On the Codebook Design for NOMA Schemes from Bent Functions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911327327354880 |
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| author | Li, Chunlei Riera, Constanza Sarkar, Palash Stanica, Pantelimon |
| author_facet | Li, Chunlei Riera, Constanza Sarkar, Palash Stanica, Pantelimon |
| contents | Uplink grant-free non-orthogonal multiple access (NOMA) is a promising technology for massive connectivity with low latency and high energy efficiency. In code-domain NOMA schemes, the requirements boil down to the design of codebooks that contain a large number of spreading sequences with low peak-to-average power ratio (PAPR) while maintaining low coherence. When employing binary Golay sequences with guaranteed low PAPR in the design, the fundamental problem is to construct a large set of $n$-variable quadratic bent or near-bent functions in a particular form such that the difference of any two is bent for even $n$ or near-bent for odd $n$ to achieve optimally low coherence. In this work, we propose a theoretical construction of NOMA codebooks by applying a recursive approach to those particular quadratic bent functions in smaller dimensions. The proposed construction yields desired NOMA codebooks that contain $6\cdot N$ Golay sequences of length $N=2^{4m}$ for any positive integer $m$ and have the lowest possible coherence $1/\sqrt{N}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_16560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Codebook Design for NOMA Schemes from Bent Functions Li, Chunlei Riera, Constanza Sarkar, Palash Stanica, Pantelimon Combinatorics Discrete Mathematics Information Theory Uplink grant-free non-orthogonal multiple access (NOMA) is a promising technology for massive connectivity with low latency and high energy efficiency. In code-domain NOMA schemes, the requirements boil down to the design of codebooks that contain a large number of spreading sequences with low peak-to-average power ratio (PAPR) while maintaining low coherence. When employing binary Golay sequences with guaranteed low PAPR in the design, the fundamental problem is to construct a large set of $n$-variable quadratic bent or near-bent functions in a particular form such that the difference of any two is bent for even $n$ or near-bent for odd $n$ to achieve optimally low coherence. In this work, we propose a theoretical construction of NOMA codebooks by applying a recursive approach to those particular quadratic bent functions in smaller dimensions. The proposed construction yields desired NOMA codebooks that contain $6\cdot N$ Golay sequences of length $N=2^{4m}$ for any positive integer $m$ and have the lowest possible coherence $1/\sqrt{N}$. |
| title | On the Codebook Design for NOMA Schemes from Bent Functions |
| topic | Combinatorics Discrete Mathematics Information Theory |
| url | https://arxiv.org/abs/2512.16560 |