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Coding for the unsourced B-channel with erasures: enhancing the linked loop code

William W. Zheng, Jamison R. Ebert, Stefano Rini, Jean-Francois Chamberland

TL;DR

This work extends unsourced random access to the unsourced B-channel with erasures (UBCE), where outputs preserve symbol multiplicity via a multiset union. It proposes an enhanced linked-loop code (eLLC) with tail-biting structure, multiple rounds of successive interference cancellation (SIC), and flexible rates, formalized as an $(LJ,RLJ)_{(M,J)}$ code with parity updates $\mathbf{p}(\ell) = \sum_{r=1}^{M} \mathbf{w}([\ell-r-1]_L) \mathbf{G}_{([\ell-r-1]_L,\ell)}$. Through simulations (e.g., $J=16$, varying $L$, $M$, and $p_e$ with $T=1$), the eLLC exhibits lower payload dropping and hallucination probabilities than the LLC and outperforms a tree-code baseline for a given active-user load, highlighting the method’s potential for scalable URA in multiplicity-preserving channels. The results underscore the benefit of flexible root selection and multi-round SIC in improving decoding robustness on the UBCE.

Abstract

In [1], the linked loop code (LLC) is presented as a promising code for the unsourced A-channel with erasures (UACE). The UACE is an unsourced multiple access channel in which active users' transmitted symbols are erased with a given probability and the channel output is obtained as the union of the non-erased symbols. In this paper, we extend the UACE channel model to the unsourced B-channel with erasures (UBCE). The UBCE differs from the UACE in that the channel output is the multiset union, or bag union, of the non-erased input symbols. In other words, the UBCE preserves the symbol multiplicity of the channel output while the UACE does not. Both the UACE and UBCE find applications in modeling aspects of unsourced random access. The LLC from [1] is enhanced and shown to outperform the tree code over the UBCE. Findings are supported by numerical simulations.

Coding for the unsourced B-channel with erasures: enhancing the linked loop code

TL;DR

This work extends unsourced random access to the unsourced B-channel with erasures (UBCE), where outputs preserve symbol multiplicity via a multiset union. It proposes an enhanced linked-loop code (eLLC) with tail-biting structure, multiple rounds of successive interference cancellation (SIC), and flexible rates, formalized as an code with parity updates . Through simulations (e.g., , varying , , and with ), the eLLC exhibits lower payload dropping and hallucination probabilities than the LLC and outperforms a tree-code baseline for a given active-user load, highlighting the method’s potential for scalable URA in multiplicity-preserving channels. The results underscore the benefit of flexible root selection and multi-round SIC in improving decoding robustness on the UBCE.

Abstract

In [1], the linked loop code (LLC) is presented as a promising code for the unsourced A-channel with erasures (UACE). The UACE is an unsourced multiple access channel in which active users' transmitted symbols are erased with a given probability and the channel output is obtained as the union of the non-erased symbols. In this paper, we extend the UACE channel model to the unsourced B-channel with erasures (UBCE). The UBCE differs from the UACE in that the channel output is the multiset union, or bag union, of the non-erased input symbols. In other words, the UBCE preserves the symbol multiplicity of the channel output while the UACE does not. Both the UACE and UBCE find applications in modeling aspects of unsourced random access. The LLC from [1] is enhanced and shown to outperform the tree code over the UBCE. Findings are supported by numerical simulations.
Paper Structure (7 sections, 13 equations, 2 figures, 2 algorithms)

This paper contains 7 sections, 13 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Channel Model
  3. Binary Vector Representation
  4. Performance Metrics for the UBCE
  5. Enhanced Linked-Loop Code
  6. Simulation Results
  7. Conclusions

Figures (2)

  • Figure 1: Characterization of the performance of the eLLC in terms of $P_{\textrm{PHP}}$ and $P_{\textrm{PDP}}$ under $K=100, L=16, J=16$. Here, text labels on points denotes the probability of erasure $p_e$.
  • Figure 2: Maximal $p_e$ s.t. $P_{\text{PDP}}\leq 0.1$ vs. $K$. Tree code here is adapted to the B-channel setting combined with SIC.

Theorems & Definitions (3)

  • Definition 2.1: Payload Dropping Probability
  • Definition 2.2: Payload Hallucination Probability
  • Remark 1: $\bigcup$ vs $\biguplus$