Elements of information theory
Elements of information theory
Error-correcting codes and finite fields (student ed.)
Error-correcting codes and finite fields (student ed.)
Practical loss-resilient codes
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
New Sequences of Linear Time Erasure Codes Approaching the Channel Capacity
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Average Coset Weight Distribution of Multi-Edge Type LDPC Code Ensembles
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Random coding techniques for nonrandom codes
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation
IEEE Transactions on Information Theory
Concatenated tree codes: a low-complexity, high-performance approach
IEEE Transactions on Information Theory
Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes
IEEE Transactions on Information Theory
On ensembles of low-density parity-check codes: asymptotic distance distributions
IEEE Transactions on Information Theory
Capacity-achieving sequences for the erasure channel
IEEE Transactions on Information Theory
Variations on the Gallager bounds, connections, and applications
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On decoding of low-density parity-check codes over the binary erasure channel
IEEE Transactions on Information Theory
Asymptotic enumeration methods for analyzing LDPC codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Rate-compatible puncturing of low-density parity-check codes
IEEE Transactions on Information Theory
Endcoding complexity versus minimum distance
IEEE Transactions on Information Theory
Capacity-achieving ensembles for the binary erasure channel with bounded complexity
IEEE Transactions on Information Theory
Nonuniform error correction using low-density parity-check codes
IEEE Transactions on Information Theory
Distance properties of expander codes
IEEE Transactions on Information Theory
Weight Distribution of Low-Density Parity-Check Codes
IEEE Transactions on Information Theory
Average Coset Weight Distribution of Combined LDPC Matrix Ensembles
IEEE Transactions on Information Theory
Asymptotic Spectra of Trapping Sets in Regular and Irregular LDPC Code Ensembles
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Capacity Achieving LDPC Codes Through Puncturing
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
| Hi-index | 754.90 |
In this paper, the existence of capacity-achieving codes for memoryless binary-input output-symmetric (MBIOS) channels under maximum-likelihood (ML) decoding with bounded graphical complexity is investigated. Graphical complexity of a code is defined as the number of edges in the graphical representation of the code per information bit and is proportional to the decoding complexity per information bit per iteration under iterative decoding. Irregular repeat-accumulate (IRA) codes are studied first. Utilizing the asymptotic average weight distribution (AAWD) of these codes and invoking Divsalar's bound on the binary-input additive white Gaussian noise (BIAWGN) channel, it is shown that simple nonsystematic IRA ensembles outperform systematic IRA and regular low-density parity-check (LDPC) ensembles with the same graphical complexity, and are at most 0.124 dB away from the Shannon limit. However, a conclusive result as to whether these nonsystematic IRA codes can really achieve capacity cannot be reached. Motivated by this inconclusive result, a new family of codes is proposed, called low-density parity-check and generator matrix (LDPC-GM) codes, which are serially concatenated codes with an outer LDPC code and an inner low-density generator matrix (LDGM) code. It is shown that these codes can achieve capacity on any MBIOS channel using ML decoding and also achieve capacity on any BEC using belief propagation (BP) decoding, both with bounded graphical complexity. Moreover, it is shown that, under certain conditions, these capacity-achieving codes have linearly increasing minimum distances and achieve the asymptotic Gilbert-Varshamov bound for all rates.