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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.
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Coding for the Unsourced A-Channel with Erasures: The Linked Loop Code
The A -channel is a noiseless multiple access channel in which users simultaneously transmit Q-ary symbols and the receiver observes the set of transmitted symbols, but not their multiplicities. An A-channel is said to be unsourced if, additionally, users' transmissions are encoded across time using a common codebook and decoding of the transmitted messages is done without regard to the identities of the active users. An interesting variant of the unsourced A -channel is the unsourced A-channel with erasures (UACE), in which transmitted symbols are erased with a given independent and identically distributed probability. In this paper, we focus on designing a code that enables a list of transmitted codewords to be recovered despite the erasures of some of the transmitted symbols. To this end, we propose the linked-loop code (LLC), which uses parity bits to link each symbol to the previous M symbols in a tail-biting manner, i.e., the first symbols of the transmission are linked to the last ones. The decoding process occurs in two phases: the first phase decodes the codewords that do not suffer from any erasures, and the second phase attempts to recover the erased symbols using the available parities. We compare the performance of the LLC over the UACE with other codes in the literature and argue for the effectiveness of the construction. Our motivation for studying the UACE comes from its relevance in machine-type communication and coded compressed sensing.
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- PAR ID:
- 10545216
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 978-9-4645-9360-0
- Page Range / eLocation ID:
- 1534 to 1538
- Subject(s) / Keyword(s):
- Forward Error Correction Signal Processing Encoding Decoding
- Format(s):
- Medium: X
- Location:
- Helsinki, Finland
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/EUSIPCO58844.2023.10289955
