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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2025年第4期43卷 1200-1213页

作者： Ozaydin, Basak Medard, Muriel Duffy, Ken R. MIT Res Lab Elect Cambridge MA 02139 USA Northeastern Univ Dept ECE Boston MA 02115 USA Northeastern Univ Dept Math Boston MA 02115 USA

We propose a novel demodulation technique that leverages developments in guesswork-based forward error correction decoders and variable-length bit-to-symbol mappings. For most common channel models, the optimal modulation schemes are known to require nonuniform probability distributions over signal points, which presents practical challenges. An established way to map uniform binary sources to non-uniform symbol distributions is to assign a different number of bits to different constellation points. Doing so, however, means that erroneous demodulation at the receiver can lead to bit insertions or deletions, turning a channel with Hamming-type errors into an insertion-deletion channel. The demodulator we propose provides error detection and correction through the use of a low-overhead padding bit sequence. We evaluate the performance of the proposed demodulator in various channel models and various communication settings. We verify that the demodulator successfully corrects the insertion-deletion errors. Using the proposed demodulator, we study different constellation design schemes and how they behave in different channel conditions. Overall, we observe considerable gains that suggest, in some circumstances, one may improve the throughput while keeping the error rate the same.

关键词： Demodulation Symbols Quadrature amplitude modulation Modulation Synchronization Signal to noise ratio Peak to average power ratio Channel models AWGN channels Rician channels Guesswork distribution matching insertion and deletion errors non-uniform modulation GRAND

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Symbol Synchronization for Diffusion-Based Molecular Communications

IEEE TRANSACTIONS ON NANOBIOSCIENCE

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IEEE TRANSACTIONS ON NANOBIOSCIENCE 2017年第8期16卷 873-887页

作者： Jamali, Vahid Ahmadzadeh, Arman Schober, Robert Friedrich Alexander Univ Inst Digital Commun D-91058 Erlangen Germany

Symbol synchronization refers to the estimation of the start of a symbol interval and is needed for reliable detection. In this paper, we develop several symbol synchronization schemes for molecular communication (MC) systems where we consider some practical challenges, which have not been addressed in the literature yet. In particular, we take into account that in MC systems, the transmitter may not be equipped with an internal clock and may not be able to emit molecules with a fixed release frequency. Such restrictions hold for practical nanotransmitters, e.g., modified cells, where the lengths of the symbol intervals may vary due to the inherent randomness in the availability of food and energy for molecule generation, the process for molecule production, and the release process. To address this issue, we develop two synchronization-detection frameworks which both employ two types of molecule. In the first framework, one type of molecule is used for symbol synchronization and the other one is used for data detection, whereas in the second framework, both types of molecule are used for joint symbol synchronization and data detection. For both frameworks, we first derive the optimal maximum likelihood (ML) symbol synchronization schemes as performance upper bounds. Since ML synchronization entails high complexity, for each framework, we also propose three low-complexity suboptimal schemes, namely a linear filter-based scheme, a peak observation-based scheme, and a threshold-trigger scheme, which are suitable for MC systems with limited computational capabilities. Furthermore, we study the relative complexity and the constraints associated with the proposed schemes and the impact of the insertion and deletion errors that arise due to imperfect synchronization. Our simulation results reveal the effectiveness of the proposed synchronization schemes and suggest that the end-to-end performance of MC systems significantly depends on the accuracy of the symbol synchroniza

关键词： Diffusive molecular communications symbol synchronization insertion and deletion errors

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Efficiently List-Decodable insertion and deletion Codes via Concatenation

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第9期67卷 5778-5790页

作者： Liu, Shu Tjuawinata, Ivan Xing, Chaoping Univ Elect Sci & Technol China Natl Key Lab Sci & Technol Commun Chengdu 611731 Peoples R China Univ Elect Sci & Technol China Yangtze Delta Reg Inst Huzhou Huzhou 313001 Peoples R China Nanyang Technol Univ Strateg Ctr Res Privacy Preserving Technol & Syst Singapore 637553 Singapore Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai 200240 Peoples R China State Key Lab Cryptog Beijing 100878 Peoples R China

In this paper, we consider the list decoding property of codes under insertion and deletion errors (insdel for short). Firstly, we analyse the list decodability of random insdel codes. Our result provides a more complete picture on the list decodability of insdel codes when both insertion and deletion errors happen. Secondly, we construct a family of insdel codes along with their efficient encoding and decoding algorithms through concatenation method which provides a Zyablov-type bound for insdel metric codes.

关键词： Decoding Upper bound Measurement Codecs Binary codes Indexing Concatenated codes Codes error correction information theory list decoding insertion and deletion errors

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Coding Over Sets for DNA Storage

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第4期66卷 2331-2351页

作者： Lenz, Andreas Siegel, Paul H. Wachter-Zeh, Antonia Yaakobi, Eitan Tech Univ Munich Inst Commun Engn D-80333 Munich Germany Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA Univ Calif San Diego Ctr Memory & Recording Res La Jolla CA 92093 USA Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel

In this paper we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where a data set is represented by an unordered set ofM sequences, each of length L. errors within that model are a loss of whole sequences and point errors inside the sequences, such as insertions, deletions and substitutions. We derive Gilbert-Varshamov lower bounds and sphere packing upper bounds on achievable cardinalities of error-correcting codes within this storage model. We further propose explicit code constructions than can correct errors in such a storage system that can be encoded and decoded efficiently. Comparing the sizes of these codes to the upper bounds, we show that many of the constructions are close to optimal.

关键词： Coding over sets DNA data storage Gilbert-Varshamov bound insertion and deletion errors sphere packing bound

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On L₁-distance error control codes

On L1-distance error control codes

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IEEE International Symposium on Information Theory (ISIT)

作者： Tallini, Luca G. Bose, Bella Univ Teramo Dip Sci Comunicaz I-64100 Teramo Italy Oregon State Univ Sch EECS Corvallis OR 97331 USA

ISBN: (纸本)9781457705953

This paper gives some theory and design of efficient codes capable of controlling (i.e., correcting/detecting/correcting erasure) errors measured under the L-1 distance defined over m-ary words, 2 <= m <= + infinity. We give the combinatorial characterizations of such codes, some general code designs and the efficient decoding algorithms. Then, we give a class of linear and systematic m-ary codes, m = sp with s is an element of IN and p a prime, which are capable of controlling d <= p-1 errors. If n and k is an element of IN are respectively the length and dimension of a BCH code over GF(p) with minimum Hamming distance d + 1 then the new codes have length n and k' = k + r log(m) s information digits.

关键词： m-ary alphabet error control codes asymmetric/unidirectional/symmetric errors Z-channel flash memories insertion and deletion errors repetition errors

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On Efficient Repetition Error Correcting Codes

On Efficient Repetition Error Correcting Codes

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2010 IEEE International Symposium on Information Theory

作者： Tallini, Luca G. Elarief, Noha Bose, Bella Univ Teramo Dip Sci Comunicaz I-64100 Coste San Agostino Teramo Italy Oregon State Univ Sch EECS Corvallis OR 97331 USA

ISBN: (纸本)9781424469604

This paper gives the theory and design of efficient codes capable of correcting errors caused by the insertion and deletion of a repeated symbol in the information sequence. Two efficient methods are described. For any fixed t(+), t(-) is an element of IN, one method gives a fixed length scheme to encode k information bits into a systematic code of length n = k + r, with r = (t(+) + t(-)) log(2) k + O(log log k), capable of correcting the insertion of t(+) repeated symbols and, simultaneously, correcting the deletion of t(-) repeated symbols in every codeword. The second method is a systematic variable length scheme which on average doubles the number of information bits k compared to the first method. The time complexity of the entire coding process for both schemes is T = O (k + (1 + min{t(-), t(+)})t) multiplication operations over a finite field containing k elements. The space complexity is S = O(k + t) field memory elements. The generalization to the m-ary case, m >= 2, is also given.

关键词： insertion and deletion errors repetition errors asymmetric errors synchronization error control codes

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On Symmetric L₁ distance error control codes and elementary symmetric functions 2012

On Symmetric L1 distance error control cod...

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IEEE International Symposium on Information Theory

作者： Tallini, Luca G. Bose, Bella Univ Teramo Dip Sci Comunicaz I-64100 Teramo Italy

ISBN: (纸本)9781467325790

Based on the elementary symmetric functions, this paper gives a new wide class of Goppa like codes capable of correcting/detecting errors measured under the (symmetric) L-1 distance defined over the m-ary words, 2 <= m <= + infinity. All these codes can be efficiently decoded by algebraic means with the Extended Euclidean Algorithm (EEA). In particular it is shown that if K is any field with characteristic char(K) not equal 2, m is an element of II boolean OR {+infinity} and n, t is an element of IN then there exist m-ary codes C of length n <= (vertical bar K vertical bar - 1)/2 and cardinality vertical bar C vertical bar >= m(n) /vertical bar K vertical bar(t) which are capable of, say, correcting t errors (i. e., the minimum L-1 distance of C is d(L1) (C) >= 2t + 1) with t steps of EEA. Also, if K is a finite field and 2t + 1 <= char(K) not equal 2 then some of these codes are (essentially) linear and, hence, easy to encode. Index Terms-m-ary alphabet, error control codes, symmetric errors, asymmetric errors, flash memories, insertion and deletion errors, repetition errors. L-1 distance, Lee distance.

关键词： m-ary alphabet error control codes symmetric errors asymmetric errors flash memories insertion and deletion errors repetition errors L-1 distance Lee distance

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On L₁ metric Asymmetric/Unidirectional error control codes, constrained weight codes and σ-codes

On L1 metric Asymmetric/Unidirectional err...

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IEEE International Symposium on Information Theory (ISIT)

作者： Tallini, Luca G. Bose, Bella Univ Teramo Dipartimento Sci Comunicaz Teramo Italy Oregon State Univ Sch Elect Engn & Comp Sci Corvallis OR 97331 USA

ISBN: (纸本)9781479904464

The general theory on partially asymmetric ( t-, t+)EC/( d-, d+)- ED m- ary codes for the L1 distance is developed. In this metric, such codes are capable of correcting t- or less negative errors, detecting d- or less negative errors, correcting t+ or less positive errors, and simultaneously detecting d+ or less positive errors. Based on the elementary symmetric function, a wide class of these codes with efficient decoding algorithms are given. Let S( m, n, w, D) be the set of all the m- ary words of length n with real sum of their components being equal to w mod D. Any subset of S( m, n, w, D) is called m- ary constrained weight ( CW) code of length n and is known to be a ( D - 1)UED code. Given a field, K, of prime characteristic p, some m- ary CW codes of length n = | K| - 1 are defined. Such codes are ( t-, t+)- EC/( d-, d+)- ED and have a redundancy of.( C) = n - logm | C| =.( S( m, n, w, d + 1)) + t logm | K|, with t = min{t- + d+, d- + t+}, d = max{t- + d+, d- + t+} and w. IIN. In particular, for t = p- 1, a class of essentially linear and systematic ( hence, easy to encode) m- ary ( t-, t+)- EC/( d-, d+)ED CW s- codes with length n = | K| + d/( m - 1) - 1, k = | K| - t logm | K| - 1 information digits and n - k = t logm | K| + d/( m - 1) check digits are given. Also, some new hybrid partially asymmetric/ unidirectional/ symmetric error control codes are given and shown to be equivalent to the partially asymmetric ( t-, t+)- EC/( d-, d+)- ED m- ary codes. .-.-.-.-.-

关键词： m ary alphabet error control codes symmetric errors unidirectional errors asymmetric errors flash memories insertion and deletion errors repetition errors L1 distance.

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Joint Iterative Decoding of Spatially Coupled Low-Density Parity-Check Codes for Position errors in Racetrack Memories

Joint Iterative Decoding of Spatially Coupled Low-Density Pa...

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40th Symposium on Information Theory and Its Applications (SITA)

作者： Shibata, Ryo Hosoya, Gou Yashima, Hiroyuki Tokyo Univ Sci Grad Sch Engn Dept Management Sci Tokyo 1258585 Japan Tokyo Univ Sci Dept Informat & Comp Technol Fac Engn Tokyo 1258585 Japan

Racetrack memory (RM) has attracted much attention. In RM, insertion and deletion (ID) errors occur as a result of an unstable reading process and are called position errors. In this paper, we first define a probabilistic channel model of ID errors in RM with multiple read-heads (RHs). Then, we propose a joint iterative decoding algorithm for spatially coupled low-density parity-check (SC-LDPC) codes over such a channel. We investigate the asymptotic behaviors of SC-LDPC codes under the proposed decoding algorithm using density evolution (DE). With DE, we reveal the relationship between the number of RHs and achievable information rates, along with the iterative decoding thresholds. The results show that increasing the number of RHs provides higher decoding performances, although the proposed decoding algorithm requires each codeword bit to be read only once regardless of the number of RHs. Moreover, we show the performance improvement produced by adjusting the order of the SC-LDPC codeword bits in RM.

关键词： insertion and deletion errors spatially coupled low-density parity-check code forward-backward algorithm iterative decoding

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On 2-dimensional insertion-deletion Reed-Solomon codes with optimal asymptotic error-correcting capability

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FINITE FIELDS AND THEIR APPLICATIONS 2021年 73卷 101841-101841页

作者： Liu, Shu Tjuawinata, Ivan Univ Elect Sci & Technol China Natl Key Lab Sci & Technol Commun Chengdu 611731 Peoples R China Univ Elect Sci & Technol China Yangtze Delta Reg Inst Huzhou Huzhou 313001 Peoples R China Nanyang Technol Univ Strateg Ctr Res Privacy Preserving Technol & Syst Singapore 637553 Singapore

Reed-Solomon codes have gained a lot of interest due to its encoding simplicity, well structuredness and list-decoding capability [6] in the classical setting. This interest also translates to other metric setting, including the insertion and deletion (insdel for short) setting which is used to model synchronization errors caused by positional information loss in communication systems. Such interest is supported by the construction of a deletion correcting algorithm of insdel Reed-Solomon code in [22] which is based on the Guruswami-Sudan decoding algorithm [6]. Nevertheless, there have been few studies [3] on the insdel error-correcting capability of Reed-Solomon codes. In this paper, we discuss a criterion for a 2-dimensional insdel Reed-Solomon codes to have optimal asymptotic error correcting capabilities, which are up to their respective lengths. Then we provide explicit constructions of 2 -dimensional insdel Reed-Solomon codes that satisfy the established criteria. The family of such constructed codes can then be shown to extend the family of codes with asymptotic error correcting capability reaching their respective lengths provided in [3, Theorem 2] which provide larger error-correcting capability compared to those defined in [25]. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Coding theory insertion and deletion errors Reed-Solomon codes

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