Codeword-Segmentation Rate-Splitting Multiple Access and Evaluation under Suboptimal Decoding

Bruno Clerckx; David Vargas; Sibo Zhang

REVIEW 3 major objections 6 minor 26 references

Codeword-Segmentation Rate-Splitting Multiple Access and Evaluation under Suboptimal Decoding

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper proposes CS-RSMA, a rate-splitting scheme that encodes each user once and then segments the codeword, and shows it improves on conventional RSMA in sum rate while cutting complexity, signaling, and retransmission overhead.

desk verdict A genuinely new RSMA architecture that removes SIC and reduces codeword count, but the reported SR gain over SIC-free RSMA is largely baked into the optimization baseline. read the letter →

arxiv 2506.17164 v2 pith:CKGPL7PY submitted 2025-06-20 cs.IT eess.SPmath.IT

Sibo Zhang , Bruno Clerckx , David Vargas This is my paper · ORCID

classification cs.ITeess.SPmath.IT

keywords rate-splittingmultipleaccesscodewordsegmentationfinite-alphabetsignallingmismatcheddecodinggeneralizedmutualinformationSIC-freereceiversum-rateoptimizationmax-minfairness

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper introduces Codeword-Segmentation Rate-Splitting Multiple Access (CS-RSMA), an architecture that first encodes each user's message into one codeword and then cuts that codeword into a common segment and a private segment, rather than splitting the message before encoding as conventional RSMA does. It aims to show that this reordering preserves the known benefits of RSMA under realistic constraints: with finite-alphabet signals and receivers that treat undesired streams as Gaussian noise, CS-RSMA achieves higher sum rate than conventional RSMA with or without successive interference cancellation, and essentially the same max-min fairness, while using fewer codewords and less control signaling. If correct, the result matters because it gives network designers an RSMA implementation that is easier to build, easier to signal, and compatible with existing retransmission mechanisms, without paying a throughput penalty. The analysis is carried through generalized mutual information for mismatched decoders, precoder optimization for sum rate and fairness, and link-level simulations with LDPC codes.

What carries the argument

The machinery is threefold. First, the CS-RSMA transceiver structure itself: one encoder per user, a stream splitter that divides each codeword into private and common segments, and a receiver that reassembles soft estimates of the segments before channel decoding. Second, the generalized mutual information (GMI) for the finite-alphabet Gaussian channel under interference (FAGCI), the achievable-rate metric for mismatched decoders that treat undesired private streams as Gaussian random variables; Eq. (10) is the approximation used in precoder optimization and Eq. (9) the exact rate used in evaluation. Third, the rate decomposition $I_{\mathrm{GMI},k} = c_k I_{c,k} + I_{p,k}^{\mathrm{nonSIC}}$: because the common stream no longer has to be decodable by every user, the sum-rate objective becomes $\max_{k} I_{c,k} + \sum_{k} I_{p,k}^{\mathrm{nonSIC}}$ instead of $\min_{k} I_{c,k} + \sum_{k} I_{p,k}^{\mathrm{nonSIC}}$. A decoding-complexity constraint ($\delta$ exponentials per received symbol) keeps the comparison fair by fixing $\delta = |\mathcal{X}_c||\mathcal{X}_{p,k}|$ across schemes.

What would settle it

Run a fixed CS-RSMA configuration at a chosen SNR, vary the common-segment fraction $c_k$, and compare the measured LDPC throughput or BER with the prediction $c_k I_{c,k} + I_{p,k}^{\mathrm{nonSIC}}$ computed from the paper's GMI formulas. If a receiver that jointly decodes the reassembled codeword achieves a rate materially different from that sum, or if the two contributions do not scale with $c_k$, the additive decomposition at the center of the sum-rate comparison is falsified.

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Extended reading notes

Core claim

On its own terms, the central claim is that the order of encoding and splitting is what creates implementation cost in RSMA, not an essential ingredient of its gain. Conventional RSMA splits messages into common and private parts before encoding, so the common stream is a single message every user must decode and the common rate is capped by the weakest user, written $\min_{k} I_{c,k}$. CS-RSMA encodes each user's message directly, segments the resulting codeword, and multiplexes the common segments, so user $k$ only decodes its own slice of the common stream. Its achievable rate is $I_{\mathrm{GMI},k} = c_k I_{c,k} + I_{p,k}^{\mathrm{nonSIC}}$ (Eq. (25)), where $c_k$ is the fraction of the common stream carrying user $k$'s segment, and the sum-rate optimization replaces the bottleneck $\min_{k} I_{c,k}$ with $\max_{k} I_{c,k}$. The paper supports this with GMI-based ergodic evaluations and link-level simulations: CS-RSMA sits slightly above conventional RSMA in sum rate, matches it in max-min fairness, and at a coded BER of $10^{-4}$ is about 0.05 dB better, while encoding, decoding, control signaling, and HARQ retransmission each simplify because one codeword per user replaces two streams.

Load-bearing premise

The load-bearing premise is that a user's achievable rate under CS-RSMA is exactly $c_k I_{c,k} + I_{p,k}^{\mathrm{nonSIC}}$, the sum of its weighted common-segment rate and private-stream rate, even though the decoder draws both from the same received signal; if these two contributions do not add, the reported sum-rate advantage of CS-RSMA shrinks or disappears.

Editorial extensions

If this is right

The sum-rate optimum of CS-RSMA is at least as large as that of SIC-free conventional RSMA, since the objectives differ only by replacing $\min_{k} I_{c,k}$ with $\max_{k} I_{c,k}$; in the medium-SNR regime this preserves RSMA's advantage over SDMA.
Each user encodes and decodes one codeword rather than two streams, so encoding, decoding, CRC, interleaving, scrambling, and the associated control signaling are reduced relative to conventional RSMA.
Retransmission reduces to the standard MU-MIMO HARQ process, because the common stream carries no standalone message needing its own HARQ design.
Under finite-alphabet inputs and a fixed decoding-complexity budget, the GMI evaluations show CS-RSMA slightly ahead of conventional RSMA with and without SIC in ergodic sum rate, and effectively equal in max-min fairness.
Link-level simulations with 5G NR LDPC codes put CS-RSMA about 0.05 dB ahead of conventional RSMA at coded BER $10^{-4}$ under the same receiver implementation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: the $\max_k I_{c,k}$ structure implies a scheduling rule in which the transmitter decides on each channel realization which user's segment is carried by the common stream, which could harvest multiuser diversity beyond the paper's ergodic averages.
Beyond the paper: the additive decomposition in Eq. (25) is an assumption about separable decoding; a finite-blocklength experiment varying $c_k$ and measuring whether the common and private contributions add in proportion would show whether it is exact or a systematic overestimate.
Beyond the paper: because SIC cannot be applied to a common stream that is a multiplex of segments, any future CS-RSMA variant needing common-stream cancellation would have to cancel at the soft-symbol level, as the soft-SLIC receiver here does.
Beyond the paper: the same encode-then-segment principle should carry over to multi-layer RSMA, where the codeword-count saving grows with the number of common streams, though the paper does not derive the rate decomposition for that case.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the architecture is real and worth taking seriously, but the headline SR comparison is rigged in the paper's favor.

What's new: CS-RSMA encodes each user's message into one codeword, then splits the codeword into common and private segments. Conventional RSMA splits the message first and encodes two codewords per user. This reordering is absent from the cited literature, and it has real practical consequences: no SIC, one codeword to decode per user, and HARQ that looks like ordinary MU-MIMO. The PHY transceiver designs and link-level simulations are a solid addition. Applying the FAGCI GMI from [20] to compare schemes under mismatched decoding is also a reasonable move, though it leans on a same-day companion preprint.

The soft spots, in order of severity. First, the SR gain over SIC-free RSMA in Fig. 3 is mostly by construction. Proposition 2 shows the two problems differ only in replacing min_k I_{c,k} with max_k I_{c,k}. CS-RSMA can put all common resources on the user with the best common rate; conventional SIC-free RSMA must make the common stream decodable by all. The paper acknowledges this in Remark 3 and even in Fig. 5, where the common-stream rate of CS-RSMA is higher for exactly that reason. So the comparison establishes the benefit of dropping the all-users-decode-common constraint, not the benefit of codeword segmentation per se. The MMF comparison, where the min is still present, shows near-identical performance, which is more credible.

Second, Eq. (25) asserts that the CS-RSMA rate is c_k I_{c,k} + I_{p,k}^{non-SIC}. That additive split is never derived from the mismatched decoder in Eq. (30). The decoder multiplies two separate metrics over disjoint time indices, and it is not obvious that the information extractable from the common segment and the private segment adds up that cleanly. If this overcounts, the SR advantage shrinks or vanishes. This needs to be proven or supported by simulation of actual codes. The LLS results show only a 0.05 dB gap at BER 1e-4, which is basically noise-level and doesn't settle the rate question.

Minor: the subgradient ascent convergence argument (“objective is upper-bounded”) is not a real convergence proof, and the baseline for conventional RSMA could be more flexible. But these are secondary.

Bottom line: the architecture is a legitimate contribution with genuine implementation benefits. The paper deserves a serious referee, but the SR claims should be reframed or the baseline generalized to allow c_k=0 for some users, and Eq. (25) needs a derivation. As is, an editor should send it out, and the referee should ask for major revision.

Referee Report

3 major / 6 minor

Summary. The paper proposes CS-RSMA, an RSMA architecture in which user messages are first encoded and the resulting codewords are then segmented into common and private parts, in contrast with conventional RSMA, which splits messages before encoding. The authors introduce a GMI-based analysis under mismatched decoding, define a decoding-complexity measure, formulate sum-rate (SR) and max-min fairness (MMF) precoder optimization problems for conventional RSMA and CS-RSMA, and evaluate them through numerical simulations and link-level simulations. They report that CS-RSMA slightly outperforms conventional RSMA in SR, performs similarly in MMF, and offers implementation benefits in encoding/decoding complexity, control signaling, and retransmission design.

Significance. If the rate expressions and comparisons were fully justified, the paper would make a useful contribution: CS-RSMA potentially preserves most of the rate benefits of RSMA while simplifying the physical-layer implementation, and the GMI framework is a relevant step toward evaluating RSMA under practical suboptimal receivers. The paper is also commendable for including link-level simulations and for explicitly defining a decoding-complexity constraint. The practical advantages discussed in Section VI-C are credible and largely independent of the contested rate analysis.

major comments (3)

[Section III-B, Eq. (25) and Eq. (30)] The achievable-rate expression for CS-RSMA, I_GMI,k = c_k I_c,k + I_non-SIC_p,k, is asserted in Remark 1 but is not derived from the mismatched-decoding metric. In the decoder of Eq. (30), for t in T_k the first product uses d(·) with the common symbol fixed and sums over private symbols, while the second product, taken over all t = 1,...,n, also includes t in T_k with the private symbol fixed and sums over common symbols; the same received symbol is thus counted twice. Even if the second product is meant to range only over t not in T_k, the sum of the two per-stream GMIs is not an immediate consequence of the GMI for the joint codeword, because the common and private streams are superposed rather than orthogonalized and the decoder is not a product of two independent per-stream decoders. Since Eqs. (23)-(25) are the objective functions for P2 and P3 and drive all SR/MMF numerical claims, this missing derivation is load-bearing. The authors should either prove the additive decomposition under the stated decoder or replace it with the correct joint GMI.
[Section IV-A, P2/P3 and Remark 1] The claimed SR advantage of CS-RSMA over SIC-free conventional RSMA is to a large extent built into the formulation. In conventional SIC-free RSMA, a user with c_k = 0 does not need to decode the common message; the common codeword only has to be decodable by users with c_k > 0. The optimization P2 nonetheless imposes min_k I_c,k on the common rate for all users. If the common-rate constraint is instead applied only to the set {k : c_k > 0} and c is optimized, the optimal common-rate contribution becomes max_k I_c,k, yielding exactly the P3 objective of CS-RSMA. Thus the comparison in Fig. 3 establishes the benefit of relaxing the all-users-decode-common constraint rather than a benefit of codeword segmentation per se. Unless the authors justify why all users must decode the common stream even when they receive no common bits (for example, for SIC or system-level reasons), the baseline is suboptimal and the abstract's SR claim is stronger than what is demonstrated.
[Section IV, Algorithms 1 and 3] The convergence justification is not sufficient. Monotone increase and boundedness of the objective sequence do not imply convergence of the iterates to a stationary point for nonconvex subgradient ascent, and the presence of min/max operators and the logarithmic barrier further complicates the argument. Since the SR/MMF comparisons in Section V are obtained from these algorithms, the authors should either state the stationarity guarantees that can be established or present the results as heuristic with appropriate caveats.

minor comments (6)

[Section III-C, Definition 1] The definition says a decoder of complexity-delta can compute exp(|·|^2) for at most n times for each received symbol; this should be delta times, not n times, since n denotes the block length.
[Eq. (30)] The second product in Eq. (30) appears to range over all t = 1,...,n, which double-counts the observations in T_k; it likely should be restricted to t not in T_k. Even with that correction, the expression should be reconciled with the rate decomposition in Eq. (25).
[Figures 3, 4, 6, 7] The axis label 'GMI (bits/channel usee)' contains a typo: 'usee' should be 'use'.
[Algorithm 3, line 10] The stopping criterion contains a stray comma in 'Omega^{,v-1}_MMF'; this should be 'Omega^{v-1}_MMF'.
[Section III-B, footnote 2] The separability of the decoding metrics for common and private streams is an assumption that underlies Eqs. (23)-(25); it should be stated more prominently and its implications for the GMI derivation should be discussed rather than relegated to a footnote.
[Eqs. (9)-(15)] The GMI formulas are imported from the companion preprint [20], which is cited as a same-day arXiv preprint. The authors should clarify the status of that work and, if space permits, include the key derivation or a more detailed citation so that the present paper is self-contained on this load-bearing point.

Circularity Check

1 steps flagged · score 6.0 of 10

CS-RSMA's advertised SR gain over SIC-free RSMA is the algebraic max-vs-min consequence of its own rate definition (Eq. 25/P3 vs Eq. 24/P2), so the numerical 'observation' of SR superiority is built into the formulation; the MMF, SIC-comparison, and LLS results are independent.

self definitional [Section IV-A, Proposition 2 and Remark 3 (Eqs. (32)-(33))]
"An interesting difference between P2 and P3 is that the ”min” operator in P2 is replaced by ”max” in P3. This indicates that CS-RSMA is expected to perform at least as well as conventional RSMA without SIC in SR, since its problem formulation only differs from the latter by changing the ”min” to a ”max”."

The advertised SR gain over SIC-free RSMA is not established by the simulations: it is an algebraic consequence of the rate expressions the paper adopts. With Eq. (24), conventional SIC-free RSMA has sum objective min_k I_c,k + sum_k I_nonSIC_p,k (P2); with Eq. (25) and the optimal allocation c_k=1 for k=argmax_k I_c,k, CS-RSMA has max_k I_c,k + sum_k I_nonSIC_p,k (P3). Since max_k I_c,k >= min_k I_c,k for every precoder P, the optimized CS-RSMA sum rate is guaranteed to be at least the optimized conventional sum rate. The 'better performance' is therefore built into the definitions, as Remark 3 concedes.

full rationale

The paper's central SR advantage over SIC-free RSMA is a max-vs-min artifact of its own rate definitions: Eq. (24) imposes min_k I_c,k on the common rate of conventional RSMA, while Eq. (25) and Proposition 2 convert the CS-RSMA sum-rate objective into max_k I_c,k + sum_k I_nonSIC_p,k. Because max >= min pointwise, the claimed SR superiority is guaranteed before any numerical optimization, and the paper acknowledges this in Remark 3. This is a partial self-definitional circularity in the comparison, not a fully independent 'observation'. The MMF results, the comparison against SIC-based RSMA, and the link-level simulations are not forced by this construction and provide independent content. The GMI metric is cited from the authors' own companion paper [20]; while this is a self-citation, the present conclusions are not identical to [20]'s theorem, so I do not treat it as a separate circular step. The baseline-fairness concern about c_k=0 users is a correctness risk but is closely tied to the same construction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the GMI framework from a self-cited companion paper, an unproven additive rate decomposition for CS-RSMA, and a complexity model that defines the comparison. The optimized precoders and allocation fractions are decision variables, while the adaptive mode selection is a fitted envelope over transmission modes.

free parameters (3)

c_k (common stream allocation/segmentation fraction) = optimized per channel realization, sum to 1
In Prop. 2, the optimal c for CS-RSMA SR is set to c_k=1 for the user with maximum I_c,k; in MMF, c is updated by Alg. 2. These fractions directly determine the reported rates and are chosen to maximize the objective.
Adaptive alphabet/mode selection = BPSK/QPSK/8QAM/16QAM per mode tables, selected per SNR
Section V-A selects the transmission mode (alphabet pair) that maximizes the ergodic objective at each SNR, so the reported CS-RSMA/RSMA curves are upper envelopes over modes.
Precoder matrix P = optimized via subgradient ascent, no global optimality guarantee
The precoders are decision variables in P1 and P5; results depend on initialization and local convergence.

assumptions (4)

domain assumption GMI expressions (9)-(11) for FAGCI channel from companion preprint [20] are valid for the MISO RSMA setting.
The paper uses these results without derivation; [20] is a same-day preprint by the same authors, not independently verified here.
ad hoc to paper Eq. (25): achievable rate of CS-RSMA is the sum of weighted per-stream GMIs, c_k I_c,k + I_non-SIC_p,k.
Stated in Remark 1 without proof; assumes additive rates for codeword segments decoded with product metric (30).
ad hoc to paper Decoding complexity is measured by the number of exp(|.|^2) evaluations per received symbol (Definition 1), and comparing schemes under equal delta is meaningful.
This complexity measure determines the transmission modes in Tables I and II and underlies the fairness of the RSMA/CS-RSMA comparison.
domain assumption Suboptimal decoder treats desired signals optimally and all undesired private streams as Gaussian noise.
Section III-B; this receiver strategy is motivated by complexity and by [20], and is used to define I_c,k and I_p,k.

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Pith. "Pith review of Codeword-Segmentation Rate-Splitting Multiple Access and Evaluation under Suboptimal Decoding." pith.science (2026). https://pith.science/paper/CKGPL7PY

@misc{pith2026250617164,
  author       = {Pith},
  title        = {Pith review of: Codeword-Segmentation Rate-Splitting Multiple Access and Evaluation under Suboptimal Decoding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CKGPL7PY}},
  note         = {Machine review of arXiv:2506.17164}
}

read the original abstract

Rate-Splitting Multiple Access (RSMA) has been recognized as a promising multiple access technique. We propose a novel architecture for downlink RSMA, namely Codeword-Segmentation RSMA (CS-RSMA). Different from conventional RSMA which splits users' messages into common and private parts before encoding, CS-RSMA encodes the users' messages directly, segments the codewords into common and private parts, and transmits the codeword segments using common and private streams. In addition to the principle of CS-RSMA, a novel performance analysis framework is proposed. This framework utilizes a recent discovery in mismatched decoding under finite-alphabet input and interference, and can better capture the receiver's complexity limits. Precoder optimization under finite alphabets and suboptimal decoders for conventional RSMA and CS-RSMA to maximize the Sum-Rate (SR) and the Max-Min Fairness (MMF) is also addressed. The numerical results reveal the theoretical performance of conventional RSMA and CS-RSMA. We observe that CS-RSMA leads to better performance than conventional RSMA in SR, and similar performance in MMF. Furthermore, a physical-layer implementation of CS-RSMA is proposed and evaluated through link-level simulations. Aside performance benefits, we also demonstrate that CS-RSMA brings significant benefits on the encoding/decoding, control signaling, and retransmission process compared to conventional RSMA.

Figures

Figures reproduced from arXiv: 2506.17164 by the authors.

**Figure 1.** Conventional RSMA for multi-user MISO. 𝑊1 𝑊𝐾 𝒔1 𝒔c cw 𝒔𝐾 cw Precoding . . . 𝒔c,1 𝒔c,𝐾 𝒔p,1 𝒔p,𝐾 . . . . . . . . . 𝒙1 𝒙𝑁T . . . Transmitter Stream splitter Encoding 𝑦𝑘 User-K 𝑦𝐾 𝑊෡𝐾 . . . Estimator 𝑊෡𝑘 User-k User-1 𝑦1 𝑊෡1 . . . 𝒔ො𝑘 cw Stream splitter Stream 𝒔ො combiner p,𝑘 𝒔ොc 𝒔ොc,𝑘 Decoding Stream combiner [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Codeword-Segmentation RSMA for multi-user MISO. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Ergodic SR performance of conventional RSMA, CS-RSMA and [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Ergodic SR performance of different modes of CS-RSMA. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: Comparing common and private stream rates with [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 8.** Figure 8: PHY transmitter design for CS-RSMA. Resource de-mapping Demod LLRc LLRc,k LLRp,k DEMUX MUX FEC−1 Wˆ LLRk k yk (a) Joint de-mapping Resource de-mapping Demod LLRc LLRc,k LLRp,kDEMUX MUX FEC−1 Wˆ LLRk k yk + − Soft Symbol Demod (b) Soft SLIC [PITH_FULL_IMAGE:figures/ful…

**Figure 9.** Figure 9: depicts two proposed receiver architectures for CS-RSMA, where ”FEC−1 ” and ”Demod” represent channel decoder and demodulator (demapper) respectively. They are based on the joint de-mapping receiver and soft Symbol Level Interference Cancellation (SLIC) receiver for co…

**Figure 10.** Figure 10: BER comparision between conventional RSMA and CS-RSMA with all streams using QPSK constellation. Code rate for RSMA: 0.85 for common [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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Rate-splitting multiple access: The first prototype and experimental validation of its superiority over SDMA and NOMA,

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Rate-splitting multiple access: Finite constellations, receiver design, and SIC-free implementation,

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SIC-free rate-splitting multiple access: Constellation constrained sum-rate optimization,

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work page Pith review arXiv 2025