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Besides all the attention given to lattice constructions, it is common to find some very interesting nonlattice constellations, as Construction C, for example, which also has relevant applications in communication problems (multi-level coding, multi-stage decoding, good quantization efficieny). In this work we present a constellation which is a subset of Construction C, based on inter-level coding, which we call Construction C*. This construction may have better immunity to noise and it also provides a simple way of describing the Leech lattice $Lambda_{24}.$ A condition under which Construction C* is a lattice constellation is given.
Construction C (also known as Forneys multi-level code formula) forms a Euclidean code for the additive white Gaussian noise (AWGN) channel from $L$ binary code components. If the component codes are linear, then the minimum distance is the same for
Construction $C^star$ was recently introduced as a generalization of the multilevel Construction C (or Forneys code-formula), such that the coded levels may be dependent. Both constructions do not produce a lattice in general, hence the central idea
In this letter, we propose a progressive rate-filling method as a framework to study agile construction of multilevel polar-coded modulation. We show that the bit indices within each component polar code can follow a fixed, precomputed ranking sequen
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of
New quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension and the minimum distance are studied. Using these constructions new famili