{ "id": "ep5z671drq", "slug": "sparse-code-multiple-access", "title": "Sparse code multiple access", "updated": "2026-10-15", "topic_path": [ { "id": "technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/topics/technology" }, { "id": "technology.communication", "label": "Communications and everyday technology", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.communication" }, { "id": "technology.communication.wireless-signal-processing-techniques", "label": "Wireless signal processing techniques", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.communication.wireless-signal-processing-techniques" }, { "id": "technology.communication.wireless-signal-processing-techniques.mimo-detection-and-equalization", "label": "MIMO detection and equalization", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.communication.wireless-signal-processing-techniques.mimo-detection-and-equalization" } ], "geo": [ { "id": "geo.asia.t2001.technology.communication", "label": "Asia (other) · 2001 to 2020: Communications and everyday technology", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.asia.t2001.technology.communication", "path": [ { "id": "geo.asia", "label": "Asia (other)", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.asia" }, { "id": "geo.asia.t2001", "label": "Asia (other) · 2001 to 2020", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.asia.t2001" }, { "id": "geo.asia.t2001.technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.asia.t2001.technology" }, { "id": "geo.asia.t2001.technology.communication", "label": "Communications and everyday technology", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.asia.t2001.technology.communication" } ] } ], "excerpt": "Sparse code multiple access (SCMA) is a code-domain non-orthogonal multiple access technique proposed at Huawei in 2013, letting several users share the same radio resources.", "snippet": "Sparse code multiple access (SCMA) is a code-domain non-orthogonal multiple access technique proposed at Huawei in 2013, letting several users share the same radio resources.", "node": "technology.communication.wireless-signal-processing-techniques.mimo-detection-and-equalization", "markdown": "# Sparse code multiple access\n\n**Sparse code multiple access** (SCMA) is a code-domain non-orthogonal multiple access technique for wireless networks in which each user's bits are mapped directly to a sparse multidimensional codeword drawn from a user-specific codebook, so that several users share the same time-frequency resources and are separated at the receiver by multi-user detection. It was proposed in 2013 by H. Nikopour and H. Baligh at Huawei at the IEEE PIMRC conference in London as a scheme that keeps the low-complexity reception of low-density signature (LDS) spreading while improving its performance[1](https://ieeexplore.ieee.org/document/6666156) • [2](https://www.comsoc.org/publications/best-readings/non-orthogonal-multiple-access). SCMA was developed as a candidate for 5G non-orthogonal multiple access (NOMA), studied in 3GPP Release 14 and 15, and ultimately not adopted in the 5G New Radio standard[3](https://doi.org/10.1109/comst.2019.2910569) • [4](https://doi.org/10.1109/ojcoms.2021.3081166).\n\n| Key fact | Detail |\n|---|---|\n| Origin | Proposed by H. Nikopour and H. Baligh, IEEE PIMRC 2013, London, pp. 332–336[1](https://ieeexplore.ieee.org/document/6666156) • [2](https://www.comsoc.org/publications/best-readings/non-orthogonal-multiple-access) |\n| Encoding | Bit-to-QAM mapping and spreading are merged; bits map directly to a sparse multidimensional codeword from a per-layer codebook[1](https://ieeexplore.ieee.org/document/6666156) |\n| Canonical loading | 6 layers over 4 resources (150% overload); studies also use K=6, J=15 (250%)[5](https://arxiv.org/html/2506.05111) • [6](https://users.aalto.fi/~oltirkko/pubs/Liu2016_WCL.pdf) |\n| Detection | Message passing algorithm (MPA) over a sparse factor graph; complexity O(I_T(|π|^d))[7](https://ar5iv.labs.arxiv.org/html/1702.01389) |\n| Link-level gain | Over 2 dB versus OFDMA and SC-FDMA at 1.5 bits/tone in the originators' simulations[8](https://arxiv.org/pdf/1408.3653) |\n| Standardization outcome | 3GPP Release 15 NOMA study item concluded without adopting NOMA; 5G NR kept orthogonal multiple access[4](https://doi.org/10.1109/ojcoms.2021.3081166) • [9](https://ieeexplore.ieee.org/document/8972353) |\n| Current status | Studied for 6G, non-terrestrial networks and satellite IoT; not deployed in 5G[10](https://ar5iv.labs.arxiv.org/html/2104.01402) • [4](https://doi.org/10.1109/ojcoms.2021.3081166) |\n\n## Technical principles: codebooks and sparse codewords\n\nIn LDS-CDMA, bits are first mapped to a QAM symbol and then spread by a sparse binary sequence across OFDM-type subcarriers. SCMA merges these two steps: several incoming bits are mapped directly to a sparse complex codeword drawn from the user's codebook[1](https://ieeexplore.ieee.org/document/6666156) • [11](https://ar5iv.labs.arxiv.org/html/2105.06860). Formally, an SCMA encoder maps Q = log2(J) bits of a J-QAM constellation to a predefined U-dimensional complex sparse codeword; the codebook is a U×J matrix whose columns are the codewords, and each codebook represents one access layer assigned to a user[12](https://link.springer.com/article/10.1186/s13638-020-01832-z).\n\nThe performance advantage over LDS comes mainly from *constellation shaping gain*: instead of repeating a QAM symbol on the nonzero positions of a sparse pattern, each codeword places different complex values on its nonzero dimensions, so the multidimensional constellation can be shaped for a better [Euclidean distance](https://www.edgepedia.org/euclidean-distance) profile[8](https://arxiv.org/pdf/1408.3653). A systematic design applies lattice rotation to build a multidimensional mother constellation, then layer-specific operators generate each layer's codebook while preserving that distance profile[8](https://arxiv.org/pdf/1408.3653). [Codebook design](https://www.edgepedia.org/codebook-design) in general is an optimization problem; the original proposal gave a systematic sub-optimal approach[1](https://ieeexplore.ieee.org/document/6666156).\n\nSCMA research divides into two major lines, codebook design and multi-user detection, with codebook design targeting spectral efficiency, bit error rate, and PAPR for specific channels[11](https://ar5iv.labs.arxiv.org/html/2105.06860). After the first codebook design in 2014, numerous designs followed, including M-PAM-based codebooks, constellation rotation and interleaving, Star-QAM codebooks, deep-learning-based codebooks, and golden angle modulation (GAM) constellations, which show strong error-rate performance in [Rayleigh fading](https://www.edgepedia.org/rayleigh-fading)[11](https://ar5iv.labs.arxiv.org/html/2105.06860).\n\n## Receiver design and multi-user detection\n\nBecause each codeword is sparse, only a few layers collide on any given time-frequency resource. This sparsity reduces inter-layer collision and enables a near-optimal message passing algorithm (MPA) detector of acceptable complexity, which exploits the codebook sparsity to mitigate inter-user interference[12](https://link.springer.com/article/10.1186/s13638-020-01832-z) • [10](https://ar5iv.labs.arxiv.org/html/2104.01402).\n\nThe complexity order of MPA detection is O(I_T(|π|^d)), where π is the codebook set size, I_T the number of iterations, and d the maximum number of superimposed signals per resource[7](https://ar5iv.labs.arxiv.org/html/1702.01389). Equivalently, sum-product detection scales as O(D^θ), where D is the constellation alphabet size at a resource node and θ the number of connections at that node[12](https://link.springer.com/article/10.1186/s13638-020-01832-z). Complexity therefore grows steeply with codebook size and with the number of colliding layers, which is the practical constraint on overloading.\n\nSeveral low-complexity variants exist. In the original MPA all users update messages until the maximum number of iterations; a threshold-based MPA applies a belief threshold to stop early, achieving lower complexity with only slight performance degradation when the threshold is set appropriately[13](https://doi.org/10.1109/lcomm.2016.2609382). Log-MPA replaces multiplications with additions: at 150% overload it needs 29% more additions but 40% fewer multiplications than MPA, and at 250% overload 36% more additions while saving 57% of the multiplications[6](https://users.aalto.fi/~oltirkko/pubs/Liu2016_WCL.pdf). Fixed-point Log-MPA loses less than 1 dB relative to its floating-point version, whereas fixed-point MPA degrades significantly in the reported study[6](https://users.aalto.fi/~oltirkko/pubs/Liu2016_WCL.pdf). A 2025 paper proposes quasi-uniform quantization of MPA messages, improving bit error rate over conventional uniform quantization in AWGN and Rayleigh frequency-selective channels, plus a Sub-log MPA that accelerates Max-log MPA convergence[14](https://www.mdpi.com/1424-8220/25/10/3098).\n\n## Performance characteristics\n\n**Overloading.** SCMA retains the multi-access benefits of LDS, including overloading, moderate complexity, and interference whitening, while avoiding LDS's poor link performance[8](https://arxiv.org/pdf/1408.3653). The canonical configuration places J = 6 layers over K = 4 resources, an overloading factor of J/K = 150% relative to orthogonal one-user-per-resource transmission; studies also use K = 6, J = 15, i.e. 250%[5](https://arxiv.org/html/2506.05111) • [6](https://users.aalto.fi/~oltirkko/pubs/Liu2016_WCL.pdf). SCMA achieves high overloading while maintaining high reliability, with iterative MPA detection of multiple data streams at symbol level[15](https://onlinelibrary.wiley.com/doi/10.1155/2018/6187580). The MPA receiver can cause large computational burden and processing delay when the number of multiplexed users is large[15](https://onlinelibrary.wiley.com/doi/10.1155/2018/6187580). SCMA's gain over LDS and OFDM grows as SNR increases[8](https://arxiv.org/pdf/1408.3653).\n\nIn massive machine-type communication (mMTC) random-access studies, SCMA outperformed the LTE random access procedure and power-domain NOMA in access success probability, average access delay, and throughput[4](https://doi.org/10.1109/ojcoms.2021.3081166).\n\n## By the numbers\n\n- Link-level simulations at spectral efficiency 1.5 bits/tone showed SCMA outperforming LDS, OFDMA, and SC-FDMA, with a gain of over 2 dB compared to OFDMA and SC-FDMA[8](https://arxiv.org/pdf/1408.3653).\n- An independent fixed-point study found that at BER 10⁻⁴ (K=4, N=2, J=6, M=4, 150% overload) SCMA loses about 2.5 dB versus baseline uncoded LTE, but achieves a 50% total symbol-rate gain[6](https://users.aalto.fi/~oltirkko/pubs/Liu2016_WCL.pdf).\n- MPA receiver complexity examples: with N=8, d=3, SCMA costs 65856 operations versus 360 for power-domain NOMA; with N=10, d=4, 5184000 versus 1920[7](https://ar5iv.labs.arxiv.org/html/1702.01389).\n- Huawei reported field validation tests with a threefold increase in upstream connections compared to OFDMA using SCMA, and over 50% downstream user throughput improvement using non-orthogonal code and power division multiplexing[16](https://www-file.huawei.com/-/media/CORPORATE/PDF/publications/communicate/80/15-up-in-the-air-with-5G.pdf).\n- A 2025 CNN-based receiver for non-terrestrial networks delivers 800 kbps aggregated throughput at −4 dB Eb/N0, where Log-MPA falls below 50 kbps; at code rate 0.188 it provides 170 kbps at −8 dB Eb/N0, a 1 dB gain over Log-MPA, and enables code rate 0.588 at −5 dB Eb/N0, an aggregated-throughput gain of 420 kbps[5](https://arxiv.org/html/2506.05111).\n\n## How it compares with other multiple access schemes\n\nSCMA is an enhanced variation of LDS in which users map bits to multidimensional constellations instead of repeating QAM symbols; LDS can be considered a special class of SCMA[3](https://doi.org/10.1109/comst.2019.2910569). Against power-domain NOMA, which separates users by transmit-power levels and uses successive interference cancellation (SIC), numerical analysis shows SCMA achieves a better sum-rate but at the cost of higher system complexity[3](https://doi.org/10.1109/comst.2019.2910569). Code-domain NOMA needs no channel-state knowledge at the transmitter, and its near-optimal MPA detection can outperform SIC, though MPA is more complex[3](https://doi.org/10.1109/comst.2019.2910569). Simulation comparisons likewise show SCMA-based systems achieving better performance than power-domain NOMA at the cost of more receiver complexity[7](https://ar5iv.labs.arxiv.org/html/1702.01389). Compared with pattern division multiple access (PDMA), SCMA performs better due to its multidimensional constellation, and among the relevant code-domain schemes it outperforms PDMA and LDS in bit error rate[3](https://doi.org/10.1109/comst.2019.2910569) • [12](https://link.springer.com/article/10.1186/s13638-020-01832-z).\n\nThe recurring tension is gains versus receiver cost. A key challenge for SCMA is designing a low-complexity receiver, since MPA complexity is higher than SIC[7](https://ar5iv.labs.arxiv.org/html/1702.01389), and the MPA receiver can cause large computational burden and processing delay when the number of multiplexed users is large[15](https://onlinelibrary.wiley.com/doi/10.1155/2018/6187580).\n\n## Standardization history and fate in 5G NR\n\nSCMA was presented as a potential uplink NOMA scheme in 3GPP Release 14 for the system design of the new radio[3](https://doi.org/10.1109/comst.2019.2910569). The Release 15 study item on NOMA, which covered SCMA among other candidates, concluded in not continuing NOMA as a work item[9](https://ieeexplore.ieee.org/document/8972353). The recorded conclusions state that, across every scenario examined, NOMA failed to offer a distinct advantage over the mechanisms of Release 15 and Release 16: numerous link-level studies submitted by various companies frequently revealed no benefit, and system-level simulations likewise failed to demonstrate a definitive improvement in performance[4](https://doi.org/10.1109/ojcoms.2021.3081166). The Release 15 NR study document instead records that synchronous, scheduling-based orthogonal multiple access is at least supported for downlink transmissions targeting eMBB[17](https://www.etsi.org/deliver/etsi_tr/138900_138999/138912/15.00.00_60/tr_138912v150000p.pdf). NOMA techniques, including SCMA, are not deployed in 5G and are not mentioned explicitly in the planning of [3GPP Release 17](https://www.edgepedia.org/3gpp-release-17) and Release 18, though NOMA may be reconsidered in very high density beyond-5G scenarios[4](https://doi.org/10.1109/ojcoms.2021.3081166).\n\nThe vendor and standards records diverge on the promise: Huawei's corporate publication reported a threefold upstream connection gain in field validation tests and positioned SCMA as a key 5G air-interface technology[16](https://www-file.huawei.com/-/media/CORPORATE/PDF/publications/communicate/80/15-up-in-the-air-with-5G.pdf), while the 3GPP study-item conclusions found no clear gain in the studied scenarios and NOMA was not adopted[4](https://doi.org/10.1109/ojcoms.2021.3081166). Link-level gain figures also differ by baseline: the originators report over 2 dB gain versus OFDMA and SC-FDMA at 1.5 bits/tone[8](https://arxiv.org/pdf/1408.3653), while an independent study reports a 2.5 dB loss versus uncoded LTE at BER 10⁻⁴ alongside a 50% symbol-rate gain[6](https://users.aalto.fi/~oltirkko/pubs/Liu2016_WCL.pdf); the two measurements use different baselines and operating points and are not directly reconcilable.\n\n## Current research and outlook\n\nOptimal SCMA codebook design remains an open problem, and it is unknown how close current codebooks are to the optimal ones; most studies use small-scale settings such as 4×6 and 5×10, limiting scalability, and closed-form bit error rate expressions for actual codebooks remain open[10](https://ar5iv.labs.arxiv.org/html/2104.01402). Learned receivers are an active line: a 2025 preprint applies SCMA to a non-terrestrial-network mobile edge computing framework with a LEO satellite hosting the MEC server and ground devices performing uplink SCMA over shared 5G NR physical resource blocks, using a multi-task-learning CNN receiver[5](https://arxiv.org/html/2506.05111). For satellite IoT, a recent journal paper proposes SPI-Log-MPA, a state-position-information log message passing algorithm for satellite-borne SCMA receivers that reduces unreliable codewords, decodes stable users in advance, and applies a reward-and-penalty mechanism, achieving lower computational complexity while maintaining bit error rate performance; the paper identifies the dual constraints of spectrum resources and onboard satellite payload capability as key challenges for massive-user access in 6G satellite IoT[18](https://doaj.org/article/b378a8835c524221b3f173ab5d4ffd9a). SCMA also continues to be studied for 6G-era massive connectivity, including a massively distributed access system based on fiber-based visible light communication, ultra-dense networks, and NOMA[10](https://ar5iv.labs.arxiv.org/html/2104.01402).\n\n## References\n\n1. [H. Nikopour, H. Baligh, \"Sparse Code Multiple Access,\" IEEE PIMRC 2013](https://ieeexplore.ieee.org/document/6666156)\n2. [IEEE ComSoc Best Readings in Non-Orthogonal Multiple Access](https://www.comsoc.org/publications/best-readings/non-orthogonal-multiple-access)\n3. [Multidimensional Constellations for Uplink SCMA Systems—A Comparative Study, IEEE Communications Surveys & Tutorials](https://doi.org/10.1109/comst.2019.2910569)\n4. [Sparse Code Multiple Access: Potentials and Challenges, IEEE Open Journal of the Communications Society, 2021](https://doi.org/10.1109/ojcoms.2021.3081166)\n5. [An SCMA Receiver for 6G NTN based on Multi-Task Learning, arXiv 2025](https://arxiv.org/html/2506.05111)\n6. [On Fixed-point Implementation of Log-MPA for SCMA Detection, IEEE Wireless Communications Letters](https://users.aalto.fi/~oltirkko/pubs/Liu2016_WCL.pdf)\n7. [Comparison Study between NOMA and SCMA](https://ar5iv.labs.arxiv.org/html/1702.01389)\n8. [SCMA Codebook Design (Nikopour, Baligh et al., Huawei), arXiv](https://arxiv.org/pdf/1408.3653)\n9. [A Survey of NOMA: Current Status and Open Research Challenges, IEEE, 2020](https://ieeexplore.ieee.org/document/8972353)\n10. [Sparse Code Multiple Access for 6G Wireless Communication Networks: Recent Advances and Future Directions](https://ar5iv.labs.arxiv.org/html/2104.01402)\n11. [A Tutorial to Sparse Code Multiple Access](https://ar5iv.labs.arxiv.org/html/2105.06860)\n12. [Sparse code multiple access on the generalized frequency division multiplexing, EURASIP JWCN, 2020](https://link.springer.com/article/10.1186/s13638-020-01832-z)\n13. [Low Complexity Message Passing Algorithm for SCMA System, IEEE Communications Letters](https://doi.org/10.1109/lcomm.2016.2609382)\n14. [An Efficient Quantized Message Passing Receiver Design for SCMA Systems, Sensors, 2025](https://www.mdpi.com/1424-8220/25/10/3098)\n15. [Uplink Nonorthogonal Multiple Access Technologies Toward 5G: A Survey, Wiley, 2018](https://onlinelibrary.wiley.com/doi/10.1155/2018/6187580)\n16. [Up in the air with 5G, Huawei Communicate, issue 80](https://www-file.huawei.com/-/media/CORPORATE/PDF/publications/communicate/80/15-up-in-the-air-with-5G.pdf)\n17. [3GPP TR 38.912 V15.0.0, Study on New Radio access technology, ETSI](https://www.etsi.org/deliver/etsi_tr/138900_138999/138912/15.00.00_60/tr_138912v150000p.pdf)\n18. [A low-complexity SCMA multi-user detection algorithm based on state position information for satellite IoT, DOAJ](https://doaj.org/article/b378a8835c524221b3f173ab5d4ffd9a)\n\n---\n*Topic: Encyclopedia › Technology and the built world › Communications and everyday technology › Wireless signal processing techniques › MIMO detection and equalization*\n\n*Initially written Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/sparse-code-multiple-access", "markdown_url": "https://www.edgepedia.org/sparse-code-multiple-access.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Sparse code multiple access\", Edgepedia (EdgeChat), https://www.edgepedia.org/sparse-code-multiple-access. Edgepedia Community License 1.0.", "credit_md": "\"[Sparse code multiple access](https://www.edgepedia.org/sparse-code-multiple-access)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/sparse-code-multiple-access](https://www.edgepedia.org/sparse-code-multiple-access). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Sparse code multiple access\", Edgepedia (EdgeChat), https://www.edgepedia.org/sparse-code-multiple-access. Edgepedia Community License 1.0.", "speakable": "Sparse code multiple access is a code-domain non-orthogonal multiple access technique proposed at Huawei in 2013, letting several users share the same radio resources." }