FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
The generalized area theorem and some of its consequences
IEEE Transactions on Information Theory
Modern Coding Theory
Capacity-achieving codes with bounded graphical complexity and maximum likelihood decoding
IEEE Transactions on Information Theory
Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding
IEEE Transactions on Information Theory
Efficient erasure correcting codes
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Capacity-achieving sequences for the erasure channel
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Bounds on achievable rates of LDPC codes used over the binary erasure channel
IEEE Transactions on Information Theory
Extrinsic information transfer functions: model and erasure channel properties
IEEE Transactions on Information Theory
Capacity-achieving ensembles for the binary erasure channel with bounded complexity
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Efficient Serial Message-Passing Schedules for LDPC Decoding
IEEE Transactions on Information Theory
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
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
Design of irregular LDPC codes with optimized performance-complexity tradeoff
IEEE Transactions on Communications
New sequences of capacity achieving LDPC code ensembles over the binary erasure channel
IEEE Transactions on Information Theory
Hi-index | 754.96 |
This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check (LDPC) codes and variations of repeat-accumulate codes). The transmission of the code ensembles is assumed to take place over a binary erasure channel, and the bounds refer to the asymptotic case where we let the block length tend to infinity. The simplicity of the bounds derived in this paper stems from the fact that they are easily evaluated and are expressed in terms of some basic parameters of the ensemble which include the fraction of degree-2 variable nodes, the target bit erasure probability, and the gap between the channel capacity and the design rate of the ensemble. This paper demonstrates that the number of iterations which is required for successful message-passing decoding scales at least like the inverse of the gap (in rate) to capacity, provided that the fraction of degree-2 variable nodes of these turbo-like ensembles does not vanish (hence, the number of iterations becomes unbounded as the gap to capacity vanishes).