Exact Joint MAP Decoding for Unknown Load and Message Counts in Orthogonal Unsourced Random Access
Abstract
We study joint recovery of the load (the number of active users) and message-count vector in type-based unsourced random access with very short messages. Each user's k-bit message activates one of M=2k orthogonal resources; coherent collisions therefore produce a noisy, unnormalized histogram of the transmitted messages. For arbitrary load and message priors, we propose an exact joint maximum-a-posteriori (MAP) decoder. Known-load allocation is separable and convex; our contribution is to show that the solutions for all candidate loads are nested prefixes of one greedy chain. Scoring these prefixes with the Bayesian posterior terms jointly estimates the load and message-count vector in O(M+Kmaxlog M) time. We compare the proposed joint MAP decoder with marginal MAP, three scalar-count two-stage receivers, oracle-load MAP, a sum-only receiver, and a soft-pilot receiver. For K∼Unif{0:60} at 2 dB, the proposed decoder cuts the no-activity false-alarm probability from 25.9% to 3.5% relative to the Bayesian-count two-stage receiver and, conditioned on K≥1, reduces normalized count error by 21.4%. The advantage concentrates under idle or sparse uncertain activity, whereas support-count processing approaches joint MAP when the possible loads are well separated. We also prove that the sum-only statistic is insufficient and quantify prior and amplitude mismatch. The model targets synchronized, power-controlled, very-short payloads rather than general URA.
Related
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BibTeX
@misc{kazemi2026exact,
title = {{Exact Joint MAP Decoding for Unknown Load and Message Counts in Orthogonal Unsourced Random Access}},
author = {Mohammad Kazemi and Mert Ozates},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20389},
eprint = {2610.20389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20389},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Joint MAP Decoding for Unknown Load and Message Counts in Orthogonal Unsourced Random Access
AU - Mohammad Kazemi
AU - Mert Ozates
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20389
UR - https://arxiv.org/abs/2610.20389
AB - We study joint recovery of the load (the number of active users) and message-count vector in type-based unsourced random access with very short messages. Each user's k-bit message activates one of M=2^k orthogonal resources; coherent collisions therefore produce a noisy, unnormalized histogram of the transmitted messages. For arbitrary load and message priors, we propose an exact joint maximum-a-posteriori (MAP) decoder. Known-load allocation is separable and convex; our contribution is to show that the solutions for all candidate loads are nested prefixes of one greedy chain. Scoring these prefixes with the Bayesian posterior terms jointly estimates the load and message-count vector in O(M+K_maxlog M) time. We compare the proposed joint MAP decoder with marginal MAP, three scalar-count two-stage receivers, oracle-load MAP, a sum-only receiver, and a soft-pilot receiver. For K∼Unif{0:60} at 2 dB, the proposed decoder cuts the no-activity false-alarm probability from 25.9% to 3.5% relative to the Bayesian-count two-stage receiver and, conditioned on K≥1, reduces normalized count error by 21.4%. The advantage concentrates under idle or sparse uncertain activity, whereas support-count processing approaches joint MAP when the possible loads are well separated. We also prove that the sum-only statistic is insufficient and quantify prior and amplitude mismatch. The model targets synchronized, power-controlled, very-short payloads rather than general URA.
ER -