面向短包通信的分组稀疏矢量码

张雪婉; 张迪; 古博

doi:10.11999/JEIT251143

面向短包通信的分组稀疏矢量码

doi: 10.11999/JEIT251143 cstr: 32379.14.JEIT251143

张雪婉¹,
张迪^2, ,,
古博³

1.
南阳师范学院物理与电子工程学院南阳 473061
2.
中山大学智能工程学院深圳 518107 & 南方海洋科学与工程广东省实验室(珠海) 珠海 519000
3.
中山大学人工智能学院 & 南方海洋科学与工程广东省实验室(珠海) 珠海 519000

基金项目: 国家自然科学基金青年科学基金(62501317)，河南省优秀青年科学基金(242300421169)，河南省自然科学基金青年项目(252300420981)

详细信息

作者简介:
张雪婉：男，讲师，硕士生导师，研究方向为多址接入技术、短包高可靠低时延通信

张迪：男，副教授，博士生导师，研究方向为智能网络通信、网络通信安全

古博：男，教授，博士生导师，研究方向为移动群智感知网络、无线网络通信

通讯作者:
张迪　zhangd263@mail.sysu.edu.cn

中图分类号: TN929.5
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- 被引次数: 0
出版历程
- 收稿日期: 2025-11-01
- 修回日期: 2026-01-03
- 录用日期: 2026-01-04
- 网络出版日期: 2026-01-12

Group-based Sparse Vector Codes for Short-Packet Communications

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 Intelligent Systems Engineering, 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)

摘要

摘要: 稀疏矢量码(SVC)技术因其实施简单、传输可靠等优点在短包高可靠低时延通信方面获得了广泛关注。构造短稀疏矢量并使用小尺寸随机扩频码本是确保其系统性能的关键。为此，该文提出一种基于分组的SVC (GSVC)方案。该方案摒弃了经典的索引调制全局稀疏变换方式，通过对索引比特分组划分，以分组稀疏变换的形式在同一预定稀疏矢量上逐次选取出各分组的非零位置，从而实现位置资源对所有分组的共享，达到压缩稀疏矢量的目的。因此，所提GSVC方案具有高的位置资源利用率，能够构造出比常规全局选取方式要短的稀疏矢量来传输既定信息比特。与现有多种SVC改进方案的仿真对比结果表明，所提方案在低阶调制模式下具有更优的误块率性能。
- 短包通信 /
- 高可靠低时延 /
- 随机扩频 /
- 稀疏矢量构造 /
- 6G
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

HTML全文

图 1 传统稀疏矢量构造方式

下载: 全尺寸图片幻灯片

图 2 所提GSVC中分选稀疏矢量构造方案(N=6, $ {N}_{\rm e}=2 $, V=3)

下载: 全尺寸图片幻灯片

图 3 MMP与OAMP算法的BLER对比

下载: 全尺寸图片幻灯片

图 4 调制阶数M不同时，BLER性能对比(K=64, $ {N}_{\rm e}=2 $, V=2, $ {b}_{s}=5 $)

下载: 全尺寸图片幻灯片

图 5 给定不同$ {b}_{s} $时，BLER性能对比(K=64, $ {N}_{\rm e}=2 $, V=2, M=2)

下载: 全尺寸图片幻灯片

图 6 子载波个数K不同时，BLER性能对比($ {N}_{\rm e}=2 $, V=2, $ {b}_{s}=4 $)

下载: 全尺寸图片幻灯片

图 7 分选组数V不同时，BLER性能对比(K=64, $ {N}_{\rm e}=2 $, $ {b}_{s}=5 $, M=2)

下载: 全尺寸图片幻灯片

图 8 所提GSVC与Polar码的BLER对比

下载: 全尺寸图片幻灯片

1 GSVC的译码过程

(1) 初始化$ {\boldsymbol{r}}_{{\mathrm{end}}}=+\mathrm{\infty } $, $ {\boldsymbol{r}}_{0}=\boldsymbol{y} $, $ \varepsilon $, D, $ {l}_{\max } $, $ l=1 $;
(2) 利用MMP获得合成矢量的位置估计$ \hat{\varOmega } $和元素估计$ \hat{s} $：
(3) while ($ \varepsilon < {\boldsymbol{r}}_{{\mathrm{end}}} $&&$ l\leq {l}_{\max } $)
(4) 　令t = l - 1;
(5) 　for n = 1 : N
(6) 　　$ {d}_{n}=\mathrm{mod}\left(t\right)+1 $; $ t=\left\lfloor t/D\right\rfloor $; // 式(19)
(7) 　end for
(8) 　for n = 1 : N
(9) 　　根据式(20)、式(21)、式(22)计算$ \tilde{\pi }_{{d}_{n}}^{l} $, $ \hat{s}_{n}^{l} $, $ \boldsymbol{r}_{n}^{l} $;
(10) end for
(11) if ($ {\boldsymbol{r}}_{{\mathrm{end}}} > \left\|\left\|\boldsymbol{r}_{N}^{l}\right\|\right\| $)
(12) $ {\boldsymbol{r}}_{{\mathrm{end}}}=\left\|\left\|\boldsymbol{r}_{N}^{l}\right\|\right\| $; $ \hat{\varOmega }=\left\{\tilde{\pi }_{{d}_{n}}^{l}\right\}_{n=1}^{N} $; $ \hat{s}=\left\{\hat{s}_{n}^{l}\right\}_{n=1}^{N} $;
(13) end if
(14) $ l=l+1 $;
(15) end while
(16) 利用$ \hat{s} $完成解层映射并输出比特流:
(17) 依据步骤1对$ \hat{s} $中N个元素实施分组;
(18) for t = 1 : T
(19) 　根据式(23)获取Val；
(20) end for
(21) 获取最小Val对应下的分组，依据步骤3输出比特流。

下载: 导出CSV

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