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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.10137 |
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| _version_ | 1866915932243230720 |
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| author | Souza, Juliana Huang, Yu-Chih |
| author_facet | Souza, Juliana Huang, Yu-Chih |
| contents | We study a space--time block code from a maximal order in the definite quaternion algebra $(-1,-3)_{\Q}$. Its embedding into $\C^{2\times 2}$ yields an Alamouti--Eisenstein code over $\Z[w]$ with full diversity, orthogonality, and non-vanishing determinant. The underlying lattice is isomorphic to $\Z[w]^2$, while the embedded lattice has $A_2\oplus A_2$ geometry, yielding a hexagonal shaping gain. We compare it with the classical Alamouti code over $\Z[i]$ in terms of shaping, constellation-constrained mutual information, and finite-blocklength achievable rates, obtaining an asymptotic energy gain of about $0.79$~dB and a small but positive mutual-information gain. At the same SNR and rate, the Alamouti--Eisenstein design also improves short-packet reliability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10137 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite-Blocklength Analysis of Alamouti Codes over Eisenstein Integers Souza, Juliana Huang, Yu-Chih Information Theory We study a space--time block code from a maximal order in the definite quaternion algebra $(-1,-3)_{\Q}$. Its embedding into $\C^{2\times 2}$ yields an Alamouti--Eisenstein code over $\Z[w]$ with full diversity, orthogonality, and non-vanishing determinant. The underlying lattice is isomorphic to $\Z[w]^2$, while the embedded lattice has $A_2\oplus A_2$ geometry, yielding a hexagonal shaping gain. We compare it with the classical Alamouti code over $\Z[i]$ in terms of shaping, constellation-constrained mutual information, and finite-blocklength achievable rates, obtaining an asymptotic energy gain of about $0.79$~dB and a small but positive mutual-information gain. At the same SNR and rate, the Alamouti--Eisenstein design also improves short-packet reliability. |
| title | Finite-Blocklength Analysis of Alamouti Codes over Eisenstein Integers |
| topic | Information Theory |
| url | https://arxiv.org/abs/2604.10137 |