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Coding Methods for for High-Density Optical Recording High-Density Optical Recording

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Abstract

Maximum-likelihood sequence estimation of binary coded and uncoded information, stored on an optical disc, corrupted with additive Gaussian noise is considered. We assume the presence of inter-symbol interference and channel/receiver mismatch. The performance of the maximum-likelihood detection of runlength-limited sequences is compared against both uncoded information and information encoded by Hamming-distance-increasing convolutional codes.
... Balanced codes have been widely studied over the years because of their applicability in the field of communication and in storage structures such as optical and magnetic recording devices like Blu-Ray, DVDs, and CDs [1,2]; error correction and detection [3,4]; cable transmission [5]; and noise attenuation in VLSI integrated circuits [6]. For some balancing techniques, the decoding of balanced codes is fast and can be done in parallel, which avoids latency in communication. ...
... ⌊log 2 c⌋ . 1 2 ⌊log 2 c⌋ + 2d. 1 2 ⌈log 2 c⌉ . ⌈log 2 c⌉ . ...
Preprint
Full-text available
A simple scheme was proposed by Knuth to generate binary balanced codewords from any information word. 4 However, this method is limited in the sense that its redundancy is twice as that of the full sets of balanced codes. The 5 gap between Knuth's algorithm redundancy and that of the full sets of balanced codes is significantly considerable. This 6 paper attempts to reduce that gap. Furthermore, many constructions assume that a full balancing can be performed 7 without showing the steps. A full balancing refers to the overall balancing of the encoded information together with 8 the prefix. We propose an efficient way to perform full balancing scheme which do not make use of lookup tables or 9 enumerative coding. 10
... Balanced codes have been widely studied over the years because of their applicability in the field of communication and in storage structures such as optical and magnetic recording devices like Blu-Ray, DVDs, and CDs [1,2]; error correction and detection [3,4]; cable transmission [5]; and noise attenuation in VLSI integrated circuits [6]. For some balancing techniques, the decoding of balanced codes is fast and can be done in parallel, which avoids latency in communication. ...
... ⌊log 2 c⌋ . 1 2 ⌊log 2 c⌋ + 2d. 1 2 ⌈log 2 c⌉ . ⌈log 2 c⌉ . ...
Article
Full-text available
A simple scheme was proposed by Knuth to generate binary balanced codewords from an information word. 4 However, this method is limited in the sense that its redundancy is twice as that of the full sets of balanced codes. The 5 gap between Knuth's algorithm redundancy and that of the full sets of balanced codes is significantly considerable. This 6 paper attempts to reduce that gap. Furthermore, many constructions assume that full balancing can be performed 7 without showing the steps. A full balancing refers to the overall balancing of the encoded information together with 8 the prefix. We propose an efficient way to perform a full balancing scheme which does not make use of lookup tables or 9 enumerative coding. 10
... Balanced codes have been widely studied over the years because of their applicability in the field of communication and in storage structures such as optical and magnetic recording devices like Blu-Ray, DVDs, and CDs [1,2]; error correction and detection [3,4]; cable transmission [5]; and noise attenuation in VLSI integrated circuits [6]. For some balancing techniques, the decoding of balanced codes is fast and can be done in parallel, which avoids latency in communication. ...
... ⌊log 2 c⌋ . 1 2 ⌊log 2 c⌋ + 2d. 1 2 ⌈log 2 c⌉ . ⌈log 2 c⌉ . ...
Article
Full-text available
A simple scheme was proposed by Knuth to generate binary balanced codewords from any information word. However, this method is limited in the sense that its redundancy is twice as that of the full sets of balanced codes. The gap between Knuth's algorithm redundancy and that of the full sets of balanced codes is significantly considerable. This paper attempts to reduce that gap. Furthermore, many constructions assume that a full balancing can be performed without showing the steps. A full balancing refers to the overall balancing of the encoded information together with the prefix. We propose an efficient way to perform full balancing scheme which do not make use of look up tables or enumerative coding.
... , x n + b). The unknown channel gain and offset mismatch may lead to a devastating loss in performance, as shown, for example, in [1]. ...
... In optical disc data storage devices and non-volatile memories, constrained codes, specifically dc-free or balanced codes, have been used and/or proposed to counter the effects of offset and gain mismatch [1]. Jiang et al. [4] addressed a q-ary balanced coding technique, called rank modulation, for circumventing the difficulties with flash memories having aging offset levels. ...
Article
Full-text available
The performance of certain transmission and storage channels, such as optical data storage and nonvolatile memory (flash), is seriously hampered by the phenomena of unknown offset (drift) or gain. We will show that minimum Pearson distance (MPD) detection, unlike conventional minimum Euclidean distance detection, is immune to offset and/or gain mismatch. MPD detection is used in conjunction with (T) -constrained codes that consist of (q) -ary codewords, where in each codeword (T) reference symbols appear at least once. We will analyze the redundancy of the new (q) -ary coding technique and compute the error performance of MPD detection in the presence of additive noise. Implementation issues of MPD detection will be discussed, and results of simulations will be given.
... Balanced codes have been intensively studied since its proposal in 1986. This is because of their important interests in applications such as magnetic and optical recording devices (DVD, Blu-Ray and CD) [1], cable transmissions [2], and very large-scale integration (VLSI) systems [3]. Balanced codes are used in digital transmission through cables for dealing with coupling effects by attenuating the cut-off at low frequencies. ...
Article
A simplified and efficient algorithm with parallel decoding capacity was presented by Knuth for balancing binary sequences (binary sequences are a combination of zeros and ones, making up a set of instructions and data that a computer understands). This study proposes a generalization of this algorithm for q-ary sequences (multiplexed sequences, clock-controlled sequences, geometric sequences). This new approach is also based on simplicity and parallel decoding for q-ary balanced codes. Furthermore, it has a fixed redundancy for short and long sequences that equals logq k, where k is the sequence length, and no lookup tables are required.
... Balanced codes have been widely studied due to its applicability in the field of communication and storage structures such as optical and magnetic recording devices like Blu-Ray, DVD and CD [1]; error correction and detection [2], [3]; cable transmission [4] and noise attenuation in VLSI systems. The decoding of balanced codes is fast, and it is done in parallel which avoids latency in communication. ...
Article
Full-text available
In this paper, the construction of binary balanced codes is revisited. Binary balanced codes refer to sets of bipolar codewords where the number of "1"s in each codeword equals that of "0"s. The first algorithm for balancing codes was proposed by Knuth in 1986; however, its redundancy is almost two times larger than that of the full set of balanced codewords. We will present an efficient and simple construction with a redundancy approaching the minimal achievable one
... B ALANCED, sometimes called dc-free, q-ary sequences have found widespread application in popular optical recording devices such as CD, DVD, and Blu-Ray [1], cable communication [2], and recently in non-volatile (flash) memories [3]. A sequence of symbols is said to be balanced if the sum of the symbols equals the prescribed balancing value. ...
Article
Full-text available
We investigate a Knuth-like scheme for balancing q-ary codewords, which has the virtue that look-up tables for coding and decoding the prefix are avoided by using precoding and error correction techniques. We show how the scheme can be extended to allow for error correction of single channel errors using a fast decoding algorithm that depends on syndromes only, making it considerably faster compared to the prior art exhaustive decoding strategy. A comparison between the new and prior art schemes, both in terms of redundancy and error performance, completes the study.
... In addition, codes have been used in practice to make the detection quality less dependent of the channel's gain and offset. In optical disc recording devices, dc-balanced binary codes have been used to counter the effects of unknown gain and offset levels [4]. Jiang et al. [2] addressed a coding technique called rank modulation for circumventing the difficulties in flash memories having aging offset levels. ...
Conference Paper
Full-text available
We will present coding techniques for transmission and storage channels with unknown gain and/or offset. It will be shown that a codebook of length-n q-ary codewords, S, where all codewords in S have equal balance and energy show an intrinsic resistance against unknown gain and/or offset. Generating functions for evaluating the size of S will be presented. We will present an approximate expression for the code redundancy for asymptotically large values of n.
Chapter
Digital transmission and recording systems invariably transport information across a band of restricted width. The center frequency of this band may be high with respect to the band width, as it is in radio transmission. It may also be of the same order of magnitude or even zero, as in cable transmission and digital recording. In the first case the information must be modulated on to a carrier in order to convert it into the passband. In the second case this step is, in principle, not needed. The adjective ‘baseband’ serves to indicate that no carrier modulation is used. Instead, baseband transmission systems typically use a modulation code to match the characteristics of the data to those of the channel. At the receiving end of the system, equalization, detection, timing recovery and adaptation techniques are combined to recover the data. In the forthcoming chapters we discuss all these subjects. By way of introduction and motivation, the. present chapter gives a survey of three important application areas of digital baseband transmission, namely digital subscriber lines, digital magnetic recording and digital optical recording. The aim is to convey a flavor of the origin, nature and importance of the various transmission impairments that arise, to exemplify some of the techniques that exist to prevent and/or counteract them, and to show that the principal types of impairment are common to all systems. For future reference we also model some of the impairments analytically. We should stress that the present survey is only meant as an introduction to the various application areas. As such it is restricted both in scope and in depth. Section 2.5 lists several references that provide much more complete treatments.
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