Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Elements of information theory
Elements of information theory
Principles of Digital Communication and Coding
Principles of Digital Communication and Coding
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Average Spectra and Minimum Distances of Low-Density Parity-Check Codes over Abelian Groups
SIAM Journal on Discrete Mathematics
Convolutional codes over groups
IEEE Transactions on Information Theory - Part 1
Some structural properties of convolutional codes over rings
IEEE Transactions on Information Theory
Minimal syndrome formers for group codes
IEEE Transactions on Information Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Random coding techniques for nonrandom codes
IEEE Transactions on Information Theory
System-theoretic properties of convolutional codes over rings
IEEE Transactions on Information Theory
Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Random codes: minimum distances and error exponents
IEEE Transactions on Information Theory
On the application of LDPC codes to arbitrary discrete-memoryless channels
IEEE Transactions on Information Theory
The dynamics of group codes: Dual abelian group codes and systems
IEEE Transactions on Information Theory
The ML decoding performance of LDPC ensembles over Zq
IEEE Transactions on Information Theory
LDPC Codes Over Rings for PSK Modulation
IEEE Transactions on Information Theory
Linear block codes over cyclic groups
IEEE Transactions on Information Theory
Group codes outperform binary-coset codes on nonbinary symmetric memoryless channels
IEEE Transactions on Information Theory
Linear universal decoding for compound channels
IEEE Transactions on Information Theory
| Hi-index | 754.96 |
The capacity of finite Abelian group codes over symmetric memoryless channels is determined. For certain important examples, such as m-PSK constellations over additive white Gaussian noise (AWGN) channels, with m a prime power, it is shown that this capacity coincides with the Shannon capacity; i.e., there is no loss in capacity using group codes. (This had previously been known for binary-linear codes used over binary-input output-symmetric memoryless channels.) On the other hand, a counterexample involving a three-dimensional geometrically uniform constellation is presented in which the use of Abelian group codes leads to a loss in capacity. The error exponent of the average group code is determined, and it is shown to be bounded away from the random-coding error exponent, at low rates, for finite Abelian groups not admitting Galois field structure.