Innovation in Constrained Codes

Immink, Kees A. Schouhamer

doi:10.1109/mcom.002.2200249

Cited by 7 publications

(6 citation statements)

References 38 publications

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“…The set of the remaining column indexes H 64×128 is the following: 19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57 156,157,158,159,161,163,165,167,169,171,173,175,177,179,181,183,185,187,189,191,192,194,196,198,200,202,204,206,208,210,212,214,216,218,220,222,225,227,229,…”

Section: Discussionmentioning

confidence: 99%

“…Taking into account (25) and observing Figure 6 it is obvious that after using an appropriate modifier, (such as will invert an uneven number of columns in each interval of codeword symbols corresponding to the bold intervals in Figure 9), the maximal RLL of the resulting coset code will be equal to 22. After transmission of each codeword from the RLL ECC (coset code of the original ECC) obtained in this way the influence of the modifier addition and column reordering will be eliminated in the receiver so that the standard decoding of LDPC codes could be used in case the underlying channel could be modeled as a BSC or an AWGN with coherent BPSK modulation.…”

Section: Approaches For Obtaining Rll-eccs From Four Ccsds Codesmentioning

confidence: 99%

“…In other words this corresponds to indexes of columns in which there are ones in the particular control equation in the parity check matrix (19). Observing the sequence and taking into account (25) it is obvious that after applying the odd number of inversions in each set represented by bold numbers in the sequence the maximal run-length of equal symbols will be RL M AX = 22.…”

Section: Approaches For Obtaining Rll-eccs From Four Ccsds Codesmentioning

confidence: 99%

“…This tradition also continues nowadays. Examples of recent advances in constructing ECCs are found in [15,16,17,18,19,20], while the up to date progress examples in constructing LCs are found in [21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

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Adding RLL Properties to Four CCSDS LDPC Codes without Increasing Their Redundancy

Farkas

Rakús²

2023

cai

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This paper presents the construction of Run Length Limited (RLL) Error Control Codes (ECCs) from four Low Density Parity Check (LDPC) Codes specified by Consultative Committee for Space Data Systems (CCSDS). The obtained RLL-ECCs present a practical alternative to the CCSDS codes with pseudorandomizers. Their advantage is that the maximal runlengths 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. In the first case if hard decoding is used and the transmission channel can be modeled as a Binary Symmetric Channel (BSC) or in the second case if soft decoding and coherent Binary Phase Shift Keying (BPSK) 158 P. Farkaš, M. Rakús modulation is used and the appropriate transmission channel model is an Additive White Gaussian Noise (AWGN) channel.

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Section: Discussionmentioning

confidence: 99%

Section: Approaches For Obtaining Rll-eccs From Four Ccsds Codesmentioning

confidence: 99%

Section: Approaches For Obtaining Rll-eccs From Four Ccsds Codesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adding RLL Properties to Four CCSDS LDPC Codes without Increasing Their Redundancy

Farkas

Rakús²

2023

cai

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“…Constrained coding is a fundamental field with a wide range of applications including magnetic and optical storage, flash memory, DNA storage, wireless communication, and satellite communication [Imm04,MRS01,Imm22]. These applications are subject to unique challenges and constraints that must be satisfied by the data encoding.…”

Section: Introductionmentioning

confidence: 99%

On Levenshtein Balls with Radius One

Bar-Lev

Etzion

Yaakobi

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints (e.g., a fixed set of substrings may not appear in transmitted messages) have a general optimal solution, there is increasing demand for supporting parametric constraints that are dependent on the message length and portray some property (e.g., no log(n) consecutive zeros). Several works have tackled such parametric constraints through iterative algorithms, yet they require complex constructions specific to each constraint to guarantee convergence through monotonic progression. In this paper, we propose a universal framework for tackling any parametric constrained-channel problem through a novel simple iterative algorithm. By reducing an execution of this iterative algorithm to an acyclic graph traversal, we prove a surprising result that guarantees convergence with efficient average time complexity even without requiring any monotonic progression.We demonstrate the effectiveness of this universal framework by applying it to a variety of both local and global channel constraints. We begin by exploring the local constraints involving illegal substrings of variable length, where the universal construction essentially iteratively replaces forbidden windows. We apply this local algorithm to the minimal periodicity, minimal Hamming weight, local almost-balanced Hamming weight and the previously-unsolved minimal palindrome constraints, and demonstrate state-of-the-art results through simple adaptations of the universal algorithm. We then continue by exploring global constraints, and demonstrate the effectiveness of the proposed construction on the repeat-free encoding, reverse-complement encoding, and the open problem of global almost-balanced encoding. For reverse-complement, we also tackle a previously-unsolved version of the constraint that addresses overlapping windows. Overall, the proposed framework generates state-of-the-art constructions with significant ease while also enabling the simultaneous integration of multiple constraints for the first time.

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