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Project log

Kees Schouhamer Immink
added a research item
We present and analyze a new systematic construction of bipolar balanced codes where each code word contains equally many −1's and +1's. The new code is minimally modified as the number of symbol changes made to the source word for translating it into a balanced code word is as small as possible. The balanced codes feature low redundancy and time complexity. Large look-up tables are avoided.
Kees Schouhamer Immink
added a research item
Channel codes, sometimes called transmission or line codes, are applied in storage systems such as magnetic tape or disc and optical discs. Applications are also found in transmission systems over fiber or metallic cable. A channel code converts the digital source information to a form suitable for a specific transmission medium. For example DC-free codes are designed in such a way that the encoded signal has suppressed frequency components in the region around zero frequency. These codes are for example applied in transmission systems having insufficient response in the low-frequency range. Another requirement imposed on a channel code originates from the fact that the maximum distance between transitions in the encoded signal, the maximum 'run length', should be limited to enable a simple system clock recovery in the receiver. This thesis deals with systematic methods of designing DC-free and run-length-limited codes. Procedures are given for a simple enumerative encoding and decoding of the codewords. Also described are several properties of channel codes such as spectral and run length distributions. Criteria derived from information theory are used to compare the channel codes.
Kees Schouhamer Immink
added a research item
In this work, given n, p>0 , efficient encoding/decoding algorithms are presented for mapping arbitrary data to and from n×n binary arrays in which the weight of every row and every column is at most pn. Such constraint, referred as p-bounded-weight-constraint, is crucial for reducing the parasitic currents in the crossbar resistive memory arrays, and has also been proposed for certain applications of the holographic data storage. While low-complexity designs have been proposed in the literature for only the case p=1/2 , this work provides efficient coding methods that work for arbitrary values of p . The coding rate of our proposed encoder approaches the channel capacity for all p .
Kees Schouhamer Immink
added a research item
We present coding methods for generating ℓ-symbol constrained codewords taken from a set, S, of allowed codewords. In standard practice, the size of the set S, denoted by M=|S|, is truncated to an integer power of two, which may lead to a serious waste of capacity. We present an efficient and low-complexity coding method for avoiding the truncation loss, where the encoding is accomplished in two steps: first, a series of binary input (user) data is translated into a series of M-ary symbols in the alphabet M = {0, ... ,M - 1}. Then, in the second step, the M-ary symbols are translated into a series of admissible ℓ-symbol words in S by using a small look-up table. The presented construction of Pearson codes and fixed-weight codes offers a rate close to capacity. For example, the presented 255B320B balanced code, where 255 source bits are translated into 32 10-bit balanced codewords, has a rate 0.1 % below capacity.
Kees Schouhamer Immink
added a research item
We report on a new class of dc-free c odes of rate (n-1)/n, n is odd. Spectral and runlength properties of the new codes have been evaluated by computer simulation.
Kees Schouhamer Immink
added a research item
In this paper we derive a formula for the number of code words of a DC2-balanced codes. This number is expressed as a coefficient of a generating function in two variables. In addition, we establish a lower as well as an upper bound for this number. In particular, we show that the information rate tends to unity when the code length tends to infinity.
Kees Schouhamer Immink
added a research item
We investigate a new approach for designing spectral shaping block codes with a target spectrum, H_t(f), that has been specified at a plurality of frequencies. We analyze the probability density function of the spectral power density function of uncoded n-symbol bipolar code words. We present estimates of the redundancy and the spectrum of spectral shaping codes with specified target spectral densities H_t(f_i) at frequencies f_i. Constructions of low-redundancy codes with suppressed low-frequency content are presented that compare favorably with conventional dc-balanced codes currently used in data transmission and data storage devices with applications in consumer electronics.
Kees Schouhamer Immink
added a research item
We describe properties and constructions of constraint-based codes for DNA-based data storage which account for the maximum repetition length and AT/GC balance. Generating functions and approximations are presented for computing the number of sequences with maximum repetition length and AT/GC balance constraint. We describe routines for translating binary runlength limited and/or balanced strings into DNA strands, and compute the efficiency of such routines. Expressions for the redundancy of codes that account for both the maximum repetition length and AT/GC balance are derived.
Kees Schouhamer Immink
added a research item
The subblock energy-constrained codes (SECCs) have recently attracted attention due to various applications in communication systems such as simultaneous energy and information transfer. In a SECC, each codeword is divided into smaller subblocks, and every subblock is constrained to carry sufficient energy. In this work, we study SECCs under more general constraints, namely bounded SECCs and sliding-window constrained codes (SWCCs), and propose two methods to construct such codes with low redundancy and linear-time complexity, based on Knuth’s balancing technique and sequence replacement technique. For certain codes parameters, our methods incur only one redundant bit.
Kees Schouhamer Immink
added a research item
This paper describes a new coding method based on binary (d, k) runlength constraints used for recording or transmitting an audio or video signal, computer data, etc. Data words of m bits are translated into codewords of n bits using a conversion table. The codewords satisfy a (d, k) runlength constraint in which at least d and not more than k '0's occur between consecutive '1's. The n-bit codewords alternate with p-bit merging words which in the prior art are selected such that the d and k are satisfied at the borders of consecutive codewords. We present a new coding method, where the codewords obey the (d, k)-constraint, but the merging words are not required to obey the (d)-constraint. The merging word that satisfies said conditions, yielding the lowest low-frequency spectral content of the encoded signal obtained after modulo-2 integration, is selected. The spectral performance of the new coding method has been appraised by computer simulations for the EFM (Eight-to-Fourteen Modulation) parameters, d = 2, k = 10, and p = 3. The low-frequency content of the signal generated by the newly presented coding method is around 4 dB lower in the relevant low-frequency range than that generated by the conventional EFM method.
Kees Schouhamer Immink
added a research item
We analyze codes for DNA-based data storage which accounts for the maximum homopolymer repetition length and GC-AT balance. We present a new precoding method for translating words with a maximum run of k zeros into words with a maximum homopolymer run m = k + 1, which is atractive for securing GC-AT balance. Generating functions are presented for enumerating the number of n-symbol k-constrained codewords of given GC-AT balance Various efficient constructions are presented of block codes that satisfy a combined balance and maximum homopolymer run.
Kees Schouhamer Immink
added a research item
We apply the central limit theorem for deriving approximations to the auto-correlation function and power density function (spectrum) of second-order spectral null (dc2-balanced) codes. We show that the auto-correlation function of dc2-balanced codes can be accurately approximated by a cubic function. We show that the difference between the approximated and exact spectrum is less than 0.03 dB for codeword length n=256.
Kees Schouhamer Immink
added a research item
We apply the central limit theorem for deriving approximations to the auto-correlation function and power density function (spectrum) of second-order spectral null (dc2-balanced) codes.We show that the auto-correlation function of dc2-balanced codes can be accurately approximated by a cubic function. We show that the difference between the approximate and exact spectrum is less than 0.04 dB for codeword length n = 256.
Kees Schouhamer Immink
added a research item
We apply the central limit theorem for deriving approximations to the auto-correlation function and power density function (spectrum) of second-order spectral null (dc^2-balanced) codes. We show that the auto-correlation function of dc^2-balanced codes can be accurately approximated by a cubic function. We compare the approximate auto-correlation function and spectrum with the exact auto-correlation function and spectrum of full set dc^2-balanced codes. We show that the difference between the approximate and exact spectrum is less than 0.04 dB for codeword length n = 256. We compare the spectral performance of dc-balanced versus dc^2-balanced codes in the low-frequency range.
Kees Schouhamer Immink
added 5 research items
We report on a new class of dc-free codes of rate (n-1)/n, n is odd. Spectral and runlength properties of the new codes have been evaluated by computer simulation
We find an analytic expression for the maximum of the normalized entropy -Σ<sub>i∈T</sub>p<sub>i</sub> ln p<sub>i</sub>/Σ<sub>i∈T</sub>ip<sub>i</sub> where the set T is the disjoint union of sets S<sub>n</sub> of positive integers that are assigned probabilities P<sub>n</sub>, Σ<sub>n</sub>P<sub>n </sub>=1. This result is applied to the computation of the capacity of weakly (d,k)-constrained sequences that are allowed to violate the (d,k)-constraint with small probability
A new coding technique is proposed that translates binary user information into a constrained sequence having the virtue that at most k `zeros' between logical `ones' will occur. The new construction offers a high rate while both the complexity for encoding and decoding are still very low. Single channel bit errors will result in at most one decoded byte error. A worked example is described with rate 16/17, k=6 code
Kees Schouhamer Immink
added 6 research items
Knuth published a very simple algorithm for constructing bipolar codewords with equal numbers of +1's and -1's, called balanced codes. In our paper we will present new code constructions that generate balanced runlength limited sequences using a modification of Knuth's algorithm.
The prior art construction of sets of balanced codewords by Knuth is attractive for its simplicity and absence of look-up tables, but the redundancy of the balanced codes generated by Knuth's algorithm falls a factor of two short with respect to capacity. We present a new construction, which is simple, does not use look-up tables, and is less redundant than Knuth's construction. In the new construction, the user word is modified in the same way as in Knuth's construction, that is by inverting a segment of user symbols. The prefix that indicates which segment has been inverted, however, is encoded and decoded in a different, more efficient, way.
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.
Kees Schouhamer Immink
added 2 research items
A method for converting m-bit information words into n-bit code words and vice versa. The code words have a limited disparity in order to obtain a d.c. free code. A reduction of the low-frequency content of the spectrum is obtained by selecting the code words in such a way that the sum ##EQU1## remains restricted over all the previously generated bits xj of the preceding code words.
A method of encoding n-bit information words into m-bit code words and the other way round is described, which code words have a specific disparity d and a digital sum value which is limited to values p and q. In order to enable encoding and decoding without the use of an extensive look-up table, use is made of a series of numbers which is a modified version of numbers in conformity with the Newton binomial. By means of this modified series, the n-bit information words, which are arranged in conformity with their binary weights, are mapped lexicographically and unambiguously onto code words with said limitations, and the other way round.
Kees Schouhamer Immink
added 3 research items
The eigenstructure of bidiagonal Hessenberg-Toeplitz matrices is determined. These matrices occur as skeleton matrices of finite-state machines generating certain asymmetrically DC-constrained binary sequences that can be used for simulating pilot tracking tones in digital magnetic recording. The eigenstructure is used to calculate the Shannon upper bound to the entropy of the finite state machine as well as the power spectrum of the maxentropic process generated by it.
We report on the performance assessment of two methods for generating DC-free runlength-limited sequences. Redundant bits used to optimize the low-frequency properties are multiplexed with user data or encoded data. In the first method, the redundant bits are multiplexed with the channel bits generated by a (d,k) encoder. In the second method, on the other hand, the redundant bits are multiplexed with the user data. i.e. prior to application of the (d,k) encoder. The second method can only be used if the (d,k) encoder satisfies the parity preserving condition, i.e., data words and code words of that code must have the same parity. In the article we describe in detail an example of a parity preserving (1, 8) code.
Kees Schouhamer Immink
added 3 research items
We present an enumerative technique for encoding and decoding DC-free runlength-limited sequences. This technique enables the encoding and decoding of sequences approaching the maxentropic performance bounds very closely in terms of the code rate and low-frequency suppression capability. Use of finite-precision floating-point notation to express the weight coefficients results in channel encoders and decoders of moderate complexity. For channel constraints of practical interest, the hardware required for implementing such a quasi-maxentropic coding scheme consists mainly of a ROM of at most 5 kB
this paper, is to directly employtheintensitycharacteristics in the frequency domain. As coding method weweuseguided scrambling [3]. Guided scrambling (GS) is a member of a larger class of related coding schemes called multi-mode code. In multi-mode codes, each source word can be represented by a member of a selection set consisting of L codewords. The encoder evaluates the "quality" of each codeword in the selection set, and transmits that codeword that "best" matches the quality criterion at hand. The members of the selection sets are not judiciously chosen and stored in memory, but are randomly picked. The basic idea is that, provided the selection set is sufficiently large, we will find, with high probability, an adequate codeword fulfilling the constraints. The advantage of this approach is clear: at the encoder site we only need a) a simple mechanism for translating source words into "random" codewords and b) a mechanism for evaluating the "quality" of the candidate words. The stumble blockofconventional large codes, the look-up table, can be avoided, and replaced by a simple randomization algorithm. The paper is organized as follows. Section 2 analyses the distribution of extreme value of power intensity. The GS coding scheme is then described in Section 3. The computer simulation results of the GS coding are provided in Section 4. Finally,inSection5we conclude the paper 2 Extrema of the Power Intensity Distribution In digital holographic data storage, the data is commonly recorded as Fourier holograms, which are the two-dimensional frequency-domain data arrays (pages). Assume the source data are random symbols drawn from the alphabet f;1# 1g, then (see Appendix) the power intensity I at an arbitrary, non-zero, frequency pointfollows, by good approximation, an...
Recently, for HD video recorders, a high density rewritable disc system using a blue laser diode has been strongly recommended. At the last ODS and ISOM, we proposed extremely efficient DC-free RLL codes for a high density rewritable optical system (K.A.S. Immink et al, ODS '01, WC1, 2001, and ISOM '01, TH-J-29, pp. 152-153, 2001). Additionally, we have shown that the newly developed GS913 (guided scrambling 9 to 13), d=1 code can achieve a 4.5% higher overall rate compared with the (1,7)PP code. In this paper, we report the performance of this GS913 code for a high density rewritable disc system using a blue laser diode (405 nm), NA 0.85 and 0.1 mm thickness cover layer.
Kees Schouhamer Immink
added 10 research items
In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of 1s and 0s, called balanced codes. Knuth's algorithm is, since look-up tables are absent, well suited for use with large codewords. The redundancy of Knuths balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In our paper we will present results of our attempts to improve the performance of Knuths balanced codes.
DC-free run-length limited codes have been the cornerstone of all three generations of optical recording, CD, DVD and BD. Research into very efficient coding methods is paramount for the upcoming fourth generation. Guided Scrambling (GS) is an efficient coding method that has been reported in the literature. Under GS rules, a user word is translated into a plurality of possible candidate words, and among the candidate words the encoder selects the codeword with the least low-frequency spectral content. In our paper, we will present results of our attempts to improve the performance of GS-based codes. We will present new selection criteria and evaluate their performance and complexity. Specifically, we will evaluate the new selection criteria to the 2/3(1,7) parity preserving code used in Blu-Ray Disc.
In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of one's and zero's, called balanced codes. Knuth's algorithm is well suited for use with large codewords. The redundancy of Knuth's balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In this paper, we will present results of our attempts to improve the performance of Knuth's balanced codes.
Kees Schouhamer Immink
added a research item
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.
Kees Schouhamer Immink
added 5 research items
The servo position information of magnetic tape or disk recorders is often recorded as low-frequency components usually called pilot tracking tones. Binary codes giving rise to a spectral null at an arbitrary frequency are used to provide space for the allocation of auxiliary pilot tones. Here, encoding methods are treated in which binary data are mapped into constrained binary sequences for shaping the spectrum. The rate and power spectral density function of memoryless codes that exhibit spectral nulls are computed. The relationship between the code redundancy and spectral notch width is quantified with a parameter called the sum variance. It is found that twice the product of the spectral notch width times the sum variance is approximately unity
The problem of appraising the spectral performance of codes based on a new algorithm for generating zero-disparity codewords presented by D.E. Knuth (1986) is addressed. In order to get some insight into the efficiency of Knuth's construction technique, the authors evaluate the spectral properties of its code streams. The structure of Knuth codes allows the derivation a simple expression for (an approximation to) the sum of variance of these codes. This quantity plays a key role in the spectral performance characterization of DC-balanced codes. The authors evaluate this expression and compare the sum variance of Knuth codes with the sum variance of the polarity bit codes for fixed redundancy. Under the premise that the sum variance can serve as a quantity to judge the width of the spectral notch, the authors conclude that codes based on Knuth's algorithm offer less spectral suppression than polarity bit codes with the same redundancy.
In this reported work, Knuth's balancing scheme, which was originally developed for unconstrained binary codewords is adapted. Presented is a simple method to balance the NRZ runlength constrained block codes corresponding to (d, k) constrained NRZI sequences. A short marker violating the maximum runlength or k constraint is used to indicate the balancing point for Knuth's inversion. The marker requires fewer overhead bits and less implementation complexity than indexing the balancing point's address by mapping it onto a (d, k) or runlength constrained prefix, such as when applying Knuth's original scheme more directly. The new code construction may be attractive for future magnetic and especially optical recording schemes. In fact the current optical storage media, such as the CD, DVD and Blue Ray Disc, all attempt to achieve some suppression of low frequency components of the constrained codes, by exploiting a limited degree of freedom within the set of candidate (d, k) words.
Kees Schouhamer Immink
added 2 research items
We report on a class of high-rate de-free codes, called multimode codes, where each source word can be represented by a codeword taken from a selection set of codeword alternatives. Conventional multimode codes will be analyzed using a simple mathematical model. The criterion used to select the "best" codeword from the selection set available has a significant bearing on the performance. Various selection criteria are introduced and their effect on the performance of multimode codes will be examined.
We will discuss the generation of DC-free runlength-limited (DCRLL) sequences. We propose to employ standard RLL codes, where DC-control is effectuated by multiplexing the source data or the encoded data with DC-control bits. The DC-control bits offer the degree of freedom required to shape to spectrum. It is shown that a new technique, called parity preserving assignment, will offer great benefits over other constructions
Kees Schouhamer Immink
added 2 research items
Suppression of the low-frequency (lf) components of the modulated data stream is a system requirement in optical recording which facilitates the usage of servo systems for reading the optical disc. Insufficient suppression of the lf components of the coded spectrum will lead to improper functioning of the servo systems, and/or acoustical noise generated by the servo systems, and/or additional power dissipation in the servo amplifiers. Low-frequency components are avoided in state of the art systems such as CD and DVD by using codes, called dc-free codes , which suppress the energy in the lf range. Clearly, the more lf suppression, the more overhead in coding rate must be spent, and a sound trade-off has to be sought between proper lf suppression and coding efficiency. It has been found that lf suppression can also be improved by coding methods, which use a look-ahead (LA) algorithm that looks ahead p codewords, and evaluates, based on a suitable metric, the full search tree of 2^p possible choices of codewords in the tree. Recently, coding schemes, which use Guided Scrambling (GS) have been proposed for suppressing the lf content. It has been shown that GS schemes can achieve a lf suppression which is very close to the theoretical maximum. In this paper, we will report on a performance comparison of coding schemes based on Look-Ahead and Guided Scrambling techniques
We report on new DC-free runlength-limited codes (DCRLL) intended for the next generation of DVD. The efficiency of the newly developed DCRLL schemes is extremely close to the theoretical maximum, and as a result, significant density gains can be obtained with respect to prior art coding schemes
Kees Schouhamer Immink
added a research item
We report on new class of dc-free codes that use the Fast Hadamard Transform (FHT) to evaluate a selection set of candidate codewords. The codeword with the least contribution to the low-frequency content is transmitted. The FHT makes it possible to efficiently evaluate the selection set of candidate codewords. Spectral properties of the new codes have been evaluated by computer simulation. 1