An introduction to low-density parity-check codes
Theoretical aspects of computer science
An Introduction to Low-Density Parity-Check Codes
Theoretical Aspects of Computer Science, Advanced Lectures [First Summer School on Theoretical Aspects of Computer Science, Tehran, Iran, July 2000]
Performance analysis of linear codes under maximum-likelihood decoding: a tutorial
Communications and Information Theory
Instanton-based techniques for analysis and reduction of error floors of LDPC codes
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Gallager's decoding algorithm A over high order modulations
IEEE Communications Letters
A channel representation method for the study of hybrid retransmission-based error control
IEEE Transactions on Communications
IEEE Transactions on Communications
Two-bit message passing decoders for LDPC codes over the binary symmetric channel
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
A differential binary message-passing LDPC decoder
IEEE Transactions on Communications
Design of irregular LDPC codes with optimized performance-complexity tradeoff
IEEE Transactions on Communications
On the hardness of approximating stopping and trapping sets
IEEE Transactions on Information Theory
An implementation-friendly binary LDPC decoding algorithm
IEEE Transactions on Communications
On fuzzy syndrome hashing with LDPC coding
Proceedings of the 4th International Symposium on Applied Sciences in Biomedical and Communication Technologies
On the wiretap channel induced by noisy tags
ESAS'06 Proceedings of the Third European conference on Security and Privacy in Ad-Hoc and Sensor Networks
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We show that for the case of the binary-symmetric channel and Gallager's decoding algorithm A the threshold can, in many cases, be determined analytically. More precisely, we show that the threshold is always upper-bounded by the minimum of (1-λ2ρ'(1))/(λ'(1)ρ'(1)-λ2ρ'(1)) and the smallest positive real root τ of a specific polynomial p(x) and we observe that for most cases this bound is tight, i.e., it determines the threshold exactly. We also present optimal degree distributions for a large range of rates. In the case of rate one-half codes, for example, the threshold x0* of the optimal degree distribution is given by x*0∼0.0513663. Finally, we outline how thresholds of more complicated decoders might be determined analytically.