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Support-Aware Telemetry Compression for 5G Positioning via Conditional Conflict Graphs

Mohammad Reza Deylam Salehi, Hakima Chaouchi

arXiv:2609.12933v1cs.NI

TL;DR

Sparse positioning support can make independent local colorings jointly undecodable even when the desired output is only a coarse service decision. The paper uses conditional conflict graphs and alternating codebook updates to preserve zero-error decoding. Controlled and measured-trace studies report reduced ideal rates within their stated support and evaluation scopes.

  • Problem

    Sparse, nonrectangular positioning support means independently valid local characteristic-graph colorings may merge complete tuples that require different LMF outputs.

    Source: §I · p. 1, §II · p. 2

  • Method

    A conditional conflict graph characterizes valid single-terminal codebook updates, and alternating DSATUR updates preserve global zero-error validity.

    Source: §I · p. 1

  • Results

    21.3–22.1% ideal reporting-rate reduction for grids up to 100 m; 83.77% of independent test bursts reproduce a training-support tuple, with 22.8–35.6% ideal-rate reductions for 2–8 m grids.

    Source: B. Conclusion and Future Directions · p. 6

  • Takeaways & Limitations

    The feasible report-tuple set also provides a static geometric-consistency screen, while zero-error preservation applies on the certified support.

    Source: B. Conclusion and Future Directions · p. 6, A. Scope and deployment implications · p. 6

    The measured data are downlink TDoA rather than NRPPa UL-RTOA, DSATUR is heuristic, and the protocol extension is not yet implemented end to end.

    Source: B. Conclusion and Future Directions · p. 6

Abstract

from arXiv · show

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 zero-error decodability. In a reproducible three-TRP study with range-equivalent timing measurements and $120$ native bins, all resulting codebooks satisfy an explicit decoder-conflict test. For service-cell 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.

I. INTRODUCTION

Positioning telemetry can be reduced to the information needed for an LMF service decision, but sparse, nonrectangular support makes independent local colorings unsafe. The paper introduces support-aware coding and evaluates its coding-layer behavior and implementation path.

I. INTRODUCTION

  • On sparse, nonrectangular positioning support, independently valid local characteristic-graph colorings can merge tuples requiring different LMF outputs.The motivating alternative is to communicate enough to compute the desired function rather than reconstruct every source value.Source: §I · p. 1
  • The paper contributes an exact global zero-error criterion and conditional conflict graph for valid single-TRP codebook updates.Its alternating DSATUR construction preserves zero-error after accepted updates and is compared with a globally valid contiguous-interval baseline.Source: §I · p. 1
  • The evaluation combines a reproducible three-TRP positioning study with explicit decoder-conflict checks and a measured six-base-station TDoA support-transfer check.The primary numerical study isolates telemetry coding with deterministic range-equivalent timing bins; neither experiment is end-to-end UL-RTOA/NRPPa validation.Source: §I · p. 1
  • The proposed reporting layer builds on existing OAI positioning components and adds support-aware reporting and geometric-consistency checks without changing the SRS procedure or positioning estimator.The paper also identifies an NRPPa/LMF integration architecture and staged OAI validation path.Source: §I · pp. 1–2

II. SYSTEM MODEL AND ZERO-ERROR REQUIREMENT

The model treats positioning telemetry as distributed zero-error computation over a finite geometry-dependent support. Local reports are valid only when their joint report tuple preserves the required service function.

II. SYSTEM MODEL AND ZERO-ERROR REQUIREMENT

  • Each of N reporting TRPs observes a quantized native symbol, and the joint input has a finite feasible support.The support incorporates deployment geometry, quantization, and any nominal uncertainty included at design time.Source: §II · p. 2
  • The deterministic service function can represent a grid cell, service zone, or alarm-relevant decision and includes the estimator and any service-grid projection.Fig. 1 depicts local quantization and coding followed by LMF decoding to the same service-grid cell as the uncompressed pipeline.Source: §II · p. 2, Figure 1 · p. 2
  • Each TRP sends a code index, with idealized rate log2 |Ci| bits per epoch; rate minimization must respect global validity.When report distributions are known, prefix coding can achieve expected length below H(ci(Xi)) + 1 bits.Source: §II · p. 2
  • The global product-partition criterion requires equal aggregate reports on support points to imply equal service outputs, making the decoder well-defined on reachable report tuples.Outputs for report tuples outside the reachable set may be assigned arbitrarily.Source: §II · p. 2
  • On nonrectangular support, separately proper local characteristic-graph colorings can still merge two complete tuples with different function values.For support {(0, 0), (1, 1)}, both local one-color assignments are proper, yet the resulting aggregate reports violate the global criterion.Source: §II · p. 2

III. CONDITIONAL CONFLICT GRAPH CODING

The conditional conflict graph tests a single terminal’s codebook against fixed codebooks at the other terminals. Its coloring condition gives an exact one-terminal update rule for maintaining zero-error decoding.

III. CONDITIONAL CONFLICT GRAPH CODING

  • With the other terminals’ encoders fixed, the conditional conflict graph captures which symbols at terminal i cannot be merged without violating zero-error decoding.The graph may contain self-loops, and with identity codebooks elsewhere it reduces to the ordinary characteristic graph.Source: §III · pp. 2–3
  • A codebook update is zero-error if and only if the conditional graph has no self-loop and the codebook properly colors every non-loop edge.A self-loop makes zero-error impossible for any update while the other encoders remain fixed.Source: §III · pp. 2–3
  • If adjacent symbols receive the same color, support points with matching other-terminal reports produce equal complete reports despite different service outputs.Conversely, a zero-error violation implies a self-loop or a same-color conflict edge.Source: §III · p. 3

A. Alternating construction and verification

The construction alternates single-TRP codebook updates and accepts only globally zero-error updates, then builds a decoder and feasible report set from the resulting codebooks.

A. Alternating construction and verification

  • The algorithm initializes identity codebooks, then updates each TRP using a conditional conflict graph and accepts a DSATUR coloring only after a global zero-error check.The graph is built by grouping support tuples with equal other-terminal reports and connecting pairs with output disagreements.Source: A. Alternating construction and… · p. 3
  • After the updates, the algorithm constructs the decoder from reachable report tuples and defines the feasible set as those tuples.The algorithm returns both together with the codebooks.Source: A. Alternating construction and… · p. 3
  • Across six terminal orders, the construction retains the globally valid result with the smallest sum of ideal rates, using three passes per order.The DSATUR cardinalities are achievable codebook sizes, not claimed chromatic numbers or global optima.Source: A. Alternating construction and… · p. 3
  • TRPs receive only their local lookup tables and encode independently, while the LMF retains the joint decoder and feasible report-tuple set.The contiguous-interval baseline uses the same conditional graphs but restricts color classes to consecutive native bins and checks each update globally.Source: A. Alternating construction and… · p. 3
  • Hashing groups equal other-terminal report tuples before a complete support scan, which provides an executable zero-error certificate.This avoids a quadratic scan over the complete support when identifying groups.Source: A. Alternating construction and… · p. 3

A. Geometry, quantization, and LMF function

The controlled geometry uses three separated TRPs and range-equivalent timing bins; the LMF maps the resulting range-based estimate to a service-grid cell.

A. Geometry, quantization, and LMF function

  • Three spatially separated TRPs and a 220×220 UE-location grid define the design geometry.The TRPs are placed at (0, 0), (1000, 0), and (0, 1000) m.Source: A. Geometry, quantization, and LMF… · p. 3
  • Each propagation distance is quantized into 120 bins over [0, 2 km], yielding 11.8 m range-equivalent timing resolution and a raw ideal rate of 6.907 bits/TRP.The raw rate is log2(120).Source: A. Geometry, quantization, and LMF… · p. 3
  • The estimate is projected onto the 1 km × 1 km service region and assigned to a square cell of length ∆; 48,400 sampled locations produce 12,772 distinct native measurement tuples.The synchronized range-equivalent model omits the common UE transmission-time term, receiver-clock bias, NLOS effects, and SRS estimation errors present in a complete UL-TDOA model.Source: A. Geometry, quantization, and LMF… · p. 3

B. Controlled compression results

In the controlled study, function-aware coding lowers ideal reporting rates while every proposed and baseline codebook remains zero-conflict on the evaluated support.

B. Controlled compression results

  • 21.3–22.1% of the ideal raw rate is saved for service-grid sizes ∆≤100 m.Every proposed and baseline point passes a complete decoder check over all 12,772 tuples, with zero conflicts.Source: B. Controlled compression results · p. 3
  • The valid contiguous-interval baseline remains close to raw reporting because many function-relevant equivalence classes are non-contiguous.The selected order (2, 1, 3) yields an asymmetric allocation; the text attributes the observed difference mainly to update order and heuristic coloring, not intrinsic TRP informativeness.Source: B. Controlled compression results · p. 4

C. Trace-driven support transfer

The paper evaluates support recurrence on independent measured trajectories and outlines how reporting, decoding, safeguards, and staged OAI validation fit into the positioning path.

C. Trace-driven support transfer

  • 83.77% of 15,722 independent test bursts reproduce a native tuple in training support, and recurrent tuples retain the same service decision under native and compressed reporting.The remaining 16.23% are outside certified support and excluded; the measured study uses downlink TDoA rather than uplink UL-RTOA and does not evaluate end-to-end NRPPa transport.Source: C. Trace-driven support transfer · p. 4

V. NRPPA INTEGRATION AND OAI TESTBED PATH

  • The proposed reporting layer adds a local codebook lookup, codebook identifier and color-index transport, LMF decoding, and a feasible-tuple check to the existing positioning transaction.The lookup may run in serving-gNB processing of a TRP measurement.Source: §V · p. 4, Figure 3 · p. 4

A. Protocol semantics and safeguards

  • An experimental Measurement Report extension must not treat a color index as a UL-RTOA value, and unknown codebooks or unsupported symbols or tuples trigger fallback or flagging.Codebook activation must be coordinated; packet savings require ASN.1/PER serialization measurement because log2 Ki does not directly determine byte reduction in a fixed-width IE.Source: A. Protocol semantics and safeguards · p. 4

B. Data path and staged proof of concept

  • The staged OAI path includes synchronized UL-RTOA trace replay, multi-TRP RFsimulator operation, and O-RAN/OTA evaluation of synchronization, multipath, NLOS, and geometry.A single-gNB/UE RFsimulator check passed a random-access Timing Advance value through a lookup table, validating extraction and lookup only—not positioning or NRPPa compression.Source: B. Data path and staged proof of concept · p. 5

C. Timing model, provisioning, and remaining validation

The timing model isolates coding with synchronized range-equivalent values, while the deployment design relies on versioned codebooks and sparse, table-based operations. The implementation footprint includes conditional graph construction and explicit decoder validation.

C. Timing model, provisioning, and remaining validation

  • The encoder can use native quantized UL-RTOA while the LMF retains ordinary differencing, compensation, positioning, and grid projection.The timing model includes an unknown transmission-time term, residual TRP clock/receiver bias, and estimation and propagation error.Source: C. Timing model, provisioning, and… · p. 5
  • A deployed codebook is tied to the measurement definition, active TRPs, support model, service function, and grid resolution; unknown or mixed versions trigger native reporting.Its versioned object stores local lookup tables, decoder, feasible set, validity interval, and integrity value.Source: C. Timing model, provisioning, and… · p. 5
  • Online operation requires one encoder lookup, one decoder lookup, and feasible-set testing.The controlled study uses synchronized range-equivalent values to isolate coding, and remains short of end-to-end UL-RTOA/NRPPa validation.Source: C. Timing model, provisioning, and… · p. 5

D. Implementation footprint and reproducibility

  • Conditional graph construction examines O(Pq) candidate comparisons within equal-context groups, followed by an O(|S|) complete decoder check after each accepted update.The offline construction avoids a direct O(|S|^2) scan over all support pairs.Source: D. Implementation footprint and… · p. 5
  • At Δ = 100 m, the three local codebooks each contain 120 native-bin entries, while only 12,180 of 74,263 possible color tuples are reachable and retained.The retained tuples populate the sparse decoder and consistency table.Source: D. Implementation footprint and… · p. 5

VI. STATIC GEOMETRIC ANOMALY SCREEN

The static screen flags report tuples outside the feasible set, including under injected positive timing bias. Its sensitivity varies with service-grid size, and nominal support misses are not RF false alarms.

VI. STATIC GEOMETRIC ANOMALY SCREEN

  • The experiment draws 30,000 held-out UE positions, reuses them across bias levels, and saturates biased measurements at the largest native bin.Zero-bias support-miss rates are 2.06%, 1.70%, and 0.32% for Δ = 5, 100, and 500 m.Source: §VI · p. 5
  • In a held-out static-screen experiment at one TRP, a 24 m positive range-equivalent bias produced flag probabilities of 53.9%, 39.2%, and 4.9%; coarser service functions reduced reporting rate and sensitivity.The zero-bias point is a support-miss rate, not an RF false-alarm probability.Source: Figure 4 · p. 6, §VI · p. 6
  • Coarser service functions reduce both reporting rate and sensitivity to biased measurements, making the screen's trade-off depend on grid size.The zero-bias point is a finite-grid support-miss rate, not an RF false-alarm probability.Source: §VI · p. 6

VII. DISCUSSION AND CONCLUSION

The paper scopes zero-error to reproducing the service decision on certified support, not to recovering physical position. Its controlled and measured studies report rate reductions, while the measured-data and implementation boundaries remain explicit.

A. Scope and deployment implications

  • Zero-error means the compressed and native reports produce the same grid-cell decision on certified support, not that they recover the true physical UE position.Localization accuracy remains determined by radio conditions, synchronization, geometry, receiver processing, and the estimator.Source: A. Scope and deployment implications · p. 6
  • Static codebooks remain valid only while active TRPs, quantizer, support model, and service function remain unchanged; other changes require coordinated version updates and safe fallback.Larger TRP sets increase support and decoder size, which can be controlled through sampling, uncertainty envelopes, symbol pruning, and repeated-context reuse if final codebooks pass the global decoder test.Source: A. Scope and deployment implications · p. 6

B. Conclusion and Future Directions

  • The controlled three-TRP study reduces ideal reporting rate by 21.3–22.1% for grids up to 100 m, with zero decoder conflicts.The global product-partition criterion and conditional conflict graph preserve the LMF service decision on the declared support.Source: B. Conclusion and Future Directions · p. 6
  • 83.77% of independent test bursts reproduce a training-support tuple and inherit exact service-decision preservation; corresponding codebooks reduce ideal rate by 22.8–35.6% for 2–8 m grids.The measured data are downlink TDoA rather than NRPPa UL-RTOA, and the protocol extension is not implemented end to end.Source: B. Conclusion and Future Directions · p. 6
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