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Communications and Information Theory
Capacity-achieving codes for finite-state channels with maximum-likelihood decoding
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
IEEE Transactions on Signal Processing
Sharp bounds for optimal decoding of low-density parity-check codes
IEEE Transactions on Information Theory
Bounds on the number of iterations for turbo-like ensembles over the binary erasure channel
IEEE Transactions on Information Theory
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
A reliability framework for visual sensor networks
PCS'09 Proceedings of the 27th conference on Picture Coding Symposium
On the fundamental system of cycles in the bipartite graphs of LDPC code ensembles
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Lower bounds on the graphical complexity of finite-length LDPC codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Capacity-achieving codes for channels with memory with maximum-likelihood decoding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Design of irregular LDPC codes with optimized performance-complexity tradeoff
IEEE Transactions on Communications
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Multipath distributed data reliability for wireless sensor networks
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Bandwidth-efficient modulation codes based on nonbinary irregular repeat-accumulate codes
IEEE Transactions on Information Theory
Capacity-achieving codes with bounded graphical complexity and maximum likelihood decoding
IEEE Transactions on Information Theory
Simple capacity-achieving ensembles of rateless erasure-correcting codes
IEEE Transactions on Communications
Systematic design of low-density parity-check code ensembles for binary erasure channels
IEEE Transactions on Communications
New sequences of capacity achieving LDPC code ensembles over the binary erasure channel
IEEE Transactions on Information Theory
| Hi-index | 755.20 |
We derive lower bounds on the density of parity-check matrices of binary linear codes which are used over memoryless binary-input output-symmetric (MBIOS) channels. The bounds are expressed in terms of the gap between the rate of these codes for which reliable communications is achievable and the channel capacity; they are valid for every sequence of binary linear block codes if there exists a decoding algorithm under which the average bit-error probability vanishes. For every MBIOS channel, we construct a sequence of ensembles of regular low-density parity-check (LDPC) codes, so that an upper bound on the asymptotic density of their parity-check matrices scales similarly to the lower bound. The tightness of the lower bound is demonstrated for the binary erasure channel by analyzing a sequence of ensembles of right-regular LDPC codes which was introduced by Shokrollahi, and which is known to achieve the capacity of this channel. Under iterative message-passing decoding, we show that this sequence of ensembles is asymptotically optimal (in a sense to be defined in this paper), strengthening a result of Shokrollahi. Finally, we derive lower bounds on the bit-error probability and on the gap to capacity for binary linear block codes which are represented by bipartite graphs, and study their performance limitations over MBIOS channels. The latter bounds provide a quantitative measure for the number of cycles of bipartite graphs which represent good error-correction codes.