Research
Last update: Nov 16, 2024
Andrew Thangaraj's research interests are in the broad areas of information theory, error-control coding and information-theoretic aspects of learning and cryptography. A list of publications sorted by area is given below. All papers are available online from respective publishers.
Recent Papers and Preprints
- A. Pananjady, V. Muthukumar and A. Thangaraj, "Just Wing It: Optimal Estimation of Missing Mass in a Markovian Sequence", Journal of Machine Learning Research, vol. 25, no. 312, pp. 1-43, 2024, jmlr:24-0511, arXiv: 2404.05819.
- P. Chandra and A. Thangaraj, "Missing g-mass: Investigating the Missings Parts of Distributions," IEEE Transactions on Information Theory, vol. 70, no. 10, pp. 7049-7065, October 2024, arXiv: 2110.01968.
- J. Mandalapu, K. Jagannathan and A. Thangaraj, "Capacity Achieving Channel Codes for an Erasure Queue-Channel," IEEE Transactions on Communications, vol. 72, no. 12, pp. 7374-7386, December 2024.
- P. Chandra and A. Thangaraj, "Missing Mass under Random Duplications," IEEE International Symposium on Information Theory 2024, Athens, Greece.
- P. Chandra, A. Thangaraj and N. Rajaraman, "How good is Good-Turing for Markov samples?" Transactions on Machine Learning Research (TMLR), April 2024.arXiv: 2102.01938.
Learning and Information Theory
- R. G. Tiwari and A. Thangaraj, "Adversarial Robustness via Class Partitioning," National Conference on Communications (NCC) 2023, IIT Guwahati, India.
- P. Chandra, A. Thangaraj and N. Rajaraman, "Missing Mass Estimation from Sticky Channels," IEEE International Symposium on Information Theory 2022, Espoo, Finland.
- P. Chandra, A. Thangaraj and N. Rajaraman, "Missing Mass of Markov Chains," IEEE International Symposium on Information Theory 2020, Jun 21-26, Los Angeles, CA, USA.
- A. Mandal, A. Chatterjee and A. Thangaraj, "Noisy Deletion, Markov Codes and Deep Decoding," National Conference on Communications (NCC) 2020, IIT Kharagpur, India.
- P. Chandra and A. Thangaraj, "Concentration and Tail Bounds for Missing Mass," IEEE International Symposium on Information Theory 2019, Jul 7-12, Paris, France.
- N. Rajaraman, P. Chandra, A. Thangaraj and A. T. Suresh, "Convergence of Chao Unseen Species Estimator," IEEE International Symposium on Information Theory 2019, Jul 7-12, Paris, France.
- P. Chandra, A. Pradeep and A. Thangaraj, "Improved Tail Bounds for Missing Mass and Confidence Intervals for Good-Turing Estimator," National Conference on Communications 2019, IISc Bangalore, India.
- Nikhilesh Rajaraman, A. Thangaraj and Ananda Theertha Suresh, "Minimax Risk for Missing Mass Estimation," IEEE International Symposium on Information Theory (ISIT) 2017, Aachen, Germany, arXiv: 1705.05006.
Wiretap channels/Coding and cryptography
- A. Rajagopalan, A. Thangaraj and S. Agrawal, "Wiretap Polar Codes in Encryption Schemes Based on Learning with Errors Problem," IEEE International Symposium on Information Theory (ISIT) 2018, Vail, USA.
- Sundara Rajan S, S. Rajakrishnan, A. Thangaraj and V. Prabhakaran, "Lower bounds and optimal protocols for three-party secure Computation," IEEE International Symposium on Information Theory 2016, Barcelona, Spain.
- M. Bloch, M. Hayashi and A. Thangaraj, "Error-control Coding for Physical-layer Secrecy," Proceedings of the IEEE, vol. 103, no. 10, pp. 1725-1746, September 2015.
- S. Vatedka, N. Kashyap and A. Thangaraj, "Secure Compute-and-Forward in a Bidirectional Relay," IEEE Transactions on Information Theory, vol.61, no.5, pp.2531-2556, May 2015.
- R. Vaidyanathaswami and A. Thangaraj, "Robustness of Physical Layer Security Primitives Against Attacks on Pseudorandom Generators," IEEE Transactions on Communications, vol. 62, no. 3, pp. 1070-1079, March 2014.
- A. Thangaraj, "Coding for wiretap channels: Channel resolvability and semantic security," 2014 IEEE Information Theory Workshop (ITW), Nov. 2014.
- S. Kambala, R. Vaidyanathaswami, and A. Thangaraj, "Implementation of Physical Layer Key Distribution using Software Defined Radios," Defence Science Journal, Vol. 63, No. 1, January 2013, pp. 6-14.
- K. V. Sreenath and A. Thangaraj, "Implementation of Physical Layer Key Sharing Schemes Using Software Defined Radios," Proc. National Conference on Communications (NCC) 2013, IIT Delhi, India, 15-17 Feb. 2013.
- N. Kashyap, V. Shashank and A. Thangaraj, "Secure Computation in a Bidirectional Relay," IEEE International Symposium on Information Theory 2012, Boston, USA, Jul 2012.
- N. Kashyap, Y. Sankarasubramaniam, A. Thangaraj, "Jamming to foil an eavesdropper," Proc. National Conference on Communications (NCC) 2012, IIT Kharagpur, India, 3-5 Feb. 2012.
- Rajaraman V. and A. Thangaraj, "Known-plaintext Attack on the Binary Symmetric Wiretap Channel," IEEE Globecom Physical Layer Security (PLS) Workshop, Dec 9, 2011, preprint.
- Arunkumar Subramanian, Andrew Thangaraj, Matthieu Bloch and Steven W. McLaughlin, "Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes," IEEE Transactions on Information Forensics and Security, vol.6, no.3, pp.585-594, Sept. 2011, http://arxiv.org/abs/1009.3130.
- Mukundan Madhavan, Y. Sankarasubramanian, K. Viswanathan and A. Thangaraj, "NLHB: A Non-linear Hopper Blum Protocol", IEEE ISIT 2010, Austin, USA, June 2010, preprint at http://arxiv.org/abs/1001.2140.
- Arunkumar Subramanian, Ananda Theertha Suresh, Safitha Raj, A. Thangaraj, M. Bloch and S. W. McLaughlin, "Strong and Weak Secrecy in Wiretap Channels", Invited paper at the Turbo Coding Conference (ISTC 2010), Brest, France, Sep 2010, preprint.
- Ananda Theertha Suresh, Arunkumar Subramanian, A. Thangaraj, M. Bloch and S. W. McLaughlin, "Strong Secrecy for Erasure Wiretap Channels", IEEE Information Theory Workshop Dublin, Ireland, Aug 2010, preprint at http://arxiv.org/abs/1004.5540.
- Rajaraman V and A. Thangaraj, "EG-LDPC Codes for the Erasure Wiretap Channel," National Conference on Communications (NCC) 2010, IIT Madras, Jan 2010 (accessible from IEEE Xplore).
- Y. Sankarasubramanian, A. Thangaraj and K. Viswanathan, "Finite State Wiretap Channels: Secrecy Under Memory Constraints," IEEE ITW Taormina, Oct 2009.
- R. Gowtham Kumar, A. Thangaraj, "Computation of Secrecy Capacity for More-Capable Channel Pairs", IEEE ISIT 2008, Toronto, Canada.
- M. Bloch, A. Thangaraj, "Confidential Messages to a Cooperative Relay", IEEE ITW 2008 Porto, Portugal.
- A. Thangaraj, S. Dihidar, A. R. Calderbank, S.W. McLaughlin, and J.-M. Merolla, "Applications of LDPC Codes to the Wiretap Channel," IEEE Transactions on Information Theory, Vol. 53, No. 8, Aug. 2007, pp. 2933-2945, preprint at arxiv.org/cs.IT/0411003.
- M. Bloch, A. Thangaraj, S. McLaughlin, J.-M. Merolla, "LDPC-based secret key agreement over the Gaussian wiretap channel", IEEE ISIT 2006, Seattle, WA, USA.
- M. Bloch, A. Thangaraj, S. W. McLaughlin and J.-M. Merolla, "LDPC-based Gaussian key reconciliation", 2006 IEEE Information Theory Workshop, Page(s):116 - 120.
- S. Dihidar, A. Thangaraj, S. McLaughlin and R. Calderbank, "Linear-time Decodable Secrecy Codes for Binary Erasure Wiretap Channels", Proceedings of the 43rd Annual Allerton Conference on Communication, Control, and Computing, September 2005.
- A. Thangaraj, S. Dihidar, R. Calderbank and S. McLaughlin, "Coding for Reliability and Security over Wire Tap Channel Systems", Proceedings of the 26th Symposium on Information Theory in the Benelux 2005, Brussels, May 2005.
- A. Thangaraj, S. Dihidar, A. R. Calderbank, S.W. McLaughlin, and J.-M. Merolla , "On Achieving Capacity on the Wire Tap channel using LDPC Codes", IEEE ISIT 2005, Adelaide.
- A. Thangaraj, A. R. Calderbank, S. McLaughlin and J.-M. Merolla, "Codes on graphs over the wire tap channel, " IEEE International Symposium on Information Theory and Applications, Parma, Italy, October 2004.
Codes on Graphs and Applications
- A. K. Pradhan and A. Thangaraj, "Protograph LDPC Codes With Block Thresholds: Extension to Degree-One and Generalized Nodes," in IEEE Transactions on Communications, vol. 66, no. 12, pp. 5876-5887, Dec. 2018.
- A. K. Pradhan and A. Thangaraj, "Block-error Threshold Analysis of Protographs in 5G-Standard," International Symposium on Information Theory and Its Applications (ISITA) 2018, Singapore.
- Asit Pradhan and A. Thangaraj, "Near-capacity protograph doubly-generalized LDPC codes with block thresholds," IEEE International Symposium on Information Theory 2016, Barcelona, Spain.
- A. K. Pradhan, A. Thangaraj and A. Subramanian, "Construction of Near-Capacity Protograph LDPC
Code Sequences with Block-Error Thresholds," IEEE Transactions on Communications, vol. 64, no. 1, pp. 27-37, January 2016.
- S. Harikumar, J. Ramesh, M. Srinivasan and A. Thangaraj, "Threshold Upper Bounds and Optimized Design of Protograph LDPC Codes for the Binary Erasure Channel", 7th International Workshop on Signal Design and its Applications in Communications (IWSDA), Bangalore, India, Sep 2015.
- S. Subramanian, A. K. Pradhan, A. Thangaraj, "Node-splitting constructions for large girth irregular and protograph LDPC codes," National Conference on Communications (NCC) 2014, IIT Kanpur, Feb. 28 - Mar. 2 2014.
- K. Ravindran, V. P. Boda, A. Thangaraj, S. Bhashyam, B. Joshi, W. Li, "Optimized codes for bidirectional relaying," National Conference on Communications (NCC) 2014, IIT Kanpur, Feb. 28 - Mar. 2 2014.
- A. Pradhan, A. Subramanian and A. Thangaraj, "Deterministic Constructions for Large Girth Protograph LDPC Codes," IEEE International Symposium on Information Theory 2013, Istanbul, Turkey, Jul 2013.
- B. Joshi and A. Thangaraj, "EXIT Chart Based Design of LDPC Codes for Higher Order Constellations," Proc. National Conference on Communications (NCC) 2013, IIT Delhi, India, 15-17 Feb. 2013.
- Srimathy Srinivasan and A. Thangaraj, "Codes on Planar Graphs," Advances in Mathematics of Communications, Vol. 6, No. 2, pp. 131-163, May 2012, preprint at http://arxiv.org/abs/0904.0768.
- Balakrishna Saradka, S. Bhashyam, A. Thangaraj, "A dirty paper coding scheme for the Multiple Input Multiple Output Broadcast Channel," Proc. National Conference on Communications (NCC) 2012, IIT Kharagpur, India, 3-5 Feb. 2012.
- Navin Kashyap and Andrew Thangaraj, "On the Treewidth of MDS and Reed-Muller Codes," IEEE ISIT 2011, St. Petersburg, Russia, July-Aug 2011.
- Shilpa Gadiraju, A. Thangaraj and S. Bhashyam, "Dirty Paper Coding Using Sign Bit Shaping and LDPC Codes," IEEE ISIT 2010, Austin, USA, June 2010, preprint at http://arxiv.org/abs/1001.3476.
- M. K. Dileep, S. Bhashyam, A. Thangaraj, "Low Density Parity Check Codes in OFDM Systems," National Conference on Communications 2009, Jan. 2009, IIT Guwahati.
- Srimathy Srinivasan and A. Thangaraj, "Codes that have Tanner graphs with non-overlapping cycles," 5th International Symposium on Turbo Codes and Related Topics, Sep. 2008, pp. 299 - 304.
- G. Sridharan, A. Kumarasubramanian, A. Thangaraj, S. Bhashyam, "Optimizing Burst Erasure Correction of LDPC Codes by Interleaving", IEEE ISIT 2008, Toronto, Canada.
- R. Upadrashta, A. Thangaraj, "Key Reconciliation Using Nested LDPC Codes", NCC 2008, IIT Bombay.
- S. Kaimalettu, A. Thangaraj, M. Bloch, S. W. McLaughlin, "Constellation Shaping using LDPC Codes," IEEE ISIT 2007, Nice, France.
- S. Kaimalettu, A. Thangaraj, S. W. McLaughlin, "Constellation Shaping using Codes with a Tree Tanner Graph," NCC 2007, IIT Kanpur.
- A. S. Mohan Vamsi, A. Thangaraj, B. Ramamurthi, "HARQ Schemes using LDPC codes with Diversity-Combining", NCC 2007, Kanpur, India.
- A. Thangaraj and S. W. McLaughlin, "Thresholds and scheduling for LDPC codes over partial response channels," IEEE Transactions on Magnetics, September 2002.
- A. Thangaraj and S. W. McLaughlin, "LDPC codes and thresholds for partial response channels," Intermag Europe 2002, April-May 2002.
- A. Thangaraj and S. W. McLaughlin, "Threshold for regular LDPC codes over PR channels," IEEE International Symposium on Information Theory, Washington DC, USA, June 2001.
Classical Coding and Applications
- A. Thangaraj and H. Pfister, "Efficient Maximum-Likelihood Decoding of Reed-Muller RM(m-3,m) Codes," IEEE International Symposium on Information Theory 2020, Jun 21-26, Los Angeles, CA, USA.
- Navin Kashyap and Andrew Thangaraj, "The Treewidth of MDS and Reed-Muller Codes," IEEE Transactions on Information Theory, vol.58, no.7, pp.4837-4847, July 2012 http://arxiv.org/abs/1102.2734.
- A. Thangaraj and S. J. Raj, "Reed-Solomon Subcodes with Nontrivial Traces: Distance Properties and Soft-Decision Decoding," preprint at http://arxiv.org/abs/0810.0567.
- Safitha J. Raj, A. Thangaraj, "Subcodes of Reed-Solomon Codes Suitable for Soft Decoding", Proc. AAECC-17, Bangalore (Dec 2007), LNCS, vol. 4851/2007, pp. 217-226.
- Sundeep B and A. Thangaraj, "Self-orthogonality of $q$-ary Images of $q^m$-ary Codes and Quantum Code Construction," IEEE Transactions on Information Theory, Vol. 52, No. 7, Jul 2007, pp. 2480-2489, preprint at arxiv.org/cs.IT/0606106.
- Sundeep B and A. Thangaraj, "Self-orthogonality of Images and Traces of Codes with Applications to Quantum Codes", IEEE ISIT 2007, Nice, France.
- A. Thangaraj and S. W. McLaughlin, "Quantum codes from cyclic codes over GF(4^m)," IEEE transactions on Information Theory, March 2001.
- A. Thangaraj, "Simple MAP decoding of binary cyclic codes", IEEE ISIT 2006, Seattle, WA, USA.
- Fijo Therattil and A. Thangaraj, "A Low-complexity Soft-decision Decoder for Extended BCH and RS-like codes", IEEE ISIT 2005, Adelaide.
Network Coding / Wireless Networks
- V. R. Aravind, P. K. Sarvepalli and A. Thangaraj, "Generalizations and Extensions to Lifting Constructions for Coded Caching," IEEE International Symposium on Information Theory 2023, Taiwan.
- V. R. Aravind, P. K. Sarvepalli and A. Thangaraj, "Lifting Constructions of PDAs for Coded Caching with Linear Subpacketization," IEEE Transactions on Communications, vol. 70, no. 12, pp. 7817-7829, Dec 2022, arXiv.
- Aravind V. R., P. Sarvepalli and A. Thangaraj, "Subpacketization in Coded Caching with Demand Privacy," National Conference on Communications (NCC) 2020, IIT Kharagpur, India.
- K. Ravindran, A. Thangaraj and S. Bhashyam, "High SNR Error Analysis for Bidirectional Relaying With Physical Layer Network Coding," in IEEE Transactions on Communications, vol. 65, no. 4, pp. 1536-1548, April 2017.
- Sourbh Bhadane and A. Thangaraj, "Unequal Locality and Recovery for Locally Recoverable Codes with Availability," National Conference on Communications 2017, IIT Madras, Chennai, India, arXiv: 1705.05005.
- K. Thekumparampil, A. Thangaraj and R. Vaze, "Combinatorial Resource Allocation Using Sub-modularity of Waterfilling," IEEE Transactions on Wireless Communications, vol. 15, no. 1, pp. 206-216, January 2016.
- K. Ravindran, A. Thangaraj and S. Bhashyam, "LDPC Codes for Network-coded Bidirectional
Relaying with Higher Order Modulation," IEEE Transactions on Communications, vol.63, no.6, pp.1975-1987, June 2015.
- A. Thangaraj and R. Vaze, "Online Algorithms for Basestation Allocation," IEEE Transactions on Wireless Communications, vol. 13, no.5, pp. 2966-2975, May 2014.
- Vignesh G and A. Thangaraj, "Quasi-Cyclic Regenerating Codes for Distributed Storage: Existence and Near-MSR Examples, " IEEE International Symposium on Information Theory 2013, Istanbul, Turkey, Jul 2013.
- Arun Ayyar, Hari Ram Balakrishnan, Andrew Thangaraj, Vinoth Nagarajan, K Giridhar, "Block Modulation for Interference Management in Heterogeneous Wireless Networks," IEEE Journal of Selected Topics in Signal Processing, vol. 6, no. 3, pp. 241-256, June 2012.
- Amaranath Alapati, Avinash Krishnakumar, A. Thangaraj, "Public-private separation in linear network-coded simultaneous multicast and unicast," Proc. National Conference on Communications (NCC) 2012, IIT Kharagpur, India, 3-5 Feb. 2012.
- M. Bama, S. Bhashyam and A. Thangaraj, "A Decode and Forward Protocol for Two-stage Gaussian Relay Networks", IEEE Transactions on Communications, vol. 60, no. 1, pp. 68-73, Jan 2012 preprint.
- A. Thangaraj and Chinnadurai Sankar, "Quasicyclic MDS Codes for Distributed Storage with Efficient Exact Repair", IEEE Information Theory Workshop 2011, Paraty, Brazil, Oct 16-20, 2011, preprint.
- Abhay Subramanian and A. Thangaraj, "Path Gain Algebraic Formulation for the Scalar Linear Network Coding Problem," IEEE Transactions on Information Theory, vol.56, no.9, pp.4520-4531, Sep 2010, preprint at http://arxiv.org/abs/0807.1158.
- M. Bama, S. Bhashyam, A. Thangaraj , "Receiver Selection Scheduling in Wireless Networks," Proceedings of the Wireless Personal Multimedia Communications (WPMC), Sendai, Japan, September 2009.
- Dinesh Kumar K. R. and A. Thangaraj, "Algebraic Network Coding: A New Perspective," IEEE International Symposium on Information Theory 2009, Jun 28 - Jul 3 2009, Seoul.
- M. Bama, S. Bhashyam, A. Thangaraj , "Throughput of Wireless Relay Networks using Interference Processing," Proceedings of the National Conference on Communications (NCC), Guwahati, India, January 2009.
- A. Subramanian and A. Thangaraj, "A Simple Algebraic Formulation for the Scalar Linear Network Coding Problem," Forty-Sixth Annual Allerton Conference on Communication, Control, and Computing, Sep. 2008, University of Illinois at Urbana-Champaign, IL, USA.
- M. Bama, S. Bhashyam, A. Thangaraj, "Capacity of Network-Coded Wireless Multicast using Node-Based Scheduling", NCC 2008, IIT Bombay.
- M. Bama, A. Thangaraj , S. Bhashyam, "Node-Based Scheduling for Network-Coded Wireless Networks," IEEE COMSWARE 2007, Workshop on WIreless Systems: Advanced Research and Development (WISARD 2008), Bangalore, India, January 2008 (Poster).
Topics in Information Theory
- J. Mandalapu, A. Chatterjee, K. Jagannathan and A. Thangaraj, "Capacity Achieving Codes for an Erasure Queue-channel," IEEE International Symposium on Information Theory (ISIT) 2023, Taipei, Taiwan.
- A. Mohanan and A. Thangaraj, "Dual Capacity Upper Bounds for Binary-Input Single-Tap ISI Channels," in IEEE Transactions on Communications, vol. 67, no. 10, pp. 6725-6734, Oct. 2019.
- A. Mohanan, A. Rajagopalan and A. Thangaraj, "Dual Capacity Upper Bounds for Binary-input ISI and Constrained BIBO Channels," IEEE International Symposium on Information Theory (ISIT) 2018, Vail, USA.
- H. Krishnamurthy, P. Hegde and A. Thangaraj, "Conditions for Optimality of Superposition Coding in Discrete Memoryless Broadcast Channels," National Conference on Communications 2019, IISc Bangalore, India.
- Andrew Thangaraj, "Dual Capacity Upper Bounds for Noisy Runlength Constrained Channels," in IEEE Transactions on Information Theory, vol. 63, no. 11, pp. 7052-7065, Nov. 2017, arXiv:1609:00189.
- Andrew Thangaraj, Gerhard Kramer, Georg Bocherer, "Capacity Bounds for Discrete-Time, Amplitude-Constrained, Additive White Gaussian Noise Channels," in IEEE Transactions on Information Theory, vol. 63, no. 7, pp. 4172-4182, July 2017, arXiv:1511.08742.
- Andrew Thangaraj, "Dual Capacity Upper Bounds for Noisy Runlength Constrained Channels," IEEE Information Theory Workshop 2016, Cambridge, UK.
- A. Thangaraj, G. Kramer and G. Boecherer, "Capacity Bounds For Amplitude-Constrained Additive White Gaussian Noise Channels," IEEE International Symposium on Information Theory 2015, Hong Kong, Jun 2015.
- R. Ganti, A. Thangaraj and A. Mondal, "Approximation of Capacity for ISI Channels with One-bit Output Quantization," IEEE International Symposium on Information Theory 2015, Hong Kong, Jun 2015.
- Gautham T. S. V., A. Thangaraj and D. Jalihal, "Common Architecture for Decoding Turbo and LDPC Codes," National Conference on Communications (NCC) 2010, IIT Madras, Jan 2010 (accessible from IEEE Xplore).
- P. Sankar, Arun Kumar Sharma, D. Jalihal, A. Thangaraj, "Turbo Product Codes for a Satellite Modem", NCC 2008, IIT Bombay.
- K. Chaitanya, A. Thangaraj, "Luby Transform Codes with Priority Encoding", NCC 2008, IIT Bombay.
- S. Planjery, T. A. Gulliver, A. Thangaraj, "Rate-Compatible Punctured Systematic Repeat - Accumulate Codes", WCNC 2007, Hong Kong.
- M. Madhavan, A. Thangaraj, "An Implementation Of A Soft-Input Stack Decoder For Tailbiting Convolutional Codes", NCC 2007, Kanpur, India.
- S. Donnet, A. Thangaraj, M. Bloch, J. Cussey, J.-M. Merolla and L. Larger, "Security of Y-00 under heterodyne measurement and fast correlation attack ", Physics Letters A, Volume 356, Issue 6, 21 August 2006, Pages 406-410.
- H. Tiwari and A. Thangaraj, "Run-length Limited Codes with Free Distance Properties: Construction and Soft-Decision Decoding", Intermag 2006, San Diego, CA, USA.
- A. Prabhakar, A. Thangaraj, M. Manickam, and E. Louis, "Effects of reader distortion on nonlinear transition shift measurements", IEEE INTERMAG 2005, April 4-8, 2005.
- J.-M. Merolla, O. Guerreau, A. Thangaraj, S. W. McLaughlin, and F. J. Malassenet, "Practical quantum cryptography system using single sideband scheme and WDM compensation technique, " The International Conference on Solid State Quantum Information processing, SSQIP 03, Amsterdam (Netherlands), p. 167, Dec. 2003.
- A. Thangaraj and S. W. McLaughlin, "On iterative hard decision decoding of EG codes," IEEE International Symposium on Information Theory, Lausanne, Switzerland, June 2002.