—Consider a linear code defined as a mapping between vector spaces of dimensions k and n. Let β∗ denote the minimal (relative) weight among all images of input vectors of full Hamming weight k. Operationally, β∗ characterizes the threshold for adversarial (erasure) noise beyond which decoder is guaranteed to produce estimate of k-input with 100% symbol error rate (SER). This paper studies the relation between β∗ and δ, the minimum distance of the code, which gives the threshold for 0% SER. An optimal tradeoff between β∗ and δ is obtained (over large alphabets) and all linear codes achieving β∗ = 1 are classified: they are repetition-like. More generally, a design criteria is proposed for codes with favorable graceful degradation properties. As an example, it is shown that in an overdetermined system of n homogeneous linear equations in k variables (over a field) it is always possible to satisfy some k − 1 equations with non-zero assignments to every unknown, provided that any subset of k equations is linearly independent. This statement is true if and only if n ≥ 2k − 1.
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Novel LoS $\beta -\gamma$ THz Channel Unifying Molecular Re-Radiation Manifestations
This paper introduces a novel line-of-sight (LoS) β−γ terahertz (THz) channel model that closely mirrors physical reality by considering radiation trapping. Our channel model provides an exhaustive modeling of the physical phenomena including the amount of re-radiation available at the receiver, parametrized by β, and the balance between scattering and noise contributions, parametrized by γ, respectively. Our findings indicate a nontrivial relationship between average limiting received signal-to-noise ratio (SNR) and distance emphasizing the significance of γ in THz system design. We further propose new maximum likelihood (ML) thresholds for pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) schemes, resulting in analytical symbol error rate (SER) expressions that account for different noise variances across constellation points. The results confirm that the analytical SER closely matches the true simulated SER when using an optimal detector. As expected, under maximum molecular re-radiation, the true SER is shown to be lower than that produced by a suboptimal detector that assumes equal noise variances.
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- PAR ID:
- 10525175
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Vehicular Technology
- ISSN:
- 0018-9545
- Page Range / eLocation ID:
- 1 to 6
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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