arXiv:2609.12933v1 [cs.NI] 11 Sep 2026
Support-Aware Telemetry Compression for 5G Positioning via Conditional Conflict Graphs Mohammad Reza Deylam Salehi
Hakima Chaouchi
Télécom SudParis, Institut Polytechnique de Paris Palaiseau, France [email protected]
Télécom SudParis, Institut Polytechnique de Paris Institut Mines-Télécom Palaiseau, France [email protected]
Abstract—Geographically separated transmission/reception points (TRPs) report quantized measurements to a Location Management Function (LMF), even when the application requires only a coarse location region. We formulate this task as a distributed zero-error function-computation problem, in which each TRP transmits an index sufficient for the LMF to reproduce the required service decision. Since positioning geometry induces a sparse and nonrectangular support, independently constructed per-terminal characteristic-graph colorings are not necessarily jointly decodable. We introduce a conditional conflict graph that exactly characterizes valid single-terminal updates and develop an alternating codebook construction that preserves global zeroerror decodability. In a reproducible three-TRP study with rangeequivalent timing measurements and 120 native bins, all resulting codebooks satisfy an explicit decoder-conflict test. For servicecell sizes up to 100 m, the achieved ideal rate is 5.38–5.44 bits per epoch per TRP, compared with 6.91 bits for raw reporting and 6.56–6.87 bits for a globally valid interval-based baseline. A complementary measured six-base-station TDoA study shows that 83.77% of the learned native support recurs on an independent trajectory. For these recurrent tuples, the codebooks preserve the service decision exactly and reduce the ideal rate by 22.8–35.6% for 2–8 m service grids. The feasible report-tuple set also provides a single-epoch geometric-consistency check under injected timing bias. Finally, we identify the NRPPa/OpenAirInterface integration points and safeguards required for experimental implementation. Index Terms—5G positioning, LMF, NRPPa, distributed function computation, graph coloring, telemetry compression, TDoA traces, anomaly detection, OpenAirInterface.
I. I NTRODUCTION 5G New Radio (NR) supports UL-TDOA, UL-AoA, multiRTT, and related positioning methods coordinated by the LMF [1], [2]. In an uplink timing procedure, a UE transmits a positioning SRS, and geographically separated TRPs obtain local quantities such as UL-RTOA. Their serving gNBs forward the measurements through NRPPa, with the AMF transparently transporting the NRPPa payload between the NG-RAN and the LMF [3]. The physically relevant positioning anchors are the TRPs: sectors mounted on one tower provide little TDOA baseline, whereas geographically distributed TRPs may be controlled by a single logical gNB. Existing signaling is measurement-oriented, but many applications are decision-oriented. A factory controller may need an This work received financial support from the French government under the EU Important Project of Common European Interest on Microelectronics and Communication Technologies (IPCEI ME/CT).
aisle, an emergency service a search tile, and a mobility function a zone. Two native measurements that differ numerically need not be distinguished when they always produce the same consumed LMF output. This motivates communication for computing [4]–[9], where each reporting point communicates enough to evaluate the desired function, rather than enabling full source reconstruction. A direct use of ordinary local characteristic graphs is unsafe for positioning because feasible range or timing tuples generally occupy only a sparse subset of the Cartesian alphabet. On such a non-rectangular support, independently valid local colorings can merge complete measurement tuples that require different LMF outputs. We address this joint-decodability problem through the following contributions: An exact global zero-error criterion and a conditional conflict graph that characterizes valid updates of one TRP codebook on an arbitrary finite support. • A support-aware alternating DSATUR algorithm that starts from native reporting, preserves zero-error after every accepted update, and is compared with a globally valid contiguous-interval baseline. • A reproducible three-TRP positioning study with explicit decoder-conflict verification, complemented by a six-basestation measured-TDoA support-transfer check and a heldout single-epoch anomaly experiment. • An NRPPa/LMF integration architecture and staged OAI validation path connecting the coding layer to an operational 5G positioning procedure.
•
The primary numerical evaluation is a coding-layer proof of concept rather than an RF-accuracy study. It uses deterministic range-equivalent timing bins to isolate the telemetrycompression problem. A complementary measured-data check in Sec. IV-C evaluates recurrence of the learned finite support across independent six-base-station TDoA trajectories. Neither experiment constitutes end-to-end UL-RTOA/NRPPa validation; Sec. V outlines that implementation path. Related Work and Scope: Characteristic graphs originate in zero-error source coding with side information [4], [5] and distributed function computation [6]–[10]. Here, the desired function determines which source values must remain distinguishable. Positioning adds geometry-dependent feasible tuples and distributed TRP encoders with centralized LMF
decoding. Prior OAI studies provide the UL-TDOA/NRPPa path [11], SRS telemetry extraction [12], and practical testbed observations [13]–[15]. We build on these components with a support-aware reporting and geometric-consistency layer, without changing the SRS procedure or positioning estimator. Organization: Sec. II defines the zero-error model, Sec. III presents the codebook construction, and Sec. IV reports the controlled and trace-driven evaluations. Secs. V and VI describe the NRPPa/OAI path and the anomaly screen, respectively. Sec. VII reports the measured support-transfer check and concludes the paper. II. S YSTEM M ODEL AND Z ERO -E RROR R EQUIREMENT
the distribution of ci (Xi ) is known, a binary prefix code can achieve the expected length below H(ci (Xi )) + 1 bits [16]. In the distributed setting considered here, any rate or entropy minimization must be restricted to local encoder collections satisfying the global validity condition detailed below. Proposition 1 (Global product-partition criterion). The local encoders (c1 , c2 , . . . , cN ) admit a decoder satisfying (4) if and only if, for every x, x′ ∈ S, c(x) = c(x′ )
→
ℓ(x) = ℓ(x′ ).
(5)
Proof. First, suppose that a zero-error decoder g exists. If c(x) = c(x′ ), then ℓ(x) = g c(x) = g c(x′ ) = ℓ(x′ ),
Consider one positioning epoch with N reporting TRPs. TRP i observes a native quantized symbol Xi ∈ Xi , and the joint input X = (X1 , X2 , . . . , XN ) has finite feasible support which proves (5). Conversely, suppose that (5) holds. For every reachable S ⊆ X1 × X2 × · · · × XN . (1) report tuple m ∈ c(S) ≜ {c(x) : x ∈ S}, define g(m) = ℓ(x) The support incorporates the deployment geometry, quantiza- for any x ∈ S satisfying c(x) = m. Condition (5) guarantees tion, and any nominal uncertainty included at design time. The that this definition is well defined. The value of g on report tuples outside c(S) may be assigned arbitrarily. The resulting uncompressed LMF applies a deterministic service function decoder satisfies (4). ℓ:S→Y , (2) The support structure is essential. Consider S = where Y may represent a grid cell, service zone, or alarm- {(0, 0), (1, 1)} with ℓ(0, 0) ̸= ℓ(1, 1). For each terminal, the relevant decision (see Fig. 1). The function ℓ includes the ordinary characteristic graph contains no edge between its ordinary positioning estimator and any subsequent projection symbols 0 and 1, because the two symbols never occur with a common value of the other terminal. Thus, a one-color to the service grid. assignment is proper for each local graph. However, these assignments yield c(0, 0) = c(1, 1) although the corresponding function values differ, violating (5). Hence, independent proper coloring of the ordinary local characteristic graphs is not sufficient for general non-rectangular supports. III. C ONDITIONAL C ONFLICT G RAPH C ODING Fix all codebooks except that of terminal i. Let x−i ≜ (xj )j̸=i and c−i ≜ (cj )j̸=i denote, respectively, the other local symbols and encoders. Define their aggregate report map by c−i (x−i ) ≜ cj (xj ) j̸=i . (6)
Fig. 1. System model of function-aware positioning telemetry. Native TRP measurements are quantized and mapped to local code indices. The LMF decodes the received index tuple into the same service-grid cell as the uncompressed pipeline. The feasible report-tuple set also enables single-epoch anomaly screening.
Definition 1 (Conditional conflict graph). For fixed c−i , define the graph Hi (c−i ) = G(Xi , Ei ), which may contain self-loops. An edge joins a, b ∈ Xi if there exist x, x′ ∈ S such that xi = a, x′i = b, and c−i (x−i ) = c−i (x′−i ),
ℓ(x) ̸= ℓ(x′ ).
(7)
If Hi (c−i ) contains a self-loop, no choice of ci can make the complete encoder collection zero-error while c−i remains fixed. TRP i sends Mi = ci (Xi ) from a finite code alphabet Ci . Otherwise, c is proper if c (a) ̸= c (b) for every edge joining i i i Define the aggregate report map distinct vertices a and b. c(x) ≜ c1 (x1 ), c2 (x2 ), . . . , cN (xN ) . (3) With identity codebooks at all other terminals, Hi (c−i ) reduces to the ordinary characteristic graph. The following A decoder g : C1 × · · · × CN → Y is zero-error on S when theorem gives an exact validity condition for updating one g c(x) = ℓ(x), ∀x ∈ S. (4) terminal. The idealized alphabet rate is log2 |Ci | bits per epoch, whereas a fixed-width binary representation requires ⌈log2 |Ci |⌉ bits. If
Theorem 1 (Exact one-terminal update). For fixed c−i , the complete encoder collection (ci , c−i ) is zero-error on S if and
Proof. If ci assigns the same color to the endpoints of a conflict edge, the corresponding support points x, x′ in Definition 1 satisfy c(x) = c(x′ ) and ℓ(x) ̸= ℓ(x′ ), violating Proposition 1. A self-loop yields the same contradiction for every possible choice of ci . Conversely, suppose that (ci , c−i ) is not zero-error. By Proposition 1, there exist x, x′ ∈ S such that c(x) = c(x′ ) and ℓ(x) ̸= ℓ(x′ ). Let a = xi and b = x′i . Equality of the reports from all other terminals implies that a and b are adjacent in Hi (c−i ), while equality of the complete report tuples implies that ci (a) = ci (b). If a = b, then Hi (c−i ) contains a selfloop. If a ̸= b, two adjacent vertices receive the same color, contradicting the coloring properness of ci . A. Alternating construction and verification Identity codebooks are initially zero-error. During offline construction, for a selected terminal order, Algorithm 1 updates each terminal using its conditional conflict graph and accepts an update only after an explicit global decoder check. Algorithm 1 Support-aware alternating codebook construction Require: Support S, labels ℓ, terminal order π, number of passes P Ensure: Codebooks (c1 , . . . , cN ), decoder g, feasible set F 1: Initialize ci (xi ) ← xi for all i and xi ∈ Xi 2: for p = 1, . . . , P do 3: for i in order π do 4: Group x ∈ S by c−i (x−i ) 5: Construct Hi (c−i ) from output disagreements 6: if Hi (c−i ) has no self-loop then 7: Color Hi (c−i ) by DSATUR to obtain e ci 8: if (e ci , c−i ) satisfies Proposition 1 then 9: ci ← e ci 10: end if 11: end if 12: end for 13: end for 14: Construct g from c(S) 15: F ← c(S) 16: return (c1 , . . . , cN ), g, F
7.0 Average ideal rate (bits/epoch/TRP)
only if Hi (c−i ) has no self-loop and ci is a proper coloring of its non-loop edges.
6.5 6.0 5.5 5.0 Raw native bins Contiguous intervals Conditional-graph codebooks
4.5 2
5
10
20 50 100 LMF grid resolution Δ (m)
250
500
Fig. 2. Globally validated ideal reporting rates versus service-grid resolution. TABLE I VALIDATED FUNCTION - AWARE CODEBOOKS AND RATES . ∆ (m) (K1 , K2 , K3 ) Rfun Rint save raw 2 5 10 20 50 100 250 500
(109, 7, 102) (109, 7, 103) (110, 7, 106) (107, 7, 102) (107, 7, 97) (103, 7, 103) (82, 3, 83) (54, 3, 54)
5.416 5.421 5.439 5.407 5.383 5.393 4.773 4.365
6.870 6.858 6.829 6.794 6.705 6.565 6.209 5.651
21.6% 21.5% 21.3% 21.7% 22.1% 21.9% 30.9% 36.8%
quadratic scan over the complete support, equal other-terminal report tuples are identified by hashing. Edges are added only within these equal-context groups, followed by a complete support scan that provides an executable zero-error certificate. IV. R EPRODUCIBLE P OSITIONING S TUDY A. Geometry, quantization, and LMF function Three spatially separated TRPs are placed at (0, 0), (1000, 0), and (0, 1000) m. A 220×220 grid of UE locations forms the design set. Each√propagation distance is quantized into M = 120 bins over [0, 2 km], giving an 11.8 m range-equivalent timing resolution and raw ideal rate log2 (120) = 6.907 bits/TRP. For native bin centers (r1 , r2 , r3 ), the LMF computes
We run Algorithm 1 for all six permutations of the three terminals and retain the globally valid construction with the smallest sum of ideal rates. Because DSATUR [17] is heuristic, r2 − r22 + 106 r2 − r32 + 106 pbx = 1 , pby = 1 , (8) the reported cardinalities Ki are achievable codebook sizes 2000 2000 rather than the claimed chromatic numbers or global optima. projects the estimate onto the 1 km × 1 km service region, and The reported controlled experiment uses P = 3 alternating assigns it to a square cell of length ∆. The 48, 400 sampled passes for each terminal order. locations produce 12, 772 distinct native measurement tuples. The construction is performed offline at the LMF or an This synchronized range-equivalent model provides a finite associated controller. After selecting the final codebooks, TRP i approximation of timing telemetry. It omits the common UE receives only its local native-symbol-to-color lookup table ci , transmission-time term, receiver-clock bias, NLOS effects, and together with a codebook identifier, activation information, and SRS estimation errors present in a complete UL-TDOA model. fallback rules. The LMF retains the joint decoder g, and the feasible report-tuple set F = c(S). During operation, the TRPs B. Controlled compression results encode independently and do not exchange measurements or Fig. 2 and Table I report average ideal rates. Every proposed coordinate their reports. For the contiguous-interval baseline, and baseline point is validated by constructing the complete the same conditional graphs are used, but every color class must report-tuple decoder over all 12, 772 tuples; the conflict count be a consecutive interval of native bins. The implementation is zero throughout. greedily selects the longest conflict-free prefix and applies the For ∆ ≤ 100 m, function-aware coding saves 21.3–22.1% same complete decoder check after every update. To avoid a of the ideal raw rate. The corresponding average per-TRP
TABLE II T RACE - DRIVEN CODING WITH B = 24 SYMBOLS PER BASE STATION . I NDEPENDENT- TEST SUPPORT RECURRENCE IS 83.77%.
UE
TRP–gNB
AMF
LMF
Positioning Information Request UE-associated NGAP/NRPPa transport
∆ (m) 2 4 8
Rraw Rfun (bit/epoch/BS) 4.585 4.585 4.585
3.538 3.215 2.954
Saving (%) 22.8 29.9 35.6
SRS resource configuration (RRC) Positioning SRS transmission PHY: SRS estimate → native UL-RTOA xi (e.g., FAPI indication / T_tracer)
fixed-field width is 5.67 bits, a 19.0% reduction from the codebook lookup ci (xi ) → mi 7-bit native field. The valid interval baseline remains close (codebook ID, color index, status) to raw reporting because many function-relevant equivalence Measurement Report: experimental extension [ID, mi ] transparent AMF transport classes are non-contiguous. The selected order (2, 1, 3) yields a strongly asymmetric allocation, with K2 much smaller than K1 and K3 . This does not indicate that TRP 2 is intrinsically less decode g(m1 , . . . , mN ) → service cell informative. Because it is updated first while the other terminals test feasible tuple m ∈ F ; otherwise flag/fallback retain identity codebooks, its conditional graph is formed with maximally detailed side context and admits aggressive merging. — existing 3GPP positioning procedure Once TRP 2 has been compressed, later updates are constructed — proposed function-aware reporting operations using coarser other-terminal contexts, which creates denser conditional graphs and requires more colors. In particular, TRPs 2 and 3 are geometrically symmetric in the present Fig. 3. Integration of the proposed mechanism into the existing NRPPa deployment, so the observed difference is primarily an effect UL-TDOA procedure. Black arrows indicate existing positioning signaling, of update order and heuristic coloring. The controlled geometry while blue arrows and labels indicate the proposed reporting, decoding, and isolates the coding mechanism. We next examine whether the anomaly-screening operations. learned finite-support structure also recurs across independent measured TDoA trajectories. A. Protocol semantics and safeguards C. Trace-driven support transfer The color index is not a UL-RTOA value and should not be We also apply the construction to the Fraunhofer IIS indoor inserted into a standardized UL-RTOA field while retaining 5G dataset, which provides synchronized TDoA measurements UL-RTOA semantics. A defensible prototype therefore uses an from six downlink base stations and separate training and test experimental extension of the Measurement Report message, trajectories [18]. Each measurement is quantized to B = 24 implemented in a modified OAI gNB and LMF, to carry at least symbols, and the quantizers, support, codebooks, and decoder a codebook identifier, color index, and status/fallback flag. The are constructed only from the 18,863 training bursts. A existing NRPPa procedure and transparent AMF transport can deterministic fingerprinting estimator maps every native tuple remain unchanged, but both endpoints require the experimental extension logic. to a two-dimensional service-grid cell. Three safeguards are required. First, an unknown or stale Among the 15,722 independent test bursts, 83.77% reproduce a native tuple contained in the training support. By Propo- codebook identifier triggers native reporting to prevent decoding sition 1, every recurrent tuple yields the same service decision with an incorrect codebook. Second, a local symbol outside under native and compressed reporting. The remaining 16.23% the provisioned alphabet triggers fallback, while a complete fall outside the certified support and are therefore excluded report tuple outside the certified feasible set triggers an LMFfrom the comparison. Table II reports the corresponding rates. side flag or fallback. Third, codebook activation must be This experiment evaluates measured-support recurrence and coordinated through O&M or an LMF-controlled procedure. A coding rate rather than end-to-end NRPPa transport. It also uses TRP cannot independently omit or reinterpret a standardized downlink TDoA measurements rather than uplink UL-RTOA. measurement. Packet savings must also be evaluated after ASN.1/PER serialization. The quantity log2 Ki measures the V. NRPPA I NTEGRATION AND OAI T ESTBED PATH codebook alphabet size and does not directly determine the Fig. 3 maps the proposed reporting layer onto the existing byte reduction of an existing fixed-width IE. UE–TRP/gNB–AMF–LMF positioning transaction. The ordinary procedure configures and receives the positioning SRS B. Data path and staged proof of concept and extracts a native UL-RTOA-like symbol. The proposed Published OAI work provides the positioning transaction, operations are a local codebook lookup, transport of a codebook LMF path, and SRS telemetry extraction required for a identifier and color index, LMF decoding, and a feasible-tuple prototype [11], [12]. Our software setup is based on the check. We refer to each input as a TRP report, although the official OAI RAN and OAI-CN5G LMF repositories [19]. The lookup may be implemented in the serving gNB processing controlled coding-layer replay is reported in Sec. IV, and that TRP’s measurement. the measured six-base-station downlink-TDoA support-transfer
check is reported in Sec. IV-C. The remaining stages are synchronized OAI UL-RTOA trace replay, multi-TRP RFsimulator operation with controlled delays, and O-RAN/OTA evaluation of synchronization, multipath, NLOS, and geometry [13], [14], [20]. We also exercised the extraction-to-lookup path on a single gNB–UE OAI RFsimulator link. A Timing Advance (TA) value from a completed Random Access procedure was converted to the native-bin representation and passed through one validated lookup table (Table III). Because TA is not UL-RTOA and the single-link setup has no positioning geometry, this check validates only software extraction and lookup, not end-to-end positioning or NRPPa compression. TABLE III TA SAMPLE FROM A COMPLETED OAI RF SIMULATOR RANDOM - ACCESS PROCEDURE , QUANTIZED WITH THE NATIVE - BIN SCHEME OF S EC . IV. Quantity
Value
Raw TA (RAR, TS 38.213 §4.2) Granularity (µ = 1) One-way distance equivalent Native bin index (of 120) Color index (TRP 2, ∆ = 100 m codebook, K2 = 7)
31 39.1 m/unit (one-way) 1212.1 m 102 3
C. Timing model, provisioning, and remaining validation The controlled study uses synchronized range-equivalent values to isolate the coding layer. A real uplink timing observation is ti = t0 +
∥p − ai ∥ + bi + n i , c0
(9)
where t0 is the unknown UE transmission-time term, bi is residual TRP clock/receiver bias, and ni contains estimation and propagation error. The encoder can operate directly on the native quantized UL-RTOA field, while ℓ retains the ordinary LMF differencing, compensation, positioning, and grid projection. A deployed codebook is tied to the measurement definition, active TRPs, support model, service function, and grid resolution. A versioned object contains the local lookup tables, decoder, feasible set, validity interval, and integrity value; unknown or mixed versions trigger native reporting. Online operation requires one encoder lookup, one decoder lookup, and feasible-set testing. End-to-end validation should also report synchronized uplink epochs, ASN.1/PER bytes, latency, fallback frequency, and raw/compressed agreement on the certified support. D. Implementation footprint and reproducibility The construction is performed offline, while online reporting is table based. For one terminal update, support points are first grouped by the current report tuple of the other terminals. If the equal-context groups have sizes n1 , n2 , . . ., graph Pconstruction examines only within-group pairs, requiring O( q n2q ) candidate comparisons rather than a direct O(|S|2 ) scan over all support pairs. Each accepted update is followed by an O(|S|) complete decoder check. During operation, a TRP performs
TABLE IV I MPLEMENTED EVIDENCE AND REMAINING INTEGRATION STEP. Component
Evidence/status
Offline coding
All six terminal orders evaluated; every reported three-TRP codebook passes a complete decoder-conflict scan on 12,772 support tuples. Six synchronized BSs, 18,863 training bursts, and 15,722 independent test bursts; native-support recurrence is 83.77%. Completed Random Access TA sample converted to native bin 102 and mapped to color 3 using the validated ∆ = 100 m TRP 2 table. Experimental NRPPa transport of codebook ID, color index, and fallback/status, including ASN.1/PER byte accounting, remains to be implemented.
Measured replay OAI lookup
Protocol step
one array lookup, and the LMF performs one sparse decoder lookup followed by feasible-set membership testing. The stored state is also sparse. For example, at ∆ = 100 m, the three local codebooks contain 120 native-bin entries each, while the validated report alphabet has (K1 , K2 , K3 ) = (103, 7, 103). Only |F| = 12,180 of the 103×7×103 = 74,263 possible color tuples are reachable and need to be retained in the sparse decoder/consistency table. Table IV separates the evidence completed in this work from the remaining protocol step. VI. S TATIC G EOMETRIC A NOMALY S CREEN Once the codebooks are fixed, define the feasible report-tuple set F ≜ c(S) = {c(x) : x ∈ S}. The zero-error requirement constrains the decoder only on F, and its values outside F may be assigned arbitrarily. Operationally, however, the LMF screens those unreachable report tuples before normal decoding. A received tuple outside F cannot arise from the design support and is flagged without trajectory history. It may reveal a codebook mismatch, receiver fault, large NLOS bias, stale report, or unsophisticated measurement injection. It cannot detect anomalies within F and therefore serves only as a consistency screen, not a complete intrusion detector. The screen captures several practical anomaly modes. A positive timing bias models NLOS excess delay or receiver calibration drift. Replacing a report with one from a previous epoch models stale telemetry or an association error, while using a different codebook version models control-plane desynchronization. Missing, duplicated, or out-of-alphabet reports are detected before geometric membership testing and are treated as explicit faults. An adversary that knows F may still select a feasible tuple and bypass the static screen. Detecting such cases requires dynamic mobility checks or physical-layer authentication. We draw 30, 000 held-out UE positions and add a positive range-equivalent bias to TRP 1 before quantization. The same held-out locations are reused across bias levels, and biased measurements are saturated at the largest native bin. Fig. 4 reports the empirical flag probability. With no injected bias, the nominal support-miss rates are 2.06%, 1.70%, and 0.32% for ∆ = 5, 100, and 500 m. These values arise from finite support discretization and should not be interpreted as RF false-alarm
Static-screen flag probability
0.8 0.7
corresponding codebooks reduce ideal rate by 22.8–35.6% for 2–8 m grids. The remaining limitations are that the measured data are downlink TDoA rather than NRPPa ULRTOA, DSATUR is heuristic, and the protocol extension is not yet implemented end to end. Future work will enlarge the declared support using calibrated uncertainty and additional traces, measure serialized bytes and latency, and validate synchronized multi-TRP OAI operation.
Δ=5 m Δ = 100 m Δ = 500 m
0.6 0.5 0.4 0.3 0.2 0.1 0.0
0 1224 48
96
192 Positive range bias at TRP 1 (m)
384
Fig. 4. Held-out static-screen response to a positive range-equivalent bias at one TRP. The zero-bias point is the nominal support-miss rate.
rates. At a 24 m bias, the corresponding flag probabilities are 53.9%, 39.2%, and 4.9%. The experiment exposes a rate–observability tradeoff: coarser service functions reduce both reporting rate and sensitivity to biased measurements. Because the finite-grid support is deliberately strict, the zero-bias point is a support-miss rate rather than an RF false-alarm probability. A deployment should enlarge S using calibrated timing uncertainty or high-coverage traces and then calibrate PFA = P (flag | nominal) and PD = P (flag | fault) for the relevant fault model. Dynamic trajectory checks can follow this inexpensive single-epoch screen when feasible-but-suspicious sequences must also be detected. VII. D ISCUSSION AND C ONCLUSION A. Scope and deployment implications Zero-error refers to recovery of the service function ℓ, not the true physical UE position: on the certified support, compressed and native reports produce the same grid-cell decision, while localization accuracy remains determined by radio conditions, synchronization, geometry, receiver processing, and the estimator. The construction applies to other finite local measurements, including UL-RTOA, AoA, RSRP, or jointly quantized features. Larger TRP sets increase support and decoder size, which can be controlled through sampling, uncertainty envelopes, symbol pruning, and repeated-context reuse, provided the final codebooks pass the global decoder test. Static codebooks remain valid only while the active TRPs, quantizer, support model, and service function are unchanged; other changes require a coordinated version update and safe fallback. B. Conclusion and Future Directions We developed support-aware function coding for distributed 5G positioning telemetry. The global product-partition criterion and conditional conflict graph preserve the LMF service decision on the declared support. In the controlled three-TRP study, the method reduces the ideal reporting rate by 21.3– 22.1% for grids up to 100 m, with zero decoder conflicts. The same feasible report set provides a static consistency screen and maps naturally to the UE–TRP/gNB–AMF–LMF data path. In measured six-base-station TDoA traces, 83.77% of independent test bursts reproduce a training-support tuple and therefore inherit exact service-decision preservation; the
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