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Rate-Splitting Multiple Access with Finite Blocklength for Short-Packet and Low-Latency Downlink Communications

Yunnuo Xu, Yijie Mao, Onur Dizdar, Bruno Clerckx

arXiv:2105.06198v3cs.ITmath.IT

TL;DR

Short-packet downlink communications use finite-blocklength codes to meet latency needs, but prior RSMA work considered infinite blocklength. This paper optimizes RSMA precoders under finite-blocklength constraints and reports shorter blocklengths than NOMA and SDMA for the same rate, especially in overloaded networks.

  • Problem

    Prior RSMA work considered infinite blocklength, while short-packet codes are used for latency-sensitive communications with stringent physical-layer latency requirements.

    Source: §I · p. 1

  • Method

    The paper formulates finite-blocklength RSMA sum-rate maximization under blocklength and transmit-power constraints and solves it with an SCA-based algorithm.

    Source: §III · pp. 2–3

  • Results

    In overloaded scenarios, SDMA requires blocklength 2500 to achieve 20.4 bit/s/Hz, while RSMA needs 300 for the same sum rate.

    Source: B. Overloaded scenario · p. 5

  • Takeaways & Limitations

    The authors conclude that RSMA is a promising low-latency strategy, particularly in overloaded multi-antenna networks.

    Source: §V · p. 5

    The study assumes perfect CSIT; RSMA with finite blocklength and imperfect CSIT is left for future investigation.

    Source: §V · p. 5

Abstract

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Rate-Splitting Multiple Access (RSMA) is an emerging flexible and powerful multiple access for downlink multiantenna networks. In this paper, we introduce the concept of RSMA into short-packet downlink communications. We design optimal linear precoders that maximize the sum rate with Finite Blocklength (FBL) constraints. The relations between the sum rate and blocklength of RSMA are investigated for a wide range of network loads and user deployments. Numerical results demonstrate that RSMA can achieve the same transmission rate as Non-Orthogonal Multiple Access (NOMA) and Space Division Multiple Access (SDMA) with shorter blocklengths (and therefore lower latency), especially in overloaded multi-antenna networks. Hence, we conclude that RSMA is a promising multiple access for low-latency communications.

I. INTRODUCTION

The paper brings RSMA into finite-blocklength downlink communications, addressing a setting not studied in prior RSMA work to the authors’ knowledge. It investigates whether RSMA can reduce blocklength and latency relative to SDMA and NOMA.

I. INTRODUCTION

  • Short packets with finite-blocklength codes address latency-sensitive applications but impose stringent physical-layer latency requirements.Examples include industrial automation, smart grids, and intelligent transportation.Source: §I · p. 1
  • Prior finite-blocklength studies examined coding rates for point-to-point channels, including quasi-static fading, AWGN, and MIMO settings.The cited MIMO work considered perfect and imperfect CSIT/CSIR.Source: §I · p. 1
  • Earlier work presents RSMA as a multi-antenna approach that unifies and can outperform SDMA, OMA, and NOMA across network loads and user deployments.The cited work also reports spectral- and energy-efficiency, robustness, and CSI-feedback benefits.Source: §I · p. 1
  • RSMA is introduced and optimized for finite-blocklength downlink communications, extending prior RSMA work based on infinite blocklength.The study investigates achievable sum rate subject to blocklength and transmit-power constraints.Source: §I · p. 1
  • At the same transmission rate, the paper reports that RSMA can use shorter blocklengths than SDMA and NOMA; at fixed blocklength, it can achieve higher sum rate.The authors describe this as the first study to optimize RSMA for finite-blocklength communications.Source: §I · p. 1

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system model uses one-layer RSMA to serve K single-antenna users from a multi-antenna base station, splitting each message into common and private parts. The paper formulates finite-blocklength sum-rate maximization under blocklength, power, and user-rate constraints.

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • One-layer RSMA splits each user’s message into common and private parts, encoding the common parts together and each private part in a user-specific stream.A linear precoder is assigned to each stream.Source: §II · pp. 1–2
  • Every user decodes the common stream first while treating private streams as noise, then removes it and decodes its own private stream.The common rate cannot exceed the minimum rate supported across users.Source: §II · p. 2
  • Finite-blocklength common and private rates depend on their stream blocklengths, BLER, and channel-dispersion parameters.The stated rate expressions assume Gaussian codebooks.Source: §II · p. 2
  • The precoder design maximizes sum rate subject to blocklength and transmit-power constraints, with per-user common-rate portions and individual rate requirements.With fixed bandwidth, blocklength is proportional to signal duration and therefore approximates latency.Source: §II · p. 2
  • As blocklength tends to infinity, the finite-blocklength rate-loss terms vanish and the formulation reduces to the infinite-blocklength problem; at finite blocklength, those terms cause sum-rate loss.The paper identifies the problem as a more general version of the infinite-blocklength formulation in.Source: §II · p. 2

III. PROPOSED ALGORITHM

The proposed successive convex approximation (SCA) algorithm addresses the non-convex finite-blocklength precoder problem through a sequence of convex subproblems. For two users, the procedure also evaluates SDMA and NOMA regimes to account for cases excluded by its incomplete-RSMA formulation.

III. PROPOSED ALGORITHM

  • The SCA algorithm jointly optimizes the precoders and common-rate vector by successively solving convex approximations of the non-convex problem.The finite-blocklength rate expressions and non-convex channel-dispersion expression add approximation challenges beyond prior RSMA SCA work.Source: §III · pp. 2–3
  • The reformulation introduces bounds on private rates, stream SINRs, and interference-plus-noise terms, and expresses dispersion using SINR.For fixed BLER and blocklength, the term involving the inverse Gaussian Q function is constant.Source: §III · p. 2
  • The algorithm’s objective is bounded by the transmit-power constraint, and its successive feasible solutions guarantee convergence.The authors summarize the procedure as Algorithm 1.Source: §III · p. 3
  • For two users, the incomplete-RSMA algorithm excludes cases where RSMA reduces to SDMA or NOMA, so the method also optimizes those regimes and selects the highest-sum-rate scheme.SDMA is obtained by turning off the common stream; NOMA by turning off one private stream and assigning the common stream to one user.Source: §III · p. 3

IV. RESULTS AND DISCUSSION

The section evaluates finite-blocklength RSMA, NOMA, and SDMA in underloaded and overloaded scenarios. The supplied passage states the comparison scope but reports no outcomes.

IV. RESULTS AND DISCUSSION

  • The evaluation compares the finite-blocklength performance of RSMA, NOMA, and SDMA.Source: §IV · p. 3
  • Both underloaded and overloaded scenarios are included in the evaluation.Source: §IV · p. 3
  • The stated evaluation scope does not specify a result, metric, or winning scheme.Source: §IV · p. 3

1) Rate comparison:

In the underloaded two-user comparison, RSMA outperforms NOMA and SDMA across the reported cases, with its advantage particularly evident as user channels become more aligned. Finite-blocklength RSMA also gains over precoders designed for infinite blocklength, especially at small blocklengths and SNRs.

1) Rate comparison:

  • RSMA outperforms NOMA and SDMA in all reported cases, especially at θ = π/9; at that angle, RSMA and SDMA are nearly identical and both outperform NOMA.The setup varies user angle and channel strength in a two-user ULA deployment with Nt = 4 and γ representing user-2 channel strength.Source: 1) Rate comparison · pp. 3–4
  • Across strategies, sum rate rises with blocklength and approaches the infinite-blocklength rate as blocklength increases.“Inf” and “Fin” denote infinite and finite blocklength, respectively.Source: 1) Rate comparison · p. 4
  • At a sum rate of 9.7 bit/s/Hz, RSMA needs blocklength 100 while SDMA needs around 2500; RSMA’s blocklength benefit grows as user channels become more aligned.The comparison is reported for the two-user deployment.Source: 1) Rate comparison · p. 4
  • Fin RSMA gains over Inf-Fin RSMA most clearly at small blocklengths, with a more pronounced difference at small SNR.Inf-Fin RSMA applies a precoder obtained under the infinite-blocklength assumption to the finite-blocklength scenario.Source: 1) Rate comparison · p. 4

2) Power allocation:

Finite-blocklength dispersion changes the value of allocating power to the common stream: RSMA may be switched off at short blocklengths, while the allocation pattern also depends on the channel setting.

2) Power allocation:

  • The common stream adds a dispersion penalty, so RSMA reallocates power to compensate and may assign zero power to the common stream below a blocklength threshold.For θ = 2π/9, the reported threshold is 500 bits; below it, forcing RS gives SDMA a higher sum rate.Source: 2) Power allocation · p. 4
  • For θ = 2π/9, S(Vc) rises as blocklength falls and exceeds 0.3 bit/s/Hz below 500 bits, so common-stream power is used for private streams instead.Fig. 3 presents common-message power and S(Vc).Source: 2) Power allocation · p. 4, Figure 3 · p. 4
  • For θ = π/9, common-stream power does not change significantly as blocklength varies.The reported power trend differs from the increase with blocklength described for the other setting.Source: 2) Power allocation · p. 4

B. Overloaded scenario

In overloaded deployments, RSMA achieves the same sum rate as SDMA with shorter blocklengths, with a large reported reduction in the eight-user example.

B. Overloaded scenario

  • The four-user case uses a two-antenna base station and four single-antenna users; the eight-user results use four antennas and eight users with random channels.The eight-user results average 100 realizations, with an individual rate constraint of 0.2 bit/s/Hz for all blocklengths.Source: B. Overloaded scenario · p. 5
  • With γ1 = 0.3 in the overloaded four-user deployment, finite-blocklength RSMA outperforms finite-blocklength SDMA and even infinite-blocklength SDMA.The reported comparison also finds that RSMA uses much smaller blocklength than SDMA for the same sum rate.Source: B. Overloaded scenario · p. 5
  • At 20.4 bit/s/Hz, SDMA requires 2500 bits while RSMA requires 300 bits in the overloaded eight-user comparison.Fig. 5 averages results over 100 random channel realizations for Nt = 4 and K = 8.Source: B. Overloaded scenario · p. 5

V. CONCLUSION

The paper introduces RSMA for FBL downlink communications and reports lower latency than NOMA and SDMA at the same transmission rate, especially in overloaded multi-antenna networks. Its analysis assumes perfect CSIT.

  • The paper introduces RSMA for FBL downlink communications targeting low latency.Source: §V · p. 5
  • At the same transmission rate, RSMA uses smaller blocklengths than NOMA and SDMA, with significantly reduced latency in overloaded multi-antenna networks.Source: §V · p. 5
  • The analysis assumes perfect CSIT, leaving FBL RSMA with imperfect CSIT for future investigation.Source: §V · p. 5
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