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Short-Boundary Signaling for Asynchronous Grant-Free Control-to-Control Communications

Massimo Battaglioni, Dania De Crescenzo, Edoardo Carnevali, Enrico Paolini

arXiv:2610.21729v1cs.ITmath.IT

TL;DR

Asynchronous grant-free receivers must locate the start and end of variable-length transmissions, while earlier decoder-aided designs tie boundary length to codeword length. The paper separates those lengths and uses a CNN with boundary-scaled waveform input and codeword-length decoder input. In the considered setting, L_b=16 gives the proposed receiver its highest effective payload efficiency at all tested loads, while the GLRT benchmark performs best at L_b=64 for λ≥10^-3.

  • Problem

    Asynchronous grant-free acquisition must identify both boundaries of variable-length commands, but earlier decoder-aided designs couple boundary and codeword lengths, imposing framing overhead on short commands.

    Source: §I · p. 1

  • Method

    The paper treats boundary length as an independent design parameter and uses a CNN whose waveform input scales with that length while decoder information retains codeword length.

    Source: §I · p. 1, 2) Branch 2 · p. 4

  • Results

    L_b=16 gives the proposed CNN the highest effective payload efficiency at every simulated activation rate, while the GLRT benchmark with truncated sequences is best at L_b=64 for λ≥10^-3.

    Source: §V · pp. 5–6

  • Takeaways & Limitations

    In the considered setting, the boundary length need not be inherited from the channel code, and the shortest tested boundary provides the highest effective payload efficiency throughout the investigated traffic range.

    Source: §VI · p. 6

    The idealized MSE analysis does not characterize whether refinement can be initiated, and the initial estimate can also include an interference projection when the candidate window overlaps an interferer.

    Source: B. Channel-Estimation Penalty and… · p. 3

Abstract

from arXiv · show

In asynchronous grant-free access, receivers must detect variable-length transmissions and identify their start and end. Existing decoder-aided receivers use start and tail sequences which are as long as one codeword, causing substantial overhead for short commands. This paper treats the boundary (i.e., start and tail sequences) length as an independent design parameter and proposes a convolutional neural network that detects both boundaries from the received waveform and the decoder soft output. Its waveform input size decreases with the boundary length, while the decoder input keeps the codeword length, so the boundary can be shortened without altering the decoder. Analysis and simulations quantify the resulting tradeoff among payload efficiency, collision exposure, and boundary detection. The results show that the proposed receiver can exploit very short boundaries: in the considered setting, the shortest tested boundary, $L_{\mathrm{b}}=16$, yields the highest effective payload efficiency at all tested loads, whereas a correlation-based benchmark with the same sequences performs best with $L_{\mathrm{b}}=64$ at moderate and high loads.

I. INTRODUCTION

Grant-free C2C access avoids access grants, but asynchronous variable-length commands require the receiver to identify both packet boundaries before reconstruction and cancellation. This paper makes boundary length independent of codeword length, addressing the overhead imposed on short commands by earlier decoder-aided designs.

I. INTRODUCTION

  • Grant-free C2C lets a controller access the shared channel when a command is generated, while asynchronous acquisition must infer both packet boundaries from the received signal.Boundary identification is required before reconstruction and interference cancellation; command length is unavailable during acquisition.Source: §I · p. 1
  • Earlier decoder-aided receivers use a start sequence, variable-length LDPC codewords, and a tail sequence, but require the sequences and one codeword to share a length.That coupling prevents independent boundary-duration optimization and is particularly costly for short commands.Source: §I · p. 1
  • The paper makes boundary length an independent physical-layer design parameter and adapts the decoder-aided receiver with separate input dimensions for waveform and decoder information.The waveform branch scales with boundary length, while the decoder-information branch retains codeword length n.Source: §I · p. 1

II. SYSTEM MODEL AND PERFORMANCE METRICS

  • The paper organizes its analysis around the system model and performance metrics, boundary-shortening analysis, receiver design, numerical results, and conclusions.The supplied system-model passage defines [a, b] as the integer interval from a through b.Source: §I · p. 1, §II · p. 1

A. Transmission and Channel Model

The system models asynchronous grant-free communication among distributed controllers sharing a wireless channel. Commands comprise start and tail sequences around one or more LDPC codewords, with boundary length varied independently of codeword length.

A. Transmission and Channel Model

  • Controllers exchange variable-length commands over a shared wireless channel, with one transmit antenna per transmission and N_R receive antennas at the receiver.The model adopts the asynchronous grant-free C2C setting and channel model of [12].Source: A. Transmission and Channel Model · p. 2
  • Command generations follow a Poisson process of rate λ, and each command is sent through N_rep replicas placed in a local virtual frame.Controllers use BPSK and a common binary (n, k) LDPC code; a command contains one or more codewords.Source: A. Transmission and Channel Model · p. 2
  • A command consists of a start sequence, ι codewords, and a tail sequence, with its length determined by the codewords and the two boundaries.The start and tail sequences have lengths L_s and L_t, while each codeword has length n.Source: A. Transmission and Channel Model · p. 2
  • Unlike, [12], the model does not require boundary lengths to equal codeword length; it studies the symmetric design L_s = L_t = L_b using prefixes of shared length-128 sequences.Virtual frames need not align across controllers, and replicas may overlap partially or completely.Source: A. Transmission and Channel Model · p. 2

B. Receiver Operations

The receiver searches for a start sequence to establish tentative alignment and channel estimation, then uses decoding and boundary validation before cancelling replicas. Tail detection combines waveform observations with decoder information.

B. Receiver Operations

  • A detected start provides tentative payload alignment and known symbols for channel estimation, after which maximal-ratio combining is applied across receive antennas.The resulting estimate is used to decode the command's codewords and is later refined over the reconstructed replica.Source: B. Receiver Operations · p. 2
  • At each n-symbol block boundary, tail detection distinguishes another codeword from the start of the tail using waveform samples and decoder outputs.The decoder supplies bit LLRs and a convergence flag; for L_b < n, the waveform detector uses the first L_b samples while the decoder processes the full block.Source: B. Receiver Operations · p. 2
  • After decoding and boundary validation, the receiver cancels all replicas, re-estimates each replica's channel over its reconstructed waveform, and repeats detection and decoding through SIC rounds.Replica positions are assumed known once one replica is decoded.Source: B. Receiver Operations · p. 2

C. Performance Metrics

The paper measures payload efficiency, end-to-end effective payload efficiency, and packet loss rate. The effective measure accounts for transmitted-symbol overhead and unsuccessful recovery, while PLR tracks command units not accepted after SIC.

C. Performance Metrics

  • Average payload efficiency is the expected information bits carried by a command divided by the expected length of a single replica, excluding replica repetition.The paper defines payload efficiency for a command containing ι codewords and averages over the random codeword count I.Source: C. Performance Metrics · p. 2
  • Effective payload efficiency counts correctly recovered command units against all transmitted symbols across replicas, including overlaps separately.It accounts for boundary overhead, replica repetition, and unsuccessful recovery, and reduces to average payload efficiency divided by N_rep when all command units are recovered.Source: C. Performance Metrics · p. 3
  • Packet loss rate is the probability that a transmitted command unit is not accepted as valid after all replicas and SIC rounds are processed.Erroneously recovered commands that are accepted as valid are instead counted in the undetected packet error rate.Source: C. Performance Metrics · p. 3

A. Payload Efficiency and Collision Exposure

The section relates boundary shortening to payload efficiency and collision exposure. It gives a concrete efficiency gain and frames collision exposure as distinct from end-to-end packet loss.

A. Payload Efficiency and Collision Exposure

B. Channel-Estimation Penalty and Refinement

Shorter start sequences reduce the known samples available for initial channel estimation. An idealized refinement analysis quantifies how correctly reconstructed codewords can reduce that penalty while noting conditions the model omits.

B. Channel-Estimation Penalty and Refinement

IV. DEEP-LEARNING-BASED LENGTH-DECOUPLED RECEIVER

The proposed receiver decouples boundary length from codeword length in a joint start-and-tail detector. Its two branches combine signal-level and decoder information while the LDPC decoder continues to process n-symbol blocks.

IV. DEEP-LEARNING-BASED LENGTH-DECOUPLED RECEIVER

  • The receiver jointly detects start and tail sequences using signal-level features for starts and decoder information for tails.Source: §IV · p. 4
  • Boundary length is independent of codeword length n, allowing Lb<n while the LDPC decoder continues operating on n-symbol blocks.Source: §IV · p. 4
  • Two parallel input branches merge into shared fully connected layers that output independent start and tail probabilities, with labels that are not mutually exclusive.Source: §IV · p. 4

1) Branch 1:

Branch 1 processes a window sized to the boundary sequences and uses the MRC observation alongside known sequences. Its input and computation shrink with boundary length.

1) Branch 1:

  • Branch 1 takes windows of length Lb and concatenates the known start and tail sequences with Lb MRC samples in Y1.Source: 1) Branch 1 · p. 4
  • The complex MRC observation retains its imaginary component because it reflects noise, interference, and channel-estimation errors, despite real-valued BPSK boundary sequences.Source: 1) Branch 1 · p. 4
  • Since Lb is decoupled from n, shortening it directly reduces Y1's size and Branch 1's computation cost.Source: 1) Branch 1 · p. 4

2) Branch 2:

Branch 2 retains a decoder-width input while supplying different evidence for start and tail detection. One network handles both boundaries, with a windowing scheme matched to each detection phase.

2) Branch 2:

  • Branch 2 keeps its input width n, matched to the decoder block length, even as the waveform input uses the boundary length L_b.This separates the decoder input dimension from the boundary-dependent waveform input.Source: 2) Branch 2 · p. 4
  • For start detection, Y2 contains replicated average normalized correlations with the known start sequence; for tail detection, it contains decoder LLRs and a convergence flag.Source: 2) Branch 2 · p. 4
  • A single trained network performs both tasks; start windows slide by one symbol, while tail windows advance by one decoder block and use decoder information.Y1 contains the first L_b samples in both phases.Source: 2) Branch 2 · p. 4
  • For n=128 and N_it=20, the forward pass costs approximately 0.91, 1.05, 1.35, and 1.94 MFLOP for L_b=16, 32, 64, and 128, respectively.Source: 2) Branch 2 · p. 4

V. NUMERICAL RESULTS

The numerical results compare boundary lengths and receiver architectures in an indoor industrial setting. The proposed CNN achieves the highest effective payload efficiency with L_b=16 at every tested load, while the GLRT benchmark favors L_b=64 at moderate and high loads.

V. NUMERICAL RESULTS

  • The evaluation adopts an indoor industrial setting with four receive antennas, two replicas, and a (128, 64) LDPC code; edge restrictions make reported PLR optimistic relative to steady-state operation.The observation interval is 20,000 symbols, and the restrictions reduce interference near its edges.Source: §V · pp. 4–5
  • For E[I]=3, η̄info is 0.462, 0.429, 0.375, and 0.300 for L_b=16, 32, 64, and 128, respectively; the Poisson-rain surrogate captures the overlap ordering and traffic trend.The shortest boundary raises average payload efficiency by 53.8% relative to the full-length design.Source: §V · p. 5, Figure 1 · p. 5
  • At λ=10^-3, the proposed receiver achieves higher detection probabilities than the GLRT benchmark; its tail detection depends less on L_b than its start detection.The CNN uses decoder LLRs and a convergence flag for tail detection.Source: Figure 2 · p. 5, §V · p. 5
  • From λ=5·10^-3 onward, the CNN with L_b=16 has the lowest PLR; the GLRT benchmark instead has the lowest PLR at L_b=64 at moderate and high loads.At λ=10^-3 and 2.5·10^-3, CNN configurations L_b=16 and 32 have comparable PLR.Source: Figure 3 · p. 6, §V · p. 6
  • L_b=16 gives the proposed CNN the highest effective payload efficiency at every simulated activation rate, while the GLRT benchmark favors L_b=64 for λ≥10^-3.The GLRT's detection losses at L_b=16 and 32 outweigh their overhead advantage.Source: §V · p. 6

VI. CONCLUSION

The paper makes boundary length an independent design parameter and analyzes the tradeoffs of shortening it. In the considered setting, the shortest tested boundary provides the highest effective payload efficiency across the investigated traffic range.

VI. CONCLUSION

  • Shorter boundaries improve framing efficiency and the probability of avoiding temporal overlap, while idealized MSE analysis quantifies decision-directed refinement.Source: §VI · p. 6
  • The proposed CNN shortens its waveform branch while retaining the complete decoder LLR trajectory for tail detection.Source: §VI · p. 6
  • The shortest tested boundary gives the proposed CNN the highest effective payload efficiency across activation rates.Fig. 4 plots effective payload efficiency versus activation rate for boundary lengths and receiver architectures.Source: Figure 4 · p. 6, §VI · p. 6

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