On coding without restrictions for the AWGN channel

Many coded modulation constructions, such as lattice codes, are visualized as restricted subsets of an infinite constellation (IC) of points in the n-dimensional Euclidean space. The author regards an IC as a code without restrictions employed for the AWGN channel. For an IC the concept of coding ra...

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Vydáno v:IEEE transactions on information theory Ročník 40; číslo 2; s. 409 - 417
Hlavní autor: Poltyrev, G.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.03.1994
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
AWGN channels
Capacity planning
Constellation diagram
Cryptography
Decoding
Error probability
Lattices
Modular construction
Modulation coding
Probability
Upper bound
Visualization
ISSN:0018-9448, 1557-9654
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Shrnutí:Many coded modulation constructions, such as lattice codes, are visualized as restricted subsets of an infinite constellation (IC) of points in the n-dimensional Euclidean space. The author regards an IC as a code without restrictions employed for the AWGN channel. For an IC the concept of coding rate is meaningless and the author uses, instead of coding rate, the normalized logarithmic density (NLD). The maximum value C/sub /spl infin// such that, for any NLD less than C/sub /spl infin//, it is possible to construct an PC with arbitrarily small decoding error probability, is called the generalized capacity of the AWGN channel without restrictions. The author derives exponential upper and lower bounds for the decoding error probability of an IC, expressed in terms of the NLD. The upper bound is obtained by means of a random coding method and it is very similar to the usual random coding bound for the AWGN channel. The exponents of these upper and lower bounds coincide for high values of the NLD, thereby enabling derivation of the generalized capacity of the AWGN channel without restrictions. It is also shown that the exponent of the random coding bound can be attained by linear ICs (lattices), implying that lattices play the same role with respect to the AWGN channel as linear-codes do with respect to a discrete symmetric channel.< >
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ISSN:0018-9448
1557-9654
DOI:10.1109/18.312163