Decoding turbo-like codes via linear programming
Journal of Computer and System Sciences - Special issue on FOCS 2002
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The price of privacy and the limits of LP decoding
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A cutting-plane method based on redundant rows for improving fractional distance
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Improved random redundant iterative HDPC decoding
IEEE Transactions on Communications
Pseudocodeword performance analysis for LDPC convolutional codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Analysis of connections between pseudocodewords
IEEE Transactions on Information Theory
Linear-programming decoding of nonbinary linear codes
IEEE Transactions on Information Theory
On Linear Programming Decoding on a Quantized Additive White Gaussian Noise Channel
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Multi-stage decoding of LDPC codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Absdet-pseudo-codewords and perm-pseudo-codewords: definitions and properties
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
On LP decoding of nonbinary expander codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
LP decoding meets LP decoding: a connection between channel coding and compressed sensing
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Improving the performance of LP decoders for cyclic codes
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Interior point decoding for linear vector channels based on convex optimization
IEEE Transactions on Information Theory
Multiple-bases belief-propagation decoding of high-density cyclic codes
IEEE Transactions on Communications
On the decomposition method for linear programming decoding of LDPC codes
IEEE Transactions on Communications
Decoding LDPC codes in MIMO systems with linear programming
ICS'06 Proceedings of the 10th WSEAS international conference on Systems
Cold boot key recovery by solving polynomial systems with noise
ACNS'11 Proceedings of the 9th international conference on Applied cryptography and network security
Linear time decoding of regular expander codes
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Linear-time decoding of regular expander codes
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
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Error-correcting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming [Ham50] and Shannon [Sha48], who used them as the basis for the field of information theory. The problem of decoding the original information up to the full error-correcting potential of the system is often very complex, especially for modern codes that approach the theoretical limits of the communication channel. In this thesis we investigate the application of linear programming (LP) relaxation to the problem of decoding an error-correcting code. Linear programming relaxation is a standard technique in approximation algorithms and operations research, and is central to the study of efficient algorithms to find good (albeit suboptimal) solutions to very difficult optimization problems. Our new “LP decoders” have tight combinatorial characterizations of decoding success that can be used to analyze error-correcting performance. Furthermore, LP decoders have the desirable (and rare) property that whenever they output a result, it is guaranteed to be the optimal result: the most likely (ML) information sent over the channel. We refer to this property as the ML certificate property. We provide specific LP decoders for two major families of codes: turbo codes and low-density parity-check (LDPC) codes. These codes have received a great deal of attention recently due to their unprecedented error-correcting performance. Our decoder is particularly attractive for analysis of these codes because the standard message-passing algorithms used for decoding are often difficult to analyze. For turbo codes, we give a relaxation very close to min-cost flow, and show that the success of the decoder depends on the costs in a certain residual graph. For the case of rate-1/2 repeat-accumulate codes (a certain type of turbo code), we give an inverse polynomial upper bound on the probability of decoding failure. For LDPC codes (or any binary linear code), we give a relaxation based on the factor graph representation of the code. We introduce the concept of fractional distance, which is a function of the relaxation, and show that LP decoding always corrects a number of errors up to half the fractional distance. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.) (Abstract shortened by UMI.)