Group-based Sparse Vector Codes for Short-Packet Communications

ZHANG Xuewan; ZHANG Di; GU Bo

doi:10.11999/JEIT251143

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ZHANG Xuewan, ZHANG Di, GU Bo. Group-based Sparse Vector Codes for Short-Packet Communications[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251143

Citation:

ZHANG Xuewan, ZHANG Di, GU Bo. Group-based Sparse Vector Codes for Short-Packet Communications[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251143

ZHANG Xuewan, ZHANG Di, GU Bo. Group-based Sparse Vector Codes for Short-Packet Communications[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251143

Citation:

ZHANG Xuewan, ZHANG Di, GU Bo. Group-based Sparse Vector Codes for Short-Packet Communications[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT251143

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Group-based Sparse Vector Codes for Short-Packet Communications

doi: 10.11999/JEIT251143 cstr: 32379.14.JEIT251143

ZHANG Xuewan¹,
ZHANG Di^{2
,
,},
GU Bo³

1.
School of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, China
2.
School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, China & Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, China
3.
School of Artificial Intelligence, Sun Yat-sen University, Sun Yat-sen University & Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, China

Funds: Youth Program of the National Natural Science Foundation of China (62501317), Outstanding Youth Science Foundation Project of Henan Province (242300421169), Youth Program of Natural Science Foundation of Henan Province (252300420981)

Received Date: 2025-11-01
Accepted Date: 2026-01-04
Rev Recd Date: 2026-01-03

Available Online: 2026-01-12

Abstract

Abstract

Objective Sparse Vector Codes (SVC) aim to construct sparse underdetermined linear systems and have attracted wide interest for short-packet Ultra-Reliable and Low-Latency Communications (URLLC) because of their simple implementation and reliable transmission. To guarantee system performance, short sparse vectors that can be transmitted using small-size random spreading codebooks are required. However, most existing sparse transformation schemes based on index modulation adopt a global selection strategy, where nonzero positions, to which transmission bits are mapped, are selected directly from the entire set of available positional resources in the sparse vector. Under high coding efficiency requirements, this strategy often leads to excessively long sparse vectors and a sharp degradation in transmission performance. To address this issue, a Group-based Sparse Vector Code (GSVC) scheme is proposed. Unlike the conventional global sparse mapping approach, GSVC divides index bits into groups and sequentially determines the nonzero positions for each group within a predefined sparse vector. This design enables positional resource sharing among all groups and generates compressed sparse vectors with higher positional resource utilization, thereby achieving Better Block Error Rate (BLER) performance than conventional SVC schemes. Methods The proposed GSVC scheme partitions the total number of nonzero positions N into V groups. Within a single predefined sparse vector, each group sequentially selects its N/V nonzero positions through index modulation. To prevent position selection conflicts among groups, a resource supplementation and elimination mechanism is applied. This mechanism ensures that the selected positions are mutually exclusive and that each group maintains the same number of available positional resources throughout the selection process. Given the sparsity of the constructed vector, a low-complexity sparse recovery algorithm is employed at the receiver. Accordingly, a GSVC decoder based on the Multipath Matching Pursuit (MMP) algorithm is designed. To enable accurate identification of the group affiliation associated with each nonzero position, GSVC adopts a multi-constellation mapping strategy for the nonzero elements. The receiver performs constellation matching by exploiting the unique characteristics of each constellation, thereby determining group affiliation and ensuring a high probability of successful decoding. Results and Discussions By enabling different groups to share positional resources through group-based nonzero position selection, GSVC effectively compresses the sparse vector and improves transmission reliability. Simulation results show that the GSVC decoder based on MMP significantly outperforms the decoder based on the Orthogonal Approximate Message Passing (OAMP) algorithm (Fig. 3). At lower modulation orders, GSVC achieves better BLER performance than existing schemes, including enhanced SVC, multi-rotation constellation-based SVC, and index-redefined SVC (Fig. 4 and Fig. 5). When the number of Orthogonal Frequency Division Multiplexing (OFDM) subcarriers is large, GSVC provides the best BLER performance among all compared schemes (Fig. 6). In addition, for a fixed number of nonzero entries per group, the BLER performance advantage of GSVC increases as the number of groups increases. A performance gain exceeding 1 dB over the second-best SVC scheme is observed at a BLER of 10-5 (Fig. 7). Compared with polar codes (Fig. 8), GSVC achieves better BLER performance without Cyclic Redundancy Check (CRC) assistance and even outperforms CRC-aided polar codes. Conclusions This paper proposes a GSVC scheme to address the excessive sparse vector length encountered in conventional index modulation-based SVC systems. The central feature of GSVC is a grouped nonzero position selection mechanism that enables multiple groups to share positional resources within a predefined sparse vector, thereby reducing the overall vector length. A dedicated multi-constellation mapping design, together with well-defined resource allocation rules, ensures conflict-free and efficient utilization of positional resources. Simulation results demonstrate that (1) the GSVC decoder implemented using MMP significantly outperforms decoders based on the OAMP algorithm; (2) GSVC achieves superior BLER performance compared with enhanced SVC, multi-rotation constellation-based SVC, and index-redefined SVC schemes, particularly at lower modulation orders and with a large number of OFDM subcarriers; and (3) GSVC surpasses the BLER performance of CRC-aided polar codes without requiring CRC. Future work will focus on optimizing the grouping strategy and examining the transmission performance of SVC under imperfect channel estimation to improve robustness in practical communication systems.
- Next-generation ultra-reliable and low-latency communications,
- Short-packet communications,
- Sparse vector construction,
- Random spreading,
- 6G

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References(24)

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