CoopSR: Cooperative Storage, RSMA & Robotics

• CoopSR is a cooperative mechanism that enables agents to work together in distributed storage, wireless communications, and multi-robot systems to resolve shared bottlenecks.
• In distributed storage, CoopSR employs a two-phase process of helper downloading and inter-newcomer exchange to jointly repair failed nodes and reduce repair bandwidth.
• In wireless and embodied AI, CoopSR underpins strategies like common stream relaying and multi-view integration to enhance rate splitting and spatial reasoning performance.

CoopSR appears in the provided literature in several technically distinct senses. In distributed storage, it denotes cooperative storage repair: the joint repair of multiple failed nodes by newcomers that download from helpers and then exchange information among themselves, as formalized by cooperative regenerating codes [(Shum, 2011); (Shum et al., 2012); (Shum et al., 2016)]. In wireless communications, closely related work uses CoopSR / CRS for cooperative rate splitting, where a stronger user relays the decoded common stream in RSMA to weaker users (Zhao et al., 2022, Zhao et al., 2024, Elhattab et al., 2024, Li et al., 2020). In embodied AI, CoopSR is also the name of a benchmark for multi-robot cooperative egocentric spatial reasoning over synchronized first-person video streams (Peng et al., 18 May 2026).

1. Semantic scope and shared structure

Across these usages, CoopSR denotes a cooperative mechanism that exploits simultaneity or distributed vantage points rather than treating participants independently. The storage literature centers on multiple-node failure recovery; the wireless literature centers on common-stream relaying in rate splitting; the embodied-AI literature centers on multi-robot team reasoning.

Domain	CoopSR meaning	Core mechanism
Distributed storage	Cooperative storage repair	Helper download plus newcomer exchange
Wireless communications	Cooperative rate splitting	Common-stream decoding plus user relaying
Embodied AI	CoopSR benchmark	Multi-robot synchronized egocentric QA

A recurring motif is a two-stage pattern: local acquisition first, inter-agent cooperation second. In storage, each newcomer first contacts helpers and then exchanges repair data with peer newcomers. In cooperative RSMA, users first decode the BS common stream and then strong users relay it. In the benchmark setting, each robot first observes its own egocentric stream and the model must then integrate team-wide evidence. This suggests a family resemblance across domains, although the underlying mathematical objects—subspaces, SINRs, and multimodal latent states—are entirely different.

2. CoopSR as cooperative storage repair

In distributed storage, CoopSR refers to the repair of multiple failed storage nodes simultaneously rather than one by one. A file of size $B$ over $\mathbb{F}_q$ is encoded across $n$ nodes with the $(n,k)$-reconstruction property, so any $k$ nodes suffice for full recovery. If $r$ failed nodes are repaired jointly, each newcomer contacts $d$ helpers, downloads $\beta_1$ units from each, and then exchanges $\beta_2$ units with each of the other $r-1$ newcomers. The per-newcomer repair bandwidth is

$\mathbb{F}_q$0

The 2016 exact-repair subspace formalization uses $\mathbb{F}_q$1 for the number of jointly repaired failures instead of $\mathbb{F}_q$2, but the two-phase structure is the same (Shum et al., 2016).

The 2011 information-flow-graph formulation introduced vertices $\mathbb{F}_q$3, $\mathbb{F}_q$4, and $\mathbb{F}_q$5 for each failed node, helper edges of capacity $\mathbb{F}_q$6, newcomer-exchange edges of capacity $\mathbb{F}_q$7, and data-collector cuts that yield

$\mathbb{F}_q$8

for every admissible $\mathbb{F}_q$9 with $n$0 and $n$1 (Shum, 2011). The exact functional tradeoff was later given in closed form. Its cooperative extremal points are the minimum-storage cooperative regenerating point

$n$2

and the minimum-bandwidth cooperative regenerating point

$n$3

which reduce to the classical MSR and MBR points when $n$4 (Shum et al., 2012).

The 2016 exact-repair treatment makes the repair phases algebraically explicit. If node $n$5 stores a subspace $n$6, reconstruction requires

$n$7

for every $n$8-subset $n$9. If nodes $(n,k)$0 fail, newcomer $(n,k)$1 downloads a subspace $(n,k)$2 from its helpers and sends subspaces $(n,k)$3 to its peers, with exact repair requiring

$(n,k)$4

This formulation cleanly separates helper download and newcomer-to-newcomer exchange, and it makes precise why cooperation can reduce the amount of information drawn from surviving nodes (Shum et al., 2016).

3. Explicit construction families

The explicit code literature develops several exact cooperative constructions at the cooperative extreme points and, in later work, for specific MSR families and sub-packetization regimes [(Shum, 2011); (Shum et al., 2016); (Liu et al., 2022); (Liu et al., 27 Feb 2025); (Zhang et al., 14 Jan 2026); (Zhang et al., 2019)].

Construction family	Parameter regime	Salient property
RS-based minimum-storage exact repair	$(n,k)$5, $(n,k)$6, $(n,k)$7	$(n,k)$8, $(n,k)$9, uncoded helpers
Bilinear-form exact MBCR	$k$0, $k$1	$k$2, $k$3, $k$4
Systematic exact MSCR via MISER / Suh–Ramchandran	$k$5, $k$6, $k$7	$k$8, $k$9, repairs any $r$0 systematic nodes and, by duality, any $r$1 parity nodes
Hadamard cooperative MSR	$r$2	Reduced sub-packetization: $r$3 when $r$4, or $r$5 when $r$6
Zigzag cooperative MSR	any $r$7, $r$8	Optimal repair for any $r$9 failed nodes, $d$0, $d$1, $d$2
Optimal-access cooperative MSR for two erasures	$d$3, $d$4	$d$5
Improved cooperative repair for RS codes	two or three erasures	Removes characteristic and failure-pattern restrictions

The earliest explicit exact-repair minimum-storage construction uses a Reed–Solomon generator matrix $d$6, stores $d$7 symbols arranged as an $d$8 message matrix $d$9, and places column $\beta_1$0 of $\beta_1$1 in node $\beta_1$2. If nodes $\beta_1$3 fail, newcomer $\beta_1$4 downloads $\beta_1$5 symbols sufficient to reconstruct row $\beta_1$6, then sends $\beta_1$7 to newcomer $\beta_1$8 for each $\beta_1$9. This achieves exact repair with $\beta_2$0 and $\beta_2$1; helper nodes simply read and forward stored packets, so the repair is uncoded on the helper side (Shum, 2011).

The 2016 MBCR construction slightly generalizes the earlier Wang–Zhang design using a bilinear-form representation. With

$\beta_2$2

it stores, at node $\beta_2$3, enough information to evaluate both $\beta_2$4 and $\beta_2$5 for $\beta_2$6. Repair proceeds in two phases: each helper sends $\beta_2$7 and $\beta_2$8, so $\beta_2$9; then newcomers exchange one symbol each, so $r-1$0. The resulting per-newcomer bandwidth

$r-1$1

matches the MBCR point exactly, and each newcomer may choose any $r-1$2 surviving helpers (Shum et al., 2016).

The companion MSCR family in the same paper is systematic and uses the MISER / Suh–Ramchandran coding structure with an invertible $r-1$3 matrix $r-1$4, a super-regular matrix $r-1$5, and a symmetric super-regular $r-1$6 matrix $r-1$7. In the regime

$r-1$8

it repairs any $r-1$9 systematic failures with $\mathbb{F}_q$00 and

$\mathbb{F}_q$01

and, by duality, it also repairs any $\mathbb{F}_q$02 parity-check node failures. The repair is interpreted explicitly as interference alignment: after phase 1, each newcomer sees mixtures of desired and interfering symbols, and phase 2 resolves the interference cooperatively (Shum et al., 2016).

Later work specializes cooperative repair to particular MSR families. For Hadamard MSR codes with $\mathbb{F}_q$03, a new pairing scheme based on inter-instance and intra-instance pairing reduces sub-packetization from Ye’s $\mathbb{F}_q$04 to $\mathbb{F}_q$05 when $\mathbb{F}_q$06, and to $\mathbb{F}_q$07 when $\mathbb{F}_q$08 (Liu et al., 2022). For Zigzag MSR codes, the first optimal cooperative repair scheme for that family achieves repair of any $\mathbb{F}_q$09 failed nodes with

$\mathbb{F}_q$10

and uses only $\mathbb{F}_q$11 with $\mathbb{F}_q$12 (Liu et al., 27 Feb 2025). For optimal-access cooperative MSR with two erasures, a recent construction reduces the sub-packetization from $\mathbb{F}_q$13 to

$\mathbb{F}_q$14

while retaining optimal bandwidth and optimal access (Zhang et al., 14 Jan 2026). A separate Reed–Solomon line improves cooperative repair of two or three erasures by removing earlier restrictions that required either $\mathbb{F}_q$15 or special failure patterns (Zhang et al., 2019).

4. Operational interpretation, neighboring models, and open problems

The storage literature explicitly motivates cooperative repair for high churn, batch-mode recovery, correlated failures, and lazy repair. If several nodes fail together, independent repair wastes bandwidth because different newcomers download overlapping information from live nodes. Cooperative repair instead lets newcomers divide the decoding task, exchange distilled side information, and reduce the amount drawn from the surviving system. At the minimum-bandwidth point, this minimizes download from survivors; at the minimum-storage point, it preserves MDS-level storage efficiency while still exploiting collaboration [(Shum, 2011); (Shum et al., 2016)].

The main trade-off is protocol complexity. Cooperative repair is inherently two-phase, requires synchronization among newcomers, and adds cross-newcomer traffic. The 2016 survey material also notes a security downside already recognized in prior work: because newcomers exchange repair data, cooperative repair is more exposed to pollution and Byzantine attacks. Another limitation is that explicit exact MSCR constructions remain much less general than MBCR ones; the MBCR family covers all legitimate MBCR parameters $\mathbb{F}_q$16, whereas the exact MSCR family in that paper is restricted to $\mathbb{F}_q$17 and $\mathbb{F}_q$18 (Shum et al., 2016).

A neighboring but distinct design line studies group-level cooperative repair under locality constraints rather than the standard multi-newcomer cut-set model. Local codes with cooperative repair build each local code from an MSR code part and a distributed local parity part

$\mathbb{F}_q$19

creating a mutual interleaving structure among adjacent local groups. In that model, one failed local group can be repaired from three adjacent local groups, and two adjacent failed local groups can be repaired with average locality $\mathbb{F}_q$20 per failed group (Wang et al., 2016). The underlying object is still cooperative regeneration, but the cooperating entities are repair groups rather than individual newcomers.

Several open directions remain explicit in the cited literature. The 2016 exact-repair paper points to repair-by-transfer at MBCR and cooperative repair methods for practical families such as Reed–Solomon and array codes (Shum et al., 2016). The optimal-access work identifies extension from $\mathbb{F}_q$21 and $\mathbb{F}_q$22 to arbitrary $\mathbb{F}_q$23 and arbitrary $\mathbb{F}_q$24, together with lower bounds on sub-packetization of cooperative MSR codes, as open problems (Zhang et al., 14 Jan 2026). These unresolved questions show that the information-theoretic tradeoff is classical, but explicit constructions with simultaneously favorable bandwidth, access, field size, and sub-packetization remain highly nonuniform across parameter regimes.

5. CoopSR / CRS in wireless communications

A separate communications literature uses CoopSR / CRS for cooperative rate splitting. Here the system model is not a storage code but a multi-user downlink—typically a MISO broadcast channel—in which each user message $\mathbb{F}_q$25 is split into a common part $\mathbb{F}_q$26 and a private part $\mathbb{F}_q$27. The BS jointly encodes all common parts into a common stream $\mathbb{F}_q$28 and encodes private parts into user-specific streams. Cooperation is centered on the common stream: a stronger user decodes it first and then forwards it to weaker users. In the two-user form, the common-rate constraint changes from the non-cooperative bottleneck to

$\mathbb{F}_q$29

so the weak user combines direct and relayed common information (Zhao et al., 2022).

This literature repeatedly stresses that the relayed object is the common stream, not the private stream. That design choice is mathematically important because it targets the RSMA bottleneck directly and avoids a second-stage multiuser interference structure in the cooperative phase. In a physical-layer security variant, the common stream also serves as artificial-noise-like interference at the eavesdropper without consuming extra power beyond the RS design itself (Li et al., 2020).

Reconfigurable surfaces are then added to reshape both direct and relay links. In RIS-aided CRS for a two-user MISO downlink, the RIS assists the BS-to-user links in phase 1 and the user-to-user relay link in phase 2, while the system jointly optimizes BS beamforming, common-rate allocation, RIS phases, and the time split $\mathbb{F}_q$30. At $\mathbb{F}_q$31 dB SNR with $\mathbb{F}_q$32 and $\mathbb{F}_q$33, the reported max–min-rate gain is at least $\mathbb{F}_q$34 over RIS RSMA and $\mathbb{F}_q$35 over no-RIS CRS, and the AO algorithm converges in about $\mathbb{F}_q$36 iterations in a representative realization (Zhao et al., 2022).

STAR-RIS extensions replace conventional RIS by a simultaneously transmitting and reflecting surface and study six coupled protocol choices: $\mathbb{F}_q$37 formed by pairing FD or HD relaying with the ES, MS, or TS STAR-RIS operating protocols. The optimization jointly treats active beamforming, common-rate allocation, STAR-RIS passive beamforming, and, where relevant, time-allocation variables such as $\mathbb{F}_q$38, $\mathbb{F}_q$39, $\mathbb{F}_q$40, and $\mathbb{F}_q$41, under BS power constraints and STAR-RIS energy-conservation constraints (Zhao et al., 2024).

The single-cell model also extends to multi-cell JT-CoMP. In coordinated HD/FD C-RSMA, multiple BSs jointly transmit to CCUs and CEUs, while CCUs relay the common stream to CEUs in HD or FD DF mode. The reported gains at BS transmit power $\mathbb{F}_q$42 dBm are $\mathbb{F}_q$43 for FD C-RSMA over FD C-NOMA and $\mathbb{F}_q$44 for HD C-RSMA over HD C-NOMA (Elhattab et al., 2024). In this communications branch, CoopSR is therefore best understood as a cooperative RSMA architecture for fairness-limited downlinks rather than as a storage-repair code.

6. CoopSR as a multi-robot benchmark

In 2026, CoopSR acquired a new, literal meaning as the name of the first benchmark for multi-robot cooperative egocentric spatial reasoning (Peng et al., 18 May 2026). The benchmark is instantiated by the EgoTeam dataset, which contains 114,227 QA pairs spanning 19 question types, four difficulty tiers, and three team sizes in Habitat and iGibson, together with a real-world test set of around 2,326 QAs collected with two quadruped robots. The task input is a set of synchronized egocentric video streams

$\mathbb{F}_q$45

from a team of robots plus a language query, and the output is an MC4 answer. During training, privileged robot-pose information may be used; at test time, only videos and the query are provided.

The four benchmark tiers are: T1 egocentric spatial QA, T2 pairwise relationship reasoning, T3 scene-level composition and robot action reasoning, and T4 multi-robot dynamic spatial reasoning. The design specifically targets spatial, temporal, visibility, and coordination questions that cannot be solved from a single viewpoint. Text-only performance remains far below multimodal performance, and random robot-stream dropout sharply degrades accuracy, indicating that the benchmark genuinely requires cooperative multi-view reasoning rather than language priors alone (Peng et al., 18 May 2026).

The accompanying model, SP-CoR, combines three modules: SE-MR$\mathbb{F}_q$46FS for CLIP- and FFT-based multi-robot frame sampling, SPI-MRF for spectral- and physics-informed multi-robot fusion, and PAPSD for physics-aligned prompt-space distillation. With Qwen2.5-VL-7B, the reported averages are 70.55 on Habitat and 70.82 on iGibson, outperforming the strongest fine-tuned baseline by +3.87\% and +7.12\%, respectively. The model also generalizes better to unseen team sizes and to the real-world robot test set (Peng et al., 18 May 2026).

This benchmark usage is semantically distinct from the storage and wireless meanings. Here CoopSR is not a repair or transmission protocol but an evaluation problem for multimodal LLMs operating over synchronized multi-robot observations. Even so, the same broad cooperative principle persists: no single agent has a complete view, and performance depends on exploiting structured inter-agent complementarity rather than independent processing.

Taken together, the literature presents CoopSR as a domain-dependent label for cooperative resolution of a shared bottleneck: multiple newcomers repairing failed storage nodes, stronger users relaying the RS common stream, or multiple robots contributing partial embodied evidence to a team-level spatial judgment. This suggests a recurring conceptual pattern rather than a single settled acronym.