Flat tori, lattices and bounds for commutative group codes
Designs, Codes and Cryptography
Structured LDPC codes over integer residue rings
EURASIP Journal on Wireless Communications and Networking - Advances in Error Control Coding Techniques
Space-time codes from structured lattices
IEEE Transactions on Information Theory
The capacity of finite Abelian group codes over symmetric memoryless channels
IEEE Transactions on Information Theory
A space-time code design for CPM: diversity order and coding gain
IEEE Transactions on Information Theory
On the linear codebook-level duality between Slepian-Wolf coding and channel coding
IEEE Transactions on Information Theory
Group codes outperform binary-coset codes on nonbinary symmetric memoryless channels
IEEE Transactions on Information Theory
| Hi-index | 755.14 |
The main building block for the construction of a geometrically uniform coded modulation scheme is a subgroup of GI, where G is a group generating a low-dimensional signal constellation and I is an index set. In this paper we study the properties of these subgroups when G is cyclic. We exploit the fact that any cyclic group of q elements is isomorphic to the additive group of Zq (the ring of integers modulo q) so that we can make use of concepts related to linearity. Our attention is focused mainly on indecomposable cyclic groups (i.e., of prime power order), since they are the elementary “building blocks” of any abelian group. In analogy with the usual construction of linear codes over fields, we define a generator matrix and a parity check matrix. Trellis construction and bounds on the minimum Euclidean distance are also investigated. Some examples of coded modulation schemes based on this theory are also exhibited, and their performance evaluated