Runlength Limited Error Control Research Articles

Run Length Limited Error Control Codes Derived from Reed Solomon Codes

Reed Solomon codes were standardized for numerous wireless communication systems. Most practical Reed Solomon codes belong to non-binary linear block codes defined over finite fields with characteristic two. Each linear block code contains one codeword composed of all zeros. The concatenation of this and also other codewords can lead to long, theoretically even infinite, runs of equal symbols. Such long runs do not support synchronization in wireless receivers and therefore are unwanted. In this paper it is shown that extended and some appropriately shortened Reed Solomon codes constructed over finite fields with characteristic two can be transformed into Run Length Limited Reed Solomon codes. The presented method, if applicable, allows for doing it without inserting additional redundancy. Another advantage is that after the transformation, if some round conditions are fulfilled, the decoding does not have to be rebuilt.

Run length limited CCSDS convolutional codes for optical communications

Abstract This paper presents the construction of RLL-ECCs (run length limited error control codes) from three selected ECCs specified by Consultative Committee for Space Data Systems (CCSDS) for optical communications. The RLL-ECCs obtained present a practical alternative to CCSDS codes with pseudo-randomizers. Their advantage is that the maximal run lengths of equal symbols in their codeword sequences are guaranteed, which is not the case if the common approach with pseudo-randomizers is used. The other advantages are that no additional redundancy is introduced into encoded codewords and that the encoding and decoding procedures of the original error control CCSDS codes do not have to be modified in the following cases: Firstly, if hard decoding is used and the transmission channel can be modeled as a BSC (binary symmetric channel) and secondly, if soft decoding and coherent BPSK (binary phase shift keying) modulation is used and the appropriate transmission channel model is an AWGN (additive white Gaussian noise) channel.

On run-length limited error control codes constructed from binary product codes

Abstract In this paper it is presented that run-length limited error control codes could be constructed from any two or more- dimensional binary product codes as long as at least one of the one-dimensional binary component codes is or can be converted to a run-length limited error control code. The advantages of this construction are as follows: It does not require any additional redundancy except that which is already contained in the original error control code and that the encoding and decoding procedure used for the underlying error control code do not to be changed

Construction for obtaining trellis run length limited error control codes from convolutional codes

Abstract Recently a new construction of run length limited block error control codes based on control matrices of linear block codes was proposed. In this paper a similar construction for obtaining trellis run length limited error control codes from convolutional codes is described. The main advantage of it, beyond its simplicity is that it does not require any additional redundancy except the one which is already contained in the original convolutional error control code. One example is presented how to get such a code from a convolutional low density parity check code.

Run length limited error control codes construction based on one control matrix property

AbstractIn this manuscript a simple method is presented for constructing run length limited error control codes from linear binary block codes. The run length limited properties are obtained via addition of a carefully chosen fixed binary vector - a modifier to all codewords without introducing any additional redundancy. Modifier selection is based on a specific property, which can be found in some of the linear binary block codes control matrices. Similar known methods are based on properties of generator matrices. However some codes are specified via control matrices, for example low density parity check codes. The method proposed in this letter could be applied to some of them directly. This is illustrated in this manuscript using example in which a run length limited low density parity check code is obtained from Gallager code.

Algorithms suitable for low complexity implementation of at class of runlength-limited error control codes

Encoding and decoding procedures which exploit the cyclic-like properties of a class of runlength-limited error control-codes are presented. These algorithms enable simple encoding and decoding circuits consisting of only a few basic circuit elements to be designed. A comparison with conventional syndrome decoding shows that they provide comparable error performance although requiring considerably less circuitry.

Soft decision decoding techniques for a class of runlength-limited error control codes

Two soft decision decoding algorithms for a new class of runlength-limited error control codes with maximum runlength constraints 2, 6 and 14 are presented. Software simulation results for illustrative codes of block length 16 and 64 provide a comparison with the general soft decision decoders proposed by Chase (1972).

Trellis decoding technique for block RLL/ECC

A new simple encoding technique that allows the design of almost all known block runlength-limited error control codes is described. Attention is focused on the most widely used codes (Hamming, Reed-Muller, Golay) with RLL properties. The trellis design procedure for the proposed codes is introduced. It is shown that the trellises of the designed codes are similar to the trellises of the coset codes designed by Forney (1988), and provide low-complexity soft maximum-likelihood performance.

Manchester-like coding with single error correction and double error detection

The spectral features of a class of maximum runlength limited error control codes are determined and are shown, apart from in a singular case, to be the same as those of the Manchester code.

New class of runlength-limited error-control codes with minimum distance 4

A new class of runlength-limited errorcontrol codes with minimum distance 4 is identified. These codes are simple to implement since they are formed by modifying linear codes. A comparison with the conventional solution of cascading a runlength-limited code with an error-control code shows that runlength-limited error-control coding schemes both have considerably reduced complexity and in many cases also attain a rate improvement.