Publications

• Book
• Survey on constrained coding
• Itemized list of journal papers

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Book

• R.M. Roth,
  Introduction to Coding Theory,
  Cambridge University Press, Cambridge, UK, 2006.

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Survey on constrained coding

• B.H. Marcus, R.M. Roth, P.H. Siegel,
  Constrained systems and coding for recording channels,
  in Handbook of Coding Theory, V.S. Pless and W.C. Huffman (Editors), Elsevier, Amsterdam, 1998, pp. 1635–1764.
  A short version of this survey, by the same authors, appeared under the title “Modulation codes for digital data storage,”
  in Different Aspects of Coding Theory, Proceedings of Symposia in Applied Mathematics, Vol. 50, R.C. Calderbank (Editor), American Mathematical Society, Providence, Rhode Island, 1995, pp. 41–87.
  An extended (incomplete) version of the survey is available in a form of Lecture Notes.

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Journal papers

• Reed–Solomon codes and MDS codes
• Array codes
• Applications of error-correcting codes
• Other ECC results
• Constrained systems and modulation codes
• Spectral-null codes
• Multi-dimensional constrained coding
• Other results

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Reed–Solomon codes and MDS codes

• R.M. Roth,
  Higher-order MDS codes,
  IEEE Trans. Inf. Theory, 68 (2022), 7798–7816.
• T. Kolan, R.M. Roth,
  Burst list decoding of interleaved Reed–Solomon codes,
  IEEE Trans. Inf. Theory, 60 (2014), 182–189.
• R.M. Roth, P.O. Vontobel,
  List decoding of burst errors,
  IEEE Trans. Inf. Theory, 55 (2009), 4179–4190.
• J. Han, P.H. Siegel, R.M. Roth,
  Single-exclusion number and the stopping redundancy of MDS codes,
  IEEE Trans. Inf. Theory, 55 (2009), 4155–4166.
• R.M. Roth, V. Skachek,
  Improved nearly-MDS expander codes,
  IEEE Trans. Inf. Theory, 52 (2006), 3650–3661.
• E. Louidor, R.M. Roth,
  Lowest density MDS codes over extension alphabets,
  IEEE Trans. Inf. Theory, 52 (2006), 3186–3197.
• G. Ruckenstein, R.M. Roth,
  Bounds on the list-decoding radius of Reed–Solomon codes,
  SIAM J. Disc. Math., 17 (2003), 171–195.
• R.M. Roth, G. Ruckenstein,
  Efficient decoding of Reed–Solomon codes beyond half the minimum distance,
  IEEE Trans. Inf. Theory, 46 (2000), 246–257.
• M. Blaum, R.M. Roth,
  On lowest density MDS codes,
  IEEE Trans. Inf. Theory, 45 (1999), 46–59.
• R.M. Roth, A. Lempel,
  On MDS codes via Cauchy matrices,
  IEEE Trans. Inf. Theory, 35 (1989), 1314–1319.
• R.M. Roth, A. Lempel,
  A construction of non-Reed–Solomon type MDS codes,
  IEEE Trans. Inform. Theory, 35 (1989), 655–657.
• R.M. Roth, A. Lempel,
  Composition of Reed–Solomon codes and geometric designs,
  IEEE Trans. Inf. Theory, 34 (1988), 810–816.
• G. Seroussi, R.M. Roth,
  On MDS extensions of generalized Reed–Solomon codes,
  IEEE Trans. Inf. Theory, IT-32 (1986), 349–354.
• R.M. Roth, G. Seroussi,
  On cyclic MDS codes of length q over GF(q),
  IEEE Trans. Inf. Theory, IT-32 (1986), 284–285.
• R.M. Roth, G. Seroussi,
  On generator matrices of MDS codes,
  IEEE Trans. Inf. Theory, IT-31 (1985), 826–830.

Array codes

• R.M. Roth,
  On decoding rank-metric codes over large fields,
  IEEE Trans. Inf. Theory, 64 (2018), 944–951.
• R.M. Roth, P.O. Vontobel,
  Coding for combined block-symbol error correction,
  IEEE Trans. Inf. Theory, 60 (2014), 2697–2713.
• R.M. Roth, G. Seroussi,
  Reduced-redundancy product codes for burst error correction,
  IEEE Trans. Inf. Theory, 44 (1998), 1395–1406.
• R.M. Roth,
  Probabilistic crisscross error correction,
  IEEE Trans. Inf. Theory, 43 (1997), 1425–1438.
• R.M. Roth,
  Tensor codes for the rank metric,
  IEEE Trans. Inf. Theory, 42 (1996), 2146–2157.
• M. Blaum, R.M. Roth,
  New array codes for multiple phased burst correction,
  IEEE Trans. Inf. Theory, 39 (1993), 66–77.
• R.M. Roth,
  Maximum-rank array codes and their application to crisscross error correction,
  IEEE Trans. Inf. Theory, 37 (1991), 328–336 (see correction in 38 (1992), 1183).

Applications of error-correcting codes

• H. Wei, R.M. Roth,
  Multiple-error-correcting codes for analog computing on resistive crossbars,
  IEEE Trans. Inf. Theory, to appear.
• R.M. Roth,
  Error-detection schemes for analog content-addressable memories,
  IEEE Trans. Comput., 73 (2024), 1795–1808.
• R.M. Roth,
  Analog error-correcting codes,
  IEEE Trans. Inf. Theory, 66 (2020), 4075–4088. See correction.
• R.M. Roth,
  Fault-tolerant dot-product engines,
  IEEE Trans. Inf. Theory, 65 (2019), 2046–2057.
• A. Bremler-Barr, D. Hay, D. Hendler, R.M. Roth,
  PEDS: A Parallel error detection scheme for TCAM devices,
  IEEE/ACM Trans. Netw., 18 (2010), 1665–1675.
• R.M. Roth, W. Robinett, P.J. Kuekes, R.S. Williams,
  Defect-tolerant demultiplexer circuits based on threshold logic and coding,
  Nanotechnology, 20 (2009), #135201 (14pp).
• P.J. Kuekes, W. Robinett, R.M. Roth, G. Seroussi, G.S. Snider, R.S. Williams,
  Resistor-logic demultiplexers for nanoelectronics based on constant-weight codes,
  Nanotechnology, 17 (2006), 1052–1061.
• E. Petrank, R.M. Roth,
  Is code equivalence easy to decide?,
  IEEE Trans. Inf. Theory, 43 (1997), 1602–1604.
• M. Naor, R.M. Roth,
  Optimal file sharing in distributed networks,
  SIAM J. Comput., 24 (1995), 158–183.
• R.M. Roth, G.M. Benedek,
  Interpolation and approximation of sparse multivariate polynomials over GF(2),
  SIAM J. Comput., 20 (1991), 291–314.

Other ECC results

• R.M. Roth,
  Asymptotic bounds on the rate of locally repairable codes,
  IEEE Trans. Inf. Theory, 68 (2022), 1581–1598.
• E. Ordentlich, R.M. Roth,
  On the pointwise threshold behavior of the binary erasure polarization subchannels,
  IEEE Trans. Inf. Theory, 65 (2019), 6044–6055.
• R.M. Roth, A. Zeh,
  On spectral design methods for quasi-cyclic codes,
  IEEE Trans. Inf. Theory, 65 (2019), 2637–2647.
• A. Sharov, R.M. Roth,
  On the capacity of generalized Ising channels,
  IEEE Trans. Inf. Theory, 63 (2017), 2338–2356.
• R.M. Roth, A. Zeh,
  Long cyclic codes over GF(4) and GF(8) better than BCH codes in the high-rate region,
  IEEE Trans. Inf. Theory, 63 (2017), 150–158.
• A. Sharov, R.M. Roth,
  New bounds and constructions for granular media coding,
  IEEE Trans. Inf. Theory, 61 (2015), 4227–4238.
• A. Sharov, R.M. Roth,
  Bounds and constructions for granular media coding,
  IEEE Trans. Inf. Theory, 60 (2014), 2010–2027.
• R.M. Roth, G. Seroussi,
  Bounds for binary codes with narrow distance distributions,
  IEEE Trans. Inf. Theory, 53 (2007), 2760–2768.
• R.M. Roth, G. Seroussi,
  Symbol-intersecting codes,
  IEEE Trans. Inf. Theory, 51 (2005), 2266–2281.
• R.M. Roth, G. Seroussi,
  Location-correcting codes,
  IEEE Trans. Inf. Theory, 42 (1996), 554–565.
• N. Alon, J. Bruck, J. Naor, M. Naor, R.M. Roth,
  Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs,
  IEEE Trans. Inf. Theory, 38 (1992), 509–516.
• R.M. Roth, A. Lempel,
  Application of circulant matrices to the construction and decoding of linear codes,
  IEEE Trans. Inf. Theory, 36 (1990), 1157–1163.
• R.M. Roth, G. Seroussi,
  Encoding and decoding of BCH codes using light and short codewords,
  IEEE Trans. Inf. Theory, 34 (1988), 593–596.

Constrained systems and modulation codes

• R.M. Roth, Paul H. Siegel,
  Variable-length constrained coding and Kraft conditions: The parity-preserving case,
  IEEE Trans. Inf. Theory, 67 (2021), 6179–6192.
• R.M. Roth, Paul H. Siegel,
  On bi-modal constrained coding,
  IEEE Trans. Inf. Theory, 67 (2021), 1609–1621.
• G. Ruckenstein, R.M. Roth,
  Lower bounds on the anticipation of encoders for input-constrained channels,
  IEEE Trans. Inf. Theory, 47 (2001), 1796–1812.
• J. Hogan, R.M. Roth, G. Ruckenstein,
  Nested block decodable runlength-limited codes,
  IEEE Trans. Inf. Theory, 47 (2001), 1630–1638.
• J. Hogan, R.M. Roth, G. Ruckenstein,
  Nested input-constrained codes,
  IEEE Trans. Inf. Theory, 46 (2000), 1302–1316.
• J.L. Fan, B.H. Marcus, R.M. Roth,
  Lossless sliding-block compression of constrained systems,
  IEEE Trans. Inf. Theory, 46 (2000), 624–633.
• J.J. Ashley, B.H. Marcus, R.M. Roth,
  On the decoding delay of encoders for input-constrained channels,
  IEEE Trans. Inf. Theory, 42 (1996), 1948–1956.
• J.J. Ashley, B.H. Marcus, R.M. Roth,
  Construction of encoders with small decoding look-ahead for input-constrained channels,
  IEEE Trans. Inf. Theory, 41 (1995), 55–76.
• B.H. Marcus, R.M. Roth,
  Improved Gilbert–Varshamov bound for constrained systems,
  IEEE Trans. Inf. Theory, 38 (1992), 1213–1221.
• B.H. Marcus, R.M. Roth,
  Bounds on the number of states in encoder graphs for input-constrained channels,
  IEEE Trans. Inf. Theory, 37 (1991), 742–758.

Spectral-null codes

• A. Mazumdar, R.M. Roth, P.O. Vontobel,
  On linear balancing sets,
  Adv. Math. Commun., 4 (2010), 345–361.
• R.M. Roth,
  On runlength-limited coding with DC control,
  IEEE Trans. Commun., 48 (2000), 351–358.
• V. Skachek, T. Etzion, R.M. Roth,
  Efficient encoding algorithm for third-order spectral-null codes,
  IEEE Trans. Inf. Theory, 44 (1998), 846–851.
• R.M. Roth,
  Spectral-null codes and null spaces of Hadamard submatrices,
  Des. Codes Cryptogr., 9 (1996), 177–191.
• R.M. Roth, P.H. Siegel, A. Vardy,
  High-order spectral-null codes: Constructions and bounds,
  IEEE Trans. Inf. Theory, 40 (1994), 1826–1840.
• R.M. Roth, P.H. Siegel,
  Lee-metric BCH codes and their application to constrained and partial-response channels,
  IEEE Trans. Inf. Theory, 40 (1994), 1083–1096.

Multi-dimensional constrained coding

• E. Ordentlich, F. Parvaresh, R.M. Roth,
  Asymptotic enumeration of binary matrices with bounded row and column sums,
  SIAM J. Disc. Math., 26 (2012), 1550–1575.
• E. Ordentlich, R.M. Roth,
  Low complexity two-dimensional weight-constrained codes,
  IEEE Trans. Inf. Theory, 58 (2012), 3892–3899.
• I. Tal, R.M. Roth,
  Convex programming upper bounds on the capacity of 2-D constraints,
  IEEE Trans. Inf. Theory, 57 (2011), 381–391.
• I. Tal, R.M. Roth,
  Bounds on the rate of 2-D bit-stuffing encoders,
  IEEE Trans. Inf. Theory, 56 (2010), 2561–2567.
• A. Sharov, R.M. Roth,
  Two-dimensional constrained coding based on tiling,
  IEEE Trans. Inf. Theory, 56 (2010), 1800–1807.
• I. Tal, T. Etzion, R.M. Roth,
  On row-by-row coding for 2-D constraints,
  IEEE Trans. Inf. Theory, 55 (2009), 3565–3576.
• E. Ordentlich, R.M. Roth,
  Independent sets in regular hypergraphs and multi-dimensional runlength-limited constraints,
  SIAM J. Disc. Math., 17 (2004), 615–623.
• S. Halevy, J. Chen, R.M. Roth, P.H. Siegel, J.K. Wolf,
  Improved bit-stuffing bounds on two-dimensional constraints,
  IEEE Trans. Inf. Theory, 50 (2004), 824–838.
• S. Halevy, R.M. Roth,
  Parallel constrained coding with application to two-dimensional constraints,
  IEEE Trans. Inf. Theory, 48 (2002), 1009–1020.
• R.M. Roth, P.H. Siegel, J.K. Wolf,
  Efficient coding schemes for the hard-square model,
  IEEE Trans. Inf. Theory, 47 (2001), 1166–1176.
• E. Ordentlich, R.M. Roth,
  Two-dimensional weight-constrained codes through improved enumeration bounds,
  IEEE Trans. Inf. Theory, 46 (2000), 1292–1301.
• R. Talyansky, T. Etzion, R.M. Roth,
  Efficient code constructions for certain two-dimensional constraints,
  IEEE Trans. Inf. Theory, 45 (1999), 794–799.

Other results

• R.M. Roth,
  On the implementation of Boolean functions on content-addressable memories,
  IEEE J. Sel. Areas Inf. Theory, 4 (2023), 379–392.
• R.N. Berman, R.M. Roth,
  On the number of factorizations of polynomials over finite fields,
  J. Comb. Theory Ser. A, 182 (2021), #105462 (39pp).
• R.M. Roth, N. Raviv, I. Tamo,
  Construction of Sidon spaces with applications to coding,
  IEEE Trans. Inf. Theory, 64 (2018), 4412–4422.
• E. Ordentlich, R.M. Roth,
  Two-dimensional maximum-likelihood sequence detection is NP hard,
  IEEE Trans. Inf. Theory, 57 (2011), 7661–7670
• R.M. Roth, K. Viswanathan,
  On the hardness of decoding the Gale–Berlekamp code,
  IEEE Trans. Inf. Theory, 54 (2008), 1050–1060.
• V. Skachek, R.M. Roth,
  Probabilistic algorithm for finding roots of linearized polynomials,
  Des. Codes Cryptogr., 46 (2008), 17–23.
• N. Merhav, R.M. Roth, E. Arikan,
  Hierarchical guessing with a fidelity criterion,
  IEEE Trans. Inf. Theory, 45 (1999), 330–337.
• R. Bar-Yehuda, D. Geiger, J. Naor, R.M. Roth,
  Approximation algorithms for the vertex feedback set problem with applications to constraint satisfaction and Bayesian inference,
  SIAM J. Comput., 27 (1998), 942–959.
• J. Naor, R.M. Roth,
  Constructions of permutation arrays for certain scheduling cost measures,
  Random Structures and Algorithms, 6 (1995), 39–50.
• R.M. Roth, A. Lempel,
  t-sum generators of finite Abelian groups,
  Discrete Math., 103 (1992), 279–292.