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Abstract
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
... Figure 20 System model for Bliss's reverse-concatenation using the (0, k) fixed-rate bit stuff codes. ...
... The FRB algorithm compares favorably with enumerative [15],[[17],Chap.6],[19], and combinatorial [20],[60] encoding: two important existing methods to generate (0, k) sequences. Specifically, the FRB encoding/decoding is simpler than enumeration , while achieving (asymptotically) similarly high encoding rates. ...
... Specifically, the FRB encoding/decoding is simpler than enumeration , while achieving (asymptotically) similarly high encoding rates. The FRB encoding rates are also far greater than that of the combinatorial construction of Immink and Wijngaarden [20], at the cost of slightly higher encoding/decoding complexity. In theory, the FRB algorithm thus provides an effective means to generate very high-rate (0, k) sequences. ...
Run-Length-Limited (RLL) channels are found in digital recording systems like the Hard Disk Drive (HDD), Compact Disc (CD), and Digital Versatile Disc (DVD). This thesis presents novel encoding algorithms for RLL channels based on a simple technique called bit stuffing. First, two new capacity-achieving variable-rate code constructions are proposed for (d,k) constraints. The variable-rate encoding ideas are then extended to (0,G/I) and other RLL constraints. Since variable-rate codes are of limited practical value, the second half of this thesis focuses on fixed-rate codes. The fixed-rate bit stuff (FRB) algorithm is proposed for the design of simple, high-rate (0,k) codes. The key to achieving high encoding rates with the FRB algorithm lies in a novel, iterative pre-processing of the fixed-length input sequence prior to bit stuffing. Detailed rate analysis for the proposed FRB algorithm is presented, and upper and lower bounds on the asymptotic (in input block length) encoding rate are derived. Several system-level issues of the proposed FRB codes are addressed, and FRB code parameters required to design rate 100/101 and rate 200/201 (0,k) codes are tabulated. Finally, the proposed fixed-rate encoding is extended to (0,G/I) constraints. Ph.D. Committee Chair: McLaughlin, Steven; Committee Member: Barnwell, Thomas; Committee Member: Barry, John; Committee Member: Fekri, Faramarz; Committee Member: Tetali, Prasad
... These are (d = 0, k) codes, where d and k denote, respectively , the minimum and maximum run-length of zeros between ones in an unprecoded channel data stream. There are several RLL codes with or without enhanced error control capabilities [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. The (d = 0, k/I) RLL codes use gated-partition logic to achieve high rates such as 8/9 [1] and 16/17 [2], while focusing on the k, I (interleave) constraints. ...
... Hence, the number of available codewords is increased sufficiently to obtain RLL codes of the highest code rate N/(N + 1) for any block length N + 1. Code rates as high as possible are required to increase the linear recording density in bandlimited systems and avoid a larger bandwidth expansion factor B e ∼ R C −1 . Low complexity high-rate constrained codes were presented in [9] with smaller constraint k. The new proposed codes are characterized by lower computational complexity independent of the chosen blocklength N + 1. ...
... They have an increased list of error-detection conditions rather than just constraints pertaining to k only as in [1, 2] of encoding/decoding bounds the decoding error propagation within a block's length only. Very low error propagation decoding is supported by the small number of manipulated bits Q = 1, 2 per codeword (Q = 8 in [9]). In Section 2, the code construction methodology is presented , with a specific construction example. ...
We present a new methodology for the construction of high-rate channel modulation run-length-limited RLL (0,k) codes. Simple modulation encoders and decoders are constructed, with low error propagation during decoding. They combine partial error detection capability (PED) to boost the performance of a concatenated outer Error Correction Code (ECC) [1]. Moreover, current systems are using low redundancy ECC, and the overall rate is mainly determined by the inner modulation code rate, which critically is to be maintained high. Code rates R c=N/(N+1), for example, 16/17, 24/25 and higher are achievable, with efficiency exceeding 0.94 and 0.96, respectively. The proposed fixed length block decodable codes, are generalized schemes of the type N/(N+1)(d=0,k=[N/2]) for N≥5.
... In certain situations, the entire source word has to be modified which makes the procedure prone to error propagation. The class of rate -constrained codes, was constructed to minimize error propagation [111]. Error propagation is confined to one decoded 8-bit symbol, irrespective of the codeword length Recently, the publications by Fair et al. [48] and Immink and Patrovics [110] on guided scrambling brought new insights into high-rate code design. ...
... Let the code rate , the codeword length , and the size of the selection set Then we observe that with probability a codeword violates the constraint. The alternative implementation [111] requires a rate of -four times the redundancy of the weakly constrained code-to strictly guarantee the same constraint. ...
... In certain situations, the entire source word has to be modified which makes the procedure prone to error propagation. The class of rate -constrained codes, was constructed to minimize error propagation [111]. Error propagation is confined to one decoded 8-bit symbol, irrespective of the codeword length Recently, the publications by Fair et al. [48] and Immink and Patrovics [110] on guided scrambling brought new insights into high-rate code design. ...
... Let the code rate , the codeword length , and the size of the selection set Then we observe that with probability a codeword violates the constraint. The alternative implementation [111] requires a rate of -four times the redundancy of the weakly constrained code-to strictly guarantee the same constraint. ...
Constrained codes are a key component in digital recording devices
that have become ubiquitous in computer data storage and electronic
entertainment applications. This paper surveys the theory and practice
of constrained coding, tracing the evolution of the subject from its
origins in Shannon's classic 1948 paper to present-day applications in
high-density digital recorders. Open problems and future research
directions are also addressed
... This translates to low hardware requirements for the encoder and the decoder. Another method with similar aims but for a different class of line codes is described in [50,51]. ...
Channel coding is an important consideration influencing the design of a communications system. In particular, error control coding is used to detect and/or correct errors and line coding to modify the characteristics of the transmitted signal to suit other constraints of the channel, such as restricted frequency response. This thesis explores aspects of channel coding for such constrained channels with emphasis given to error control coding. Specifically, the hrst chapter of this thesis presents a general overview of channel coding, presents the organisation of the thesis and details the main contributions. The second chapter gives an overview of the principles of error control coding and line coding and explains a few terms that are connnonly used in the remainder of the thesis. One kind of constrained channel investigated here is the binary asymmetric error channel, where error transitions from one to zero occur with different probability than from zero to one. Error correcting codes for this channel and their properties are investigated in the third chapter. The fourth chapter introduces disparity control coding, and proposes a new error control coding structure that satisfies disparity constraints for both binary asymmetric and symmetric error channels. Run length limited channels are the subject of the hfth chapter. A new coding structure is proposed that offers advantages in performance over the one conventionally used for error control in such channels. The sixth chapter introduces peak power constraints present in multi-carrier systems. Codes that can be used limit the peak to average power ratio of such systems are presented and the application of the coding structure of the fifth chapter is also discussed. The final chapter brings the thesis to a conclusion by summarising the main results and proposing areas where further work may be fruitful.
... For example, let the user data be "11 000 110." We find , and transmit "010 111 110." The aforementioned code can be turned into a rate 16/17 code by interleaving with eight uncoded data bits as presented by Immink and Wijngaarden [11]. ...
In this paper, we will present coding techniques for the character-constrained channel, where information is conveyed using q-bit characters (nibbles), and where w prescribed characters are disallowed. Using codes for the character-constrained channel, we present simple and systematic constructions of high-rate binary maximum runlength constrained codes. The new constructions have the virtue that large lookup tables for encoding and decoding are not required. We will compare the error propagation performance of codes based on the new construction with that of prior art codes.
... For example, let the user data be "11 000 110." We find , and transmit "010 111 110." The aforementioned code can be turned into a rate 16/17 code by interleaving with eight uncoded data bits as presented by Immink and Wijngaarden [11]. ...
In this paper, we will present coding techniques for the character-constrained channel, where information is conveyed using q-bit characters (nibbles), and where w prescribed characters are disallowed. Using codes for the character-constrained channel, we present simple and systematic constructions of high-rate binary maximum runlength constrained codes. The
new constructions have the virtue that large lookup tables for encoding and decoding are not required. We will compare the error propagation performance of codes based on the new construction with that of prior art codes.
... For encoding from binary message sequences, we consider a subset of , denoted , which consists of sequences, where . The coding rate will be reduced to (5) In general, the decoding/encoding complexity of may be high. However, in case that is an integer, the encoding/decoding complexity can be very low. ...
We propose two constructions for multilevel run-length-limited (RLL) block codes for which the rates are very close to the capacity. For each code construction, we propose a variation that has the advantage of low complexity of encoding and decoding. We conducted a simulation to see the combined effect of channel coding and our proposed RLL coding over an optical recording channel.
... The parameters l = dk=2e and r = k ; l denote the maximum numberof 'zeros' with which t h e words start or end, respectively. For large codeword length n the numberofcodewords can be approximated by N(n) A n (11) where is the largest real root of the characteristic equation z k+2 ; 2z k+1 + 1 = 0 (12) and the constant A, which is independent o f n, equals A = ; q(1= ) p 0 (1= ) : (13) Note that the channel capacity C(0 k ) satis es C(0 k ) = log 2 : ...
The construction of high-rate codes is far from obvious, as table look-up for encoding and decoding is an engineering impracticality. The usual approach is to supplementthep source bits with m = q;p bits. Under certain, usually simple, rules the source word is modified in suchawaythat the modified word plus supplement bits comply with the constraints. The information that certain modifications have been made is carried by the m supplement bits. The receiver, on reception of the word, will undo the modifications. In order to reduce complexity and error propagation, the number of bits affected by a modification should be as small as possible. We will survey some examples of code constructions. 1 1
We construct some multilevel RLL block codes which can be implemented with low complexity of encoding and decoding. The coding rates of the constructed codes can closely approach the capacity. Simulation for two recording system models is implemented to see the combined effect of channel coding and the constructed RLL coding.
We propose non-DC-free generalized PRML (GPRML) that are suppressed DC contents for matching to the response of perpendicular magnetic recording channel with a ring-head. In addition, DC-free encoding is considered to prevent low-frequency disturbances. The SNR performance is obtained by combining the various PRML channels with DC-free and non-DC-free codes during the normalized recording density increases from 2.5 to 3.5. The GPRML detections without using DC-free code get SNR gains more than 1dB compared to the conventional PRML systems at 10/sup -5/BER. We confirmed that the rate 127/136 DC-free coded GPRML systems show good performances compared with the 16/17 non-DC-free coded GPRML systems. In results, DC-free coded GPRML detections get gains about 1.4dB and 2.0dB at the density of 3.3 and 3.5, respectively.
The author reports on the performance of a new class of
constrained codes, called weakly constrained codes. These codes do not
strictly guarantee the imposed channel constraints, but rather generate
codewords that violate, with a given (small) probability, the prescribed
constraint. Weakly constrained codes are specifically of interest when
it is desirable that the code rate R=p/q is very high, requiring
codewords of length q>100
We present advanced combinatorial techniques for constructing
maximum runlength-limited (RLL) block codes and maximum transition run
(MTR) codes. These codes find widespread application in recording
systems. The proposed techniques are used to construct a high-rate
multipurpose modulation code for recording systems. The code, a rate
16/17, (0,3,2,2) MTR code, that also fulfills (0,15,9,9) RLL constraints
is a high-rate distance-enhancing code with additional constraints for
improving timing and gain control. The encoder and decoder have a
particularly efficient architecture and allow an instantaneous
translation of 16-bit source words into 17-bit codewords and vice versa.
The code has been implemented in Lucent read-channel chips and has
excellent performance
We introduce the fixed-rate bit stuff (FRB) algorithm for efficiently encoding and decoding maximum-runlength-limited (MRL) sequences. Our approach is based on a simple, variable-rate technique called bit stuffing . Bit stuffing produces near-capacity achieving codes for a wide range of constraints, but encoding is variable-rate, which is unacceptable in most applications. In this work, we design near-capacity fixed-rate codes using a three-step procedure. The fixed-length input data block first undergoes iterative preprocessing, followed by variable-rate bit stuffing, and finally dummy-bit padding to a fixed output length. The iterative preprocessing is key to achieving high encoding rates. We discuss rate computation for the proposed FRB algorithm and show that the asymptotic (in input block length) encoding rate is close to the average rate of the variable-rate bit stuff code. Then, we proceed to explore the effect of decreasing/increasing the number of preprocessing iterations. Finally, we derive a lower bound on the encoding rate with finite-length input blocks and tabulate the parameters required to design FRB codes with rate close to 100/101 and 200/201.
Self-clocking five bit record playback system
- G E Milligan