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Energy Efficient Semantic Communication over Wireless Networks with Rate Splitting

Zhaohui Yang, Mingzhe Chen, Zhaoyang Zhang, Chongwen Huang

arXiv:2301.01987v1cs.ITeess.SP

TL;DR

The paper addresses energy-efficient semantic communication with rate splitting under limited wireless and computation resources. It models semantic extraction, common/private transmission, and computation jointly, then solves the resulting problem with an alternating algorithm whose numerical evaluation shows effective energy allocation and favorable energy behavior for RSMA.

  • Problem

    The paper studies how to jointly allocate wireless resources and extract semantic information for energy-efficient semantic communication under limited resources and computation, latency, and transmit-power constraints.

  • Method

    The BS extracts semantic information from large-scale data, transmits it using RSMA common and private messages, and solves the joint nonconvex problem with alternating optimization and successive convex approximation.

  • Results

    Numerical results show that the proposed RSMA achieves lower total energy than FDMA, NOMA, and, especially at high transmit power, SDMA.

  • Takeaways & Limitations

    The proposed framework provides an energy-efficient joint communication-computation design in which RSMA energy grows more slowly with user data size than NOMA and FDMA.

Abstract

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In this paper, the problem of wireless resource allocation and semantic information extraction for energy efficient semantic communications over wireless networks with rate splitting is investigated. In the considered model, a base station (BS) first extracts semantic information from its large-scale data, and then transmits the small-sized semantic information to each user which recovers the original data based on its local common knowledge. At the BS side, the probability graph is used to extract multi-level semantic information. In the downlink transmission, a rate splitting scheme is adopted, while the private small-sized semantic information is transmitted through private message and the common knowledge is transmitted through common message. Due to limited wireless resource, both computation energy and transmission energy are considered. This joint computation and communication problem is formulated as an optimization problem aiming to minimize the total communication and computation energy consumption of the network under computation, latency, and transmit power constraints. To solve this problem, an alternating algorithm is proposed where the closed-form solutions for semantic information extraction ratio and computation frequency are obtained at each step. Numerical results verify the effectiveness of the proposed algorithm.

I. INTRODUCTION

The paper combines semantic communication with rate splitting to reduce transmitted information while jointly optimizing wireless and computation resources for energy-efficient operation. It introduces this integration as a joint allocation and semantic-extraction problem and proposes an iterative solution.

  • Novelty: The paper identifies the integration of semantic communication and RSMA as a previously unconsidered combination.The introduction states that prior work had not considered their integration.
  • System motivation: The BS extracts small-sized semantic information from large-scale data, and users recover the original data using local common knowledge.This model shifts part of information recovery to semantic processing and shared knowledge at the receivers.
  • System motivation: Rate splitting transmits private semantic information through private messages and shared knowledge through a common message.The common and private message structure matches the shared and user-specific parts of semantic communication.
  • Optimization problem: The paper formulates joint communication and computation resource allocation as minimizing total network energy under latency and resource constraints.The stated formulation accounts for both computational and transmission energy.
  • Solution approach: An iterative algorithm derives closed-form solutions for the semantic information extraction ratio and computation frequency at each step.The algorithm addresses the proposed joint optimization problem through alternating updates.

A. Semantic Communication Model

The semantic communication model extracts multi-level semantic information from each user's large data using a directional probability graph, then selects a smaller subset for transmission and reconstructs the data at the user.

  • Graph-based extraction: A directional probability graph represents semantic entities as vertices organized across semantic levels.Higher semantic levels correspond to more complicated semantic structures.
  • Graph-based extraction: Training data is used to estimate links between semantic entities, and links above a threshold are fused into a multi-tier graph.The link probabilities are calculated through convolutional neural networks before semantic information fusion.
  • Transmission representation: The extraction pipeline first obtains G(Dk) and then selects a subset Sk for efficient data transmission.The subset is selected from the extracted semantic representation for user k.
  • Receiver reconstruction: Each user uses a shared common directional probability graph to recover the original data from the received semantic information.The recovered data is denoted by R(Sk).

B. RSMA Model

The RSMA model divides each user's message into common and private parts, encodes them into shared and user-specific streams, and assigns common-message rates to shared knowledge and individual users.

  • Message structure: Each user message is split into a common part and a private part, with all common parts combined into one common message.The common message is encoded using a shared codebook and must be decoded by all users.
  • Message structure: The private part for user k is encoded into a private stream sk intended only for that user.The BS uses a user-specific beamforming vector and power for each private stream.
  • Decoding order: All users decode the common message before decoding their private messages.The decoded common message is subtracted before private-message decoding.
  • Rate allocation: The common message carries shared knowledge and user-specific allocations, with ak denoting the rate allocated to user k.The common-message rate constraint includes both updated common knowledge and portions allocated to individual users.

C. Transmission and Computation Model

The model accounts for computation and communication time and energy as semantic information is extracted, transmitted, and recovered. These quantities are jointly optimized under latency, accuracy, capacity, rate, and power constraints.

  • Semantic extraction at the BS requires CPU cycles determined by the input data and extracted semantic information.
  • Transmission includes private semantic information, common knowledge, and updated directional probability-graph information.
  • User recovery time depends on the computation cycles required to reconstruct the original data and the user's computation capacity.
  • The completion time includes BS computation, downlink transmission, and user-side computation.
  • The optimization minimizes total communication and computation energy subject to completion time, accuracy, computation capacity, rate allocation, and power constraints.

III. ALGORITHM DESIGN

The algorithm design uses an alternating procedure to solve the joint resource-allocation problem through separate optimization subproblems. Its semantic extraction component is supported by the accuracy and computation-rate relationships shown in Fig. 5.

  • III. ALGORITHM DESIGN: The alternating algorithm iteratively optimizes semantic extraction, computation capacity, and joint power, rate, and beamforming variables.
  • III. ALGORITHM DESIGN: Fig. 5 relates semantic accuracy and computation functions to the extraction rate.

A. Semantic Information Extraction

Semantic information extraction is reformulated using an extraction rate to address discrete semantic selection and implicit accuracy and computation functions. The resulting subproblem is convex and admits an optimal solution obtained through KKT-based analysis.

  • A. Semantic Information Extraction: With other variables fixed, the extraction subproblem is convex, and its optimal solution is characterized through KKT conditions and bisection.
  • A. Semantic Information Extraction: The original extraction problem is difficult because semantic selection is discrete and the accuracy and computation functions are implicit.
  • A. Semantic Information Extraction: The extraction rate ρ_k replaces the discrete semantic-information variable and satisfies ρ_k ∈ (0,1].
  • A. Semantic Information Extraction: Accuracy increases with extraction rate, so the minimum-accuracy constraint can be represented by a minimum feasible extraction rate Γ_k.
  • A. Semantic Information Extraction: The extraction computation first increases with the rate and is lowest at the endpoint cases, while recovery computation decreases as more semantic information is extracted.

B. Optimal Computation Capacity

The computation-capacity subproblem is solved within the alternating framework after fixing semantic extraction and transmission variables. Iterative updates of capacities and multipliers yield the global optimum of the stated subproblem.

  • B. Optimal Computation Capacity: With semantic extraction, power control, rate allocation, and beamforming fixed, the computation-capacity problem is isolated.
  • B. Optimal Computation Capacity: The associated Lagrangian uses multipliers for the completion-time and computation-capacity constraints.
  • B. Optimal Computation Capacity: The BS computation capacity f_k is obtained by solving a cubic function, while the multipliers are updated iteratively by gradient methods.
  • B. Optimal Computation Capacity: Iteratively updating (f_k, g_k) and their multipliers yields the global optimal solution of the computation-capacity subproblem.

C. Joint Power Control, Rate Allocation, and Beamforming Design

The joint design transforms the nonconvex power-control, rate-allocation, and beamforming problem using auxiliary variables and successive convex approximations, yielding a convex subproblem.

  • Problem decomposition: Given semantic extraction and computation capacity, the joint design is solved after simplifying the original optimization problem.The subproblem is conditioned on fixed semantic information extraction and computation-capacity variables.
  • Problem reformulation: Auxiliary variables transform the objective and selected constraints before successive convex approximation addresses the remaining nonconvex constraints.The reformulation introduces r_k, γ_k, η_k, α_k, and β_k, then approximates constraints using first-order Taylor expansions.
  • Convex solution: The resulting convex problem can be solved using an existing convex optimization toolbox.The convex formulation is given as problem (55), with nonnegative slack variables α_k and β_k.

D. Algorithm Analysis

Algorithm 1 alternates among semantic extraction, computation capacity, and joint transmission-design subproblems until convergence, with complexity determined by their inner and outer iterations.

  • Subproblem complexity: The semantic extraction subproblem has complexity O(K log2(1/ε1)), while computation-capacity optimization has complexity O(N1K).The first complexity uses bisection accuracy ε1; N1 is the number of dual-method iterations.
  • Subproblem complexity: The joint power, rate, and beamforming subproblem is solved through an approximated convex problem and successive convex approximation.Its complexity depends on the number of variables, constraints, and SCA iterations.
  • Alternating algorithm: Algorithm 1 alternates semantic information extraction, computation capacity, and joint power-control, rate-allocation, and beamforming updates until the objective converges.Each iteration updates S, then f and g, then p, a, and w.

IV. SIMULATION RESULTS

Simulations compare RSMA with FDMA, NOMA, SDMA, and an exhaustive-search reference across transmit power, bandwidth, data size, and computation capacity. RSMA achieves near-EXH-RSMA performance and favorable energy trends across these settings.

  • Simulation setup: The simulations use K = 5 users, B = 20 MHz, and maximum transmit power P_max = 30 dBm unless otherwise specified.The setup also specifies a pathloss model, shadow-fading deviation, noise power spectral density, and computation parameters.
  • Transmit power: RSMA outperforms FDMA and NOMA in total energy and remains better than SDMA particularly at high maximum transmit power.The paper attributes this to RSMA’s higher spectral efficiency and SDMA’s tendency to leave poor-channel users with longer transmission times and higher computation power.
  • Transmit power: The proposed RSMA achieves near performance as EXH-RSMA, indicating that the proposed algorithm approaches the exhaustive-search reference.EXH-RSMA uses 1000 initial solutions to obtain a near globally optimal solution.
  • Bandwidth: Total communication and computation energy decreases as system bandwidth increases because higher bandwidth reduces transmission time and local computation energy.This trend is reported for all evaluated schemes.
  • Transmit data size: Total energy increases with each user’s transmit data size, but RSMA’s growth is slower than NOMA’s and FDMA’s.The paper links larger data sizes to increased transmission and computation power.
  • Computation capacity: Total energy first decreases rapidly and then approaches a fixed value as maximum computation capacity increases.At high computation capacity, users select an optimal capacity allocation, so further increases do not change energy consumption.

V. CONCLUSIONS

The paper jointly optimizes semantic information extraction and wireless resource allocation for energy-efficient semantic communication with rate splitting. An iterative method derives optimal extraction ratios and computation frequencies at each step, and simulations support its effectiveness.

  • System and objective: The BS extracts semantic information from large-scale data and transmits compact semantic information, which users recover using local common knowledge.Rate splitting carries private semantic information through private messages and common knowledge through a common message.
  • System and objective: The optimization minimizes total communication and computation energy under task-completion and semantic-accuracy constraints.Both transmission energy and computational energy are included in the joint problem.
  • Proposed solution: An iterative algorithm derives optimal semantic information extraction ratios and computation frequencies at each step.The algorithm addresses the coupled computation and communication resource-allocation problem.
  • Conclusion: Numerical results show the effectiveness of the proposed algorithm.
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