Groups of Complex Integers Used as QAM Signals

Josep Rifà

doi:10.1109/18.412699

Groups of Complex Integers Used as QAM Signals

Josep Rifà

Research output: Contribution to journal › Article › Research › peer-review

18 Citations (Scopus)

Abstract

Block codes which allow error correction in a two-dimensional QAM signal space are given. The properties of these codes are used to demodulate QAM signals in a differentially coherent detection scheme on a noisy channel. Block codes presented are not group codes; however, their components belong to a group Gn or Gn′ which is constructed starting from the Gaussian integers G = Z[i] modulo a nonprime ideal (2n + 2ni) and taking on it the multiplicative group of units. We classify and factor these multiplicative groups and use them to construct the block codes which become optimal and efficient from the point of view of transmission rate and decoding. © 1995 IEEE.

Original language	English
Pages (from-to)	1512-1517
Journal	IEEE Transactions on Information Theory
Volume	41
DOIs	https://doi.org/10.1109/18.412699
Publication status	Published - 1 Jan 1995

Keywords

Gaussian integers
QAM signals
differentially coherent detection
error-correcting codes
multiplicative groups of units

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10.1109/18.412699

Cite this

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abstract = "Block codes which allow error correction in a two-dimensional QAM signal space are given. The properties of these codes are used to demodulate QAM signals in a differentially coherent detection scheme on a noisy channel. Block codes presented are not group codes; however, their components belong to a group Gn or Gn′ which is constructed starting from the Gaussian integers G = Z[i] modulo a nonprime ideal (2n + 2ni) and taking on it the multiplicative group of units. We classify and factor these multiplicative groups and use them to construct the block codes which become optimal and efficient from the point of view of transmission rate and decoding. {\textcopyright} 1995 IEEE.",

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N2 - Block codes which allow error correction in a two-dimensional QAM signal space are given. The properties of these codes are used to demodulate QAM signals in a differentially coherent detection scheme on a noisy channel. Block codes presented are not group codes; however, their components belong to a group Gn or Gn′ which is constructed starting from the Gaussian integers G = Z[i] modulo a nonprime ideal (2n + 2ni) and taking on it the multiplicative group of units. We classify and factor these multiplicative groups and use them to construct the block codes which become optimal and efficient from the point of view of transmission rate and decoding. © 1995 IEEE.

AB - Block codes which allow error correction in a two-dimensional QAM signal space are given. The properties of these codes are used to demodulate QAM signals in a differentially coherent detection scheme on a noisy channel. Block codes presented are not group codes; however, their components belong to a group Gn or Gn′ which is constructed starting from the Gaussian integers G = Z[i] modulo a nonprime ideal (2n + 2ni) and taking on it the multiplicative group of units. We classify and factor these multiplicative groups and use them to construct the block codes which become optimal and efficient from the point of view of transmission rate and decoding. © 1995 IEEE.

KW - Gaussian integers

KW - QAM signals

KW - differentially coherent detection

KW - error-correcting codes

KW - multiplicative groups of units

U2 - 10.1109/18.412699

DO - 10.1109/18.412699

M3 - Article

SN - 0018-9448

VL - 41

SP - 1512

EP - 1517

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

ER -

Groups of Complex Integers Used as QAM Signals

Abstract

Keywords

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