Decoding Turbo-Like Codes via Linear Programming
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Decoding error-correcting codes via linear programming
Decoding error-correcting codes via linear programming
An efficient algorithm to find all small-size stopping sets of low-density parity-check matrices
IEEE Transactions on Information Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
On the stopping distance and the stopping redundancy of codes
IEEE Transactions on Information Theory
Pseudo-Codeword Analysis of Tanner Graphs From Projective and Euclidean Planes
IEEE Transactions on Information Theory
Pseudocodewords of Tanner Graphs
IEEE Transactions on Information Theory
Adaptive Methods for Linear Programming Decoding
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
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In this paper, we consider the pairwise error probability (PEP) of a linear programming (LP) decoder for a general binary linear code as formulated by Feldman et al. (IEEE Trans. Inf. Theory, Mar. 2005) on an independent (or memoryless) Rayleigh flat-fading channel with coherent detection and perfect channel state information (CSI) at the receiver. Let H be a parity-check matrix of a binary linear code and consider LP decoding based on H. The output of the LP decoder is always apseudocodeword. We will show that the PEP of decoding to a pseudocodeword ω when the all-zero codeword is transmitted on the above-mentioned channel, behaves asymptotically as K(ω) ċ (Es/N0)-|χ(ω)|, where χ(ω) is the support set of ω, i.e., the set of nonzero coordinates, Es/N0 is the average signal-to-noise ratio (SNR), and K(ω) is a constant independent of the SNR. Note that the support set χ(ω) of ω is a stopping set. Thus, the asymptotic decay rate of the error probability with the average SNR is determined by the size of the smallest nonempty stopping set in the Tanner graph of H. As an example, we analyze the well-known (155,64) Tanner code and present performance curves on the independent Rayleigh flat-fading channel.