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We report a new method for designing (M,d, k) constrained codes for use in multi-level optical recording channels. The method allow us to design practical codes, which have simple encoder tables and decoders having fixed window length. The codes presented here for the d = 1 and d = 2 cases, achieve higher storage densities than previously reported codes, and come within 0.3 - 0.7% of capacity.
One challenge in intensity modulation and direct detection communication systems is the power consumption at the transmitter-side driving circuit. For binary-switched LED-based transmission, boosting the data rate leads to an increased number of switching operations. Consequently, a larger fraction of the available power budget is dissipated in the driver. Hence the performance of communication and possibly illumination is affected by the reduced optical transmit power. The key idea is to lower the driver power consumption by decreasing the number of switching operations necessary for transmitting a fixed amount of data. This is possible by superimposing multiple binary sequences, where the individual sequences are matched to the hardware characteristics of the transmitter. We introduce a method to derive a graph-based representation for superimposing individually constrained binary sequences, and analyze the achievable constrained capacity.
Runlength-limited (RLL) codes, generically designated as (d, k) RLL codes, have been widely and successfully applied in modern magnetic and optical recording systems. The design of codes for optical recording is essentially the design of combined dc-free and runlength limited (DCRLL) codes. We will discuss the development of very efficient DCRLL codes, which can be used in upcoming generations of high-density optical recording products.
Ideas which have origins in C. E. Shannon's work in information theory have arisen independently in a mathematical discipline called symbolic dynamics. These ideas have been refined and developed in recent years to a point where they yield general algorithms for constructing practical coding schemes with engineering applications. In this work we prove an extension of a coding theorem of B. Marcus and trace a line of mathematics from abstract topological dynamics to concrete logic network diagrams.
Recent interest in recording schemes employing ternary input signaling motivates the study of run-length constrained ternary codes. In this paper, a more general class of codes known as Mary (D,K) codes (D and K are matrices) is introduced. The capacities, or maximum rates, of these codes are derived. Next, some special cases of M-ary (D,K) codes are described and their capacities are calculated. Some specific codes are then generated using the sliding block code algorithm. Finally, a new ternary signaling scheme that uses ternary (D,K) constraints combined with write equalization is suggested for use on a magnetic recording channel.
In this paper we consider the coding and signal processing aspects of MultiLevel (ML<sup>TM</sup>) DVD. Using a turbo-like code, on a standard DVD platform and DVD-like rewritable media, we demonstrate a density of 3.08 bits per 388 nm data cell using 12 levels. This density comes very close to the fundamental limits predicted by theoretical models. We also discuss efficient decoding algorithms that are ideally suited to low-cost consumer applications. The 12-level, 3.08 bit code can be used as part of a ML<sup>TM</sup> DVD (re)writable system that stores 10 Gbytes on the standard DVD base.
Calimetrics Inc. has worked previously on multi-level (MIL) ROM
systems to prove that this concept could be implemented using existinand
manufacturing infrastructure. Pit-depth modulation (PDM) technology was
the result and simple proof-of-concept systems were created for both CD
and DVD-ROM. Since then, Calimetrics Inc. has been focusing on
multi-level RW phase-change systems, given the greater business
interests that were exhibited for the rewritable market. We report here
on progress to date on multi-level CDRW technology and look forward to
its application to DVD-based RW systems
We consider the problem of coding for a high density recording channel. New recording media have been developed that support unsaturated, M-ary (M ≥ 3) signaling. This paper is concerned with the analysis and design of M-ary runlength limited (RLL) codes for multi-amplitude, linear recording channels. The codes achieve the largest known coding density and have improved minimum distance over an ordinary Adler-Coppersmith-Hassner code designed via the state splitting algorithm. Comparisons are made with Ungerboeck-style trellis codes with comparable complexity.
Multilevel run-length-limited (RLL) DC-free codes for optical
storage systems are introduced. Theoretically achievable code rates are
calculated and spectra determined, and it is demonstrated that the
proposed modulating codes have good spectral characteristics. An example
of code construction is given using the Adler, Coppersmith and Hassner
A 4-ary run-length limited (RLL) code with minimum run-length
constraint d=1 and maximum run-length constraint k=2 is presented. The
proposed code can be represented by a finite state diagram with two
states. This is the lowest number of states necessary for representing
the code yet presented. A simple decoding rule for the code is also
introduced and a scheme for reducing the DC content of the coded
sequence in the sense of multilevel running digital sum (RDS) is
This paper develops coding and signal processing approaches for a
novel optical recording channel that arises from electron-trapping
phosphor materials. The recording medium allows multiple reads and
writes, and one important feature is that the read process serves to
erase the disk. This feature would enable vendors of prerecorded video
to provide customers with one-time services. For applications where this
feature is not desirable, the data can be immediately rewritten. From a
communications viewpoint, the most important feature of this new channel
is that, subject to a peak constraint, it supports a continuum of
recording levels. The combination of read and write processes creates a
partial-response channel, and the ability to write a continuum of levels
makes it possible to employ precoding techniques, such as the one
developed by Tomlinson (1971) and by Miyakawa and Harashima (1969). This
is fundamentally different from magnetic data storage, where the
read/write process creates a partial-response channel but where it is
only possible to write two levels at the input to that channel. This
paper shows that the use of precoding and coset codes can significantly
improve upon the recording densities (and recording rates) that can be
achieved by using M-ary run length constrained codes to eliminate
intersymbol interference (ISI) at the output of the read/write process.
The approach presented is applicable to any optical recording channel
that supports a continuum of recording levels
This paper is concerned with M-ary runlength-limited (RLL) codes
for nonbinary recording channels. The codes have fixed-rate finite state
encoders, sliding block decoders, and large coding density. Five codes
are given achieving coding densities of 24 bit/minimum-recorded-mark as
compared with 1-1.5 for binary recording channels. The codes are
93-98.5% efficient and either achieve or come close to achieving the
fewest number of encoder states possible. One of these codes has been
implemented in a prototype system that supports M=6 discrete recording
In this work, we consider the analysis and design of optimal
block-decodable M-ary runlength-limited (RLL) codes. We present two
general construction methods: one based on permutation codes due to
Datta and McLaughlin (1999), and the other, a nonbinary generalization
of the binary enumeration methods of Patrovics and Immink (1996), and Gu
and Fuja (1994). The construction based on permutation codes is simple
and asymptotically (in block length) optimal, while the other
construction is optimal in the sense that the resulting codes have the
highest rate among all block-decodable codes for any block length. In
the process, we shall also extend a result due to Zehavi and Wolf (1988)
on the capacity of binary (d, k) constraints to M-ary channels. Finally,
we present examples of template codes: remarkably low-complexity (M,d,k)
block codes which achieve the optimal rate without the use of
Presents two results on the Shannon capacity of M-ary (d,k) codes.
First the authors show that 100% efficient fixed-rate codes are
impossible for all values of (M,d,k), 0⩽d<k<∞,
M<∞, thereby extending a result of Ashley and Siegel (1987) to
M-ary channels. Second, they show that for k=∞, there exist an
infinite number of 100% efficient M-ary (d,k) codes, and they construct
three such capacity-achieving codes