Orthogonal Semantic Sequency Multiplexing

• Orthogonal Semantic Sequency Division Multiplexing is a semantic-aware waveform design that maps semantic symbols directly into Walsh-domain coefficients to preserve crucial information.
• It constructs time-domain waveforms using the inverse Walsh transform and enforces spectral mask constraints to enable controlled degradation and enhanced semantic fidelity.
• Performance tradeoffs show improved noise robustness and effective semantic spectral efficiency in AWGN settings, while challenges in multipath fading and explicit semantic resource allocation remain.

Searching arXiv for papers on OSSDM and closely related sequency/semantic multiplexing work. {"query": "\"Orthogonal Semantic Sequency Division Multiplexing\" OR OSSDM semantic waveform Walsh sequency", "max_results": 10, "sort_by": "submittedDate", "sort_order": "descending"} Search results indicate the directly relevant recent source is "Semantic Waveforms for AI-Native 6G Networks" (Hello et al., 10 Feb 2026), with adjacent foundations in OTSM (Thaj et al., 2021), MIMO-OSDM (Han et al., 2019), robust orthogonal waveform design via Weyl–Heisenberg sets (Cvetkovic et al., 2013), and multi-user semantic orthogonalization by shuffle-based mappings (Zhang et al., 28 Jul 2025). Orthogonal Semantic Sequency Division Multiplexing (OSSDM) is a semantic-aware waveform design for AI-native 6G systems in which each semantic symbol is mapped to a vector of coefficients over an orthogonal Walsh basis ordered by sequency, and the corresponding time-domain waveform is synthesized by an inverse Walsh transform (IWT) (Hello et al., 10 Feb 2026). In this formulation, the waveform is not treated as a neutral carrier of already-produced bits or modulation symbols; rather, semantic representations are mapped into Walsh-domain coefficients so that the physical signal structure itself participates in preserving information relevant to downstream semantic reconstruction. The stated purpose of OSSDM is to enable controlled degradation of the wireless transmitted signal so as to preserve semantically significant content while minimizing resource consumption, while improving semantic robustness and effective semantic spectral efficiency by encoding meaningful information directly at the waveform level (Hello et al., 10 Feb 2026).

1. Definition, scope, and nomenclature

OSSDM was introduced in the context of semantic waveform co-design for AI-native 6G networks (Hello et al., 10 Feb 2026). Its defining characteristic is the replacement of conventional Fourier-subcarrier symbol placement by semantic-symbol-to-Walsh-coefficient mapping. The basis is Walsh rather than Fourier, the transform is WT/IWT rather than FFT/IFFT, and the rows are ordered by sequency rather than frequency. The paper frames this as a “parametrizable, orthogonal-base waveform design” that supports “direct encoding of semantics at the waveform level” (Hello et al., 10 Feb 2026).

The term requires careful separation from several adjacent acronyms. In particular, OSDM in the multicarrier literature denotes orthogonal signal-division multiplexing rather than orthogonal semantic sequency division multiplexing, and OTSM denotes orthogonal time sequency multiplexing, a sequency-domain physical-layer modulation without semantic encoding (Han et al., 2019, Thaj et al., 2021). OSSDM is therefore not merely a renaming of earlier sequency-domain schemes; it is a semantic communication architecture in which the mapping from source semantics to waveform coefficients is learned and integrated into the end-to-end objective (Hello et al., 10 Feb 2026).

Scheme	Basis / transform	Stated role
OFDM	Fourier basis, IFFT	Conventional physical-layer baseline
OSDM	${\bf F}_N^H \otimes {\bf I}_M$	Orthogonal signal-division multiplexing between OFDM and SCBT
OTSM	Walsh-Hadamard transform	Delay-sequency physical-layer modulation
OSSDM	Walsh transform / inverse Walsh transform	Semantic-aware waveform design

A common misconception is to interpret OSSDM as simply “OFDM with Walsh functions.” The defining novelty is not the substitution of one orthogonal transform for another in isolation, but the joint semantic/physical design in which semantic symbols are mapped directly into Walsh-domain coefficients under task-level objectives and spectral-mask constraints (Hello et al., 10 Feb 2026).

2. Mathematical construction in the Walsh–sequency domain

The mathematical construction in the OSSDM paper is distributed across the system model and codebook design rather than presented as a single boxed definition (Hello et al., 10 Feb 2026). Let

$\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$

where $N$ is determined by the Walsh order $n$. The Walsh transform is

$\mathbf{a} = \mathbf{W}_N \mathbf{x},$

with $\mathbf{W}_N$ obtained from the Hadamard matrix by reordering rows according to increasing sequency, that is, increasing number of zero crossings (Hello et al., 10 Feb 2026). The waveform generator reconstructs the time-domain signal through the intended IWT expression

$\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$

with normalization by $\sqrt{2^n}$ used to preserve energy between Walsh and time domains (Hello et al., 10 Feb 2026).

In OSSDM, the semantic symbol is mapped into sequency-domain coefficients rather than Fourier-frequency coefficients. The paper repeatedly calls the Walsh basis orthogonal and notes that $\mathbf{W}_N$ is binary-valued with entries in $\{-1,+1\}$ (Hello et al., 10 Feb 2026). A faithful restatement of the implied orthogonality is that

$\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$0

or, under normalization,

$\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$1

The paper does not typeset these relations explicitly, but they are consistent with its energy-preservation discussion (Hello et al., 10 Feb 2026).

The waveform construction is constrained by a Walsh codebook. Each codeword

$\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$2

represents a waveform composed of $\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$3 Walsh blocks of length $\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$4, with

$\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$5

For block $\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$6, the Walsh coefficients of a localized fragment $\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$7 are

$\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$8

The resulting codebook is

$\mathbf{x} \in \mathbb{R}^N, \qquad N = 2^n,$9

The codebook is generated from sinewaves spanning a frequency range that respects the emission mask, with a Gaussian perturbation added to block powers with mean

$N$0

and small variance $N$1 (Hello et al., 10 Feb 2026).

The Walsh order $N$2 is a principal design parameter. Higher $N$3 yields higher-dimensional coefficient vectors and more expressive waveform representations, and in the reported experiments better robustness in AWGN, but lower semantic symbol density and therefore smaller E-SSE gain at high order (Hello et al., 10 Feb 2026). The semantic symbol duration is defined as

$N$4

where $N$5 is the waveform generator refresh rate (Hello et al., 10 Feb 2026).

3. End-to-end semantic architecture and optimization

The OSSDM system model extends a prior semantic communication architecture for knowledge graph transmission, with the task of reconstructing knowledge graph triplets at the receiver (Hello et al., 10 Feb 2026). On the transmitter side, the semantic encoder processes a knowledge graph using an LLM encoder to extract feature vectors from concept nodes and relation edges, a GNN to produce compact node-level embeddings, and an FFN that maps each node embedding to a sequence of semantic complex symbols, with trainable parameters $N$6 (Hello et al., 10 Feb 2026).

These semantic symbols are then passed to a semantic-symbol-to-Walsh-coefficients mapper, implemented as an FFN with parameters $N$7, which produces Walsh coefficient vectors close to entries in a Walsh codebook designed to satisfy spectral emission mask constraints (Hello et al., 10 Feb 2026). The waveform generator applies the inverse Walsh transform to produce the time-domain signal. At the receiver, the reverse chain applies the Walsh transform, uses an FFN with parameters $N$8 to reconstruct the semantic symbol from noisy Walsh coefficients, and then uses an FFN plus node and relation decoders, with parameters $N$9, to reconstruct the knowledge graph (Hello et al., 10 Feb 2026).

The paper considers AWGN and Rayleigh fading, specifically 3GPP TDL-B in the numerical section (Hello et al., 10 Feb 2026). The source/task model uses knowledge graphs from the WebNLG dataset. The end-to-end loss is

$n$0

with

$n$1

The first two terms are concept and relation cross-entropy losses, the third is mutual information between transmitted and noisy semantic symbols, and the fourth enforces proximity to the spectral-mask-compliant codebook (Hello et al., 10 Feb 2026).

The paper repeatedly emphasizes semantic significance and controlled degradation, but its implementation of semantic importance is implicit rather than explicit. Semantic priority is embedded through representation learning in the semantic encoder/decoder and end-to-end training; the paper does not provide an explicit semantic-importance coefficient, a formal power-allocation rule based on semantic saliency, or a pruning formula (Hello et al., 10 Feb 2026). This is important for interpretation: OSSDM formalizes semantic waveform learning, but not a closed-form semantic weighting law.

4. Performance metrics, empirical behavior, and tradeoffs

The principal semantic fidelity metric is F1 score on reconstructed knowledge graph triplets, with precision and recall defined at the triplet level (Hello et al., 10 Feb 2026). The paper also defines effective semantic spectral efficiency (E-SSE) as

$n$2

where $n$3 is the number of semantic symbols successfully interpreted at the receiver, $n$4 is channel bandwidth, and $n$5 is communication duration. The semantic symbol rate is

$n$6

Spectrum-mask conformity is also reported relative to ETSI mask requirements (Hello et al., 10 Feb 2026).

The numerical study uses the WebNLG dataset, 16-dimensional latent embeddings generated by the GNN, and four complex-valued semantic symbols. Training uses SNR $n$7 dB, mini-batch size $n$8 graphs, $n$9, and $\mathbf{a} = \mathbf{W}_N \mathbf{x},$0. For the Walsh/codebook evaluation, the reported parameters are $\mathbf{a} = \mathbf{W}_N \mathbf{x},$1, $\mathbf{a} = \mathbf{W}_N \mathbf{x},$2, $\mathbf{a} = \mathbf{W}_N \mathbf{x},$3, $\mathbf{a} = \mathbf{W}_N \mathbf{x},$4, and $\mathbf{a} = \mathbf{W}_N \mathbf{x},$5 codebook entries. OFDM baselines use 5G NR FR1 parameters with $\mathbf{a} = \mathbf{W}_N \mathbf{x},$6 kHz subcarrier spacing, $\mathbf{a} = \mathbf{W}_N \mathbf{x},$7 MHz bandwidth, $\mathbf{a} = \mathbf{W}_N \mathbf{x},$8 resource blocks, and $\mathbf{a} = \mathbf{W}_N \mathbf{x},$9 cyclic prefix duration. Transmit power per semantic symbol is $\mathbf{W}_N$0 watts for both OSSDM and S-OFDM (Hello et al., 10 Feb 2026).

In AWGN, the reported gains are substantial. OSSDM with $\mathbf{W}_N$1 reaches maximum F1 score at an SNR $\mathbf{W}_N$2 dB lower than S-OFDM; $\mathbf{W}_N$3 shows a similar gain; $\mathbf{W}_N$4 gains $\mathbf{W}_N$5 dB; $\mathbf{W}_N$6 gains $\mathbf{W}_N$7 dB; and $\mathbf{W}_N$8 reaches maximum F1 at the same SNR as S-OFDM. Relative to traditional non-semantic OFDM, OSSDM with $\mathbf{W}_N$9 requires up to $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$0 dB less SNR (Hello et al., 10 Feb 2026).

Under Rayleigh fading with 3GPP TDL-B, the picture is more mixed. S-OFDM significantly outperforms OSSDM with $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$1 when MMSE equalization is applied, and S-OFDM achieves $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$2 at $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$3 dB. OSSDM with $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$4 can outperform S-OFDM, particularly at low SNR. The explanation given is that OFDM exploits frequency diversity under multipath, whereas lower-order OSSDM lacks that frequency diversity and high-order OSSDM compensates only partly through coefficient spreading and redundancy (Hello et al., 10 Feb 2026).

E-SSE exhibits the opposite trend from AWGN robustness. The reported E-SSE gain decreases with increasing OSSDM order. At order $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$5, OSSDM yields more than $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$6 gain over OFDM with $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$7 kHz, while at order $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$8 the gain falls below $\mathbf{x} = \mathbf{a}_{\text{norm}} \mathbf{W}_N^T,$9 across the OFDM variants considered (Hello et al., 10 Feb 2026). This makes the robustness–density tradeoff central: low order favors semantic symbol density and E-SSE, whereas high order favors representational diversity and noise robustness.

The paper also claims potential hardware advantages because the Walsh basis is binary-valued and the transform can be implemented as simple matrix operations rather than FFT/IFFT blocks, and it discusses potential ADC/DAC efficiency benefits and Walsh-based arbitrary waveform generation. However, it does not provide operation-count comparisons or a full implementation-complexity analysis (Hello et al., 10 Feb 2026).

5. Relation to adjacent modulation and waveform research

OSSDM sits within a broader lineage of orthogonal waveform design, sequency-domain multiplexing, and structured receiver design, but it differs from each of these lines in scope and objective. In OSDM, the transmitted block is

$\sqrt{2^n}$0

so modulation is performed by $\sqrt{2^n}$1 parallel length-$\sqrt{2^n}$2 IDFTs across partitioned vectors rather than by one full-length IDFT, yielding PAPR reduction and enabling low-complexity MIMO equalization with transformed-domain linear complexity for both TI and TV channels (Han et al., 2019). That literature is directly relevant to OSSDM on the receiver-architecture side, but it is not semantic and does not use Walsh/sequency ordering as a semantic waveform representation.

OTSM is closer in transform choice. It places symbols in the delay-sequency domain, applies a normalized WHT row-wise,

$\sqrt{2^n}$3

and performs column-wise serialization, with modulation and demodulation that do not require complex domain multiplications (Thaj et al., 2021). OTSM demonstrates that sequency-domain orthogonal multiplexing can yield OTFS-like performance at lower complexity owing to WHT. This suggests a physical-layer precedent for sequency-based orthogonality, but OTSM remains a single-carrier modulation for doubly selective channels rather than a semantic waveform co-design framework (Thaj et al., 2021).

A more abstract orthogonality foundation appears in the Weyl–Heisenberg literature, where orthogonal waveform families are constructed over a time–frequency lattice and parameterized via paraunitary polyphase matrices (Cvetkovic et al., 2013). That work is not sequency-domain and does not address semantics, but it establishes a rigorous design philosophy: parameterize exact orthogonality through structured matrix factorizations and then optimize localization and robustness within that exact-reconstruction family. A plausible implication is that OSSDM can be interpreted as a semantic analogue of this principle, with sequency or semantic coordinates replacing time–frequency coordinates (Cvetkovic et al., 2013).

Multi-user semantic orthogonalization has also been investigated through shuffle-based mappings rather than deterministic sequency bases. In that setting, user-specific permutations of JSCC latent features are designed so that, after the wrong inverse mapping, cross-user interference becomes approximately Gaussian-like and can be removed by a diffusion model (Zhang et al., 28 Jul 2025). This is not OSSDM, and its orthogonality is statistical rather than algebraic, but it shows that the semantic-symbol-to-channel-symbol mapping layer is itself a first-class multiplexing mechanism. Relative to that work, OSSDM is more explicitly transform-based and waveform-centric (Zhang et al., 28 Jul 2025).

6. Limitations, misconceptions, and open problems

Several limitations are explicit or strongly implied in the OSSDM paper. First, lower-order OSSDM performs weakly in multipath fading relative to OFDM because it lacks OFDM-style frequency diversity; only high-order OSSDM partially compensates through coefficient spreading and redundancy (Hello et al., 10 Feb 2026). Second, the paper motivates semantic significance and controlled degradation extensively but does not provide an explicit semantic-importance allocation rule, a formal semantic weighting variable, or a closed-form resource-allocation law (Hello et al., 10 Feb 2026).

Third, the optimization framework is end-to-end neural training rather than an explicit constrained optimization over power, basis sparsity, RF-chain variables, or semantic pruning. There is no KKT analysis, no alternating optimization derivation, and no formal theorem/proposition/proof structure (Hello et al., 10 Feb 2026). Fourth, the evaluation scope is narrow: knowledge graph transmission under a specific semantic architecture, with no MIMO, RIS, ISAC, sensing coexistence, or hardware demonstration (Hello et al., 10 Feb 2026).

These points clarify two common misunderstandings. OSSDM is not, on the available evidence, a complete replacement for OFDM in general fading environments; its advantages are strongest in semantic fidelity and E-SSE under the studied settings, especially AWGN and low-SNR high-order cases, not uniformly across all channels (Hello et al., 10 Feb 2026). Nor does “orthogonal semantic sequency” mean that semantic importance has been explicitly decomposed into orthogonal resource layers. In the present formulation, orthogonality belongs to the Walsh basis, while semantic saliency is learned implicitly through the end-to-end model (Hello et al., 10 Feb 2026).

The open directions stated or implied by the literature are correspondingly concrete. The OSSDM paper points toward semantic waveform co-design, hardware-aware semantic communications, AI-native PHY, extensions to MIMO, RIS, and ISAC, better fading robustness, and explicit semantic resource allocation (Hello et al., 10 Feb 2026). Related sequency-domain work suggests that low-complexity channel estimation, structured equalization, and transform-domain receiver design remain central if OSSDM is to evolve beyond proof-of-concept semantic waveform synthesis (Thaj et al., 2021, Han et al., 2019). A plausible implication is that the next phase of OSSDM research will require integrating its semantic waveform layer with more explicit channel-robust receiver architectures and more formal notions of semantic orthogonality.