table to ensure RLL(2,10) constraints and control DSV for DC balance, eliminating the need for merge bits. The core modifications in EFMPlus extend the codeword length from 14 bits to 16 bits, enabling finer control over the RLL(2,10) constraints—ensuring no fewer than 2 and no more than 10 consecutive zeros between ones—through a with four states that selects codewords guaranteeing smooth transitions without dedicated merge bits. DC balance is maintained by choosing codewords that minimize the running digital sum variation (DSV), effectively suppressing low-frequency components and reducing baseline wander in readout signals. These enhancements, combined with the absence of fixed merge bits, improve encoding efficiency by approximately 6% over EFM in terms of spectral properties, allowing for physically smaller features such as minimum pit lengths of 0.4 µm and a track pitch of 0.74 µm—roughly half the dimensions of a CD's 0.83 µm pits and 1.6 µm track pitch—facilitated by the 650 nm . In terms of performance, EFMPlus operates at a constant linear of 3.49 m/s, yielding a channel bit rate of approximately 26.2 Mbit/s and supporting effective user data transfer rates around 10.08 Mbit/s after correction overhead, which accommodates streams with peak bit rates up to 9.8 Mbps for compressed video and audio. The improved DC balance and resilience stem from the encoding mechanism and extended maximum run length of 11T (via state transitions), which enhance tolerance to defects like scratches and fingerprints compared to alternative modulation schemes considered during DVD development. This robustness contributed to its selection over more efficient but less reliable options, such as Toshiba's proposed code. EFMPlus was standardized as part of the DVD read-only format in ECMA-267 (first edition, December 1997), which defines the 120 mm specifications including the 8-to-16 modulation with DC control for data interchange. It is employed in both DVD-ROM and discs, ensuring consistent compatibility across read-only applications, though incorporates additional application-specific formatting for audiovisual content. EFMPlus is also used in Super Audio CDs (SACD) for (DSD) encoding. Eight-to-fourteen modulation (EFM) achieves a coding rate of approximately 0.471 data bits per channel bit, slightly lower than Manchester coding's rate of 0.5, but offers superior run-length limited (RLL) constraints with parameters (d=2, k=10), enabling better control over pit and land lengths in optical media to minimize and clock . In contrast, coding, a biphase used in early Ethernet standards for its simplicity and inherent self-clocking properties, enforces stricter (d=0, k=1) constraints that result in frequent transitions, increasing bandwidth requirements and making it less suitable for high-density where manufacturing small, closely spaced pits is challenging. While provides excellent DC balance and without additional circuitry, EFM's higher complexity—relying on a and merge bits for DC suppression—trades efficiency for robustness in optical playback, achieving error rates below 3.5×10^{-5} when combined with cross-interleaved Reed-Solomon coding (CIRC). Compared to 4B/5B block coding, employed in (FDDI) and early for its high rate of 0.8, EFM sacrifices efficiency to impose RLL constraints tailored to optical physics, preventing excessive short runs that would degrade due to optical limits. 4B/5B lacks inherent run-length limits, allowing denser packing in non-optical channels but risking higher error rates in compact discs where minimum pit lengths must be at least three channel bits to ensure reliable detection; EFM's design thus enables smaller features on the disc while maintaining comparable DC balance through merge bits, though at the cost of increased decoding complexity via table lookups. EFM outperforms (MFM), an RLL(1,3) code common in magnetic hard disks, by supporting longer maximum runs (k=10 versus k=3), which reduces timing and improves servo stability in constant linear velocity optical systems like CDs. MFM's shorter maximum run length demands more frequent transitions, complicating in optical environments sensitive to low-frequency components, whereas EFM's merge bits actively minimize digital sum variation for better low-frequency suppression, enhancing overall density by 25-40% over simpler non-block codes in practical optical implementations. Overall, EFM's custom constraints and merge-bit mechanism optimize for the unique demands of optical media, influencing subsequent codes such as those in Blu-ray, which incorporate low-density parity-check (LDPC) error correction alongside similar RLL principles for even higher densities. EFMPlus represents a direct evolution, refining these trade-offs for DVD applications.

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