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![Fig. 4. WER performance of RM [8] and PR codes at block length n = 20...](profile/Mahyar-Shirvanimoghaddam/publication/354302302/figure/fig4/AS:1068160191049733@1631680643532/WER-performance-of-RM-8-and-PR-codes-at-block-length-n-20-with-ML-decoding-The_Q320.jpg)
![Fig. 5. WER performance of RM [8] and PR codes at block length n = 32...](profile/Mahyar-Shirvanimoghaddam/publication/354302302/figure/fig5/AS:1068160191053826@1631680643580/WER-performance-of-RM-8-and-PR-codes-at-block-length-n-32-with-ML-decoding-The_Q320.jpg)
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... also closely approach the UB (12) at sufficiently high SNRs. Moreover, when k = 32 and R = 0.25, normal approximation [7] is not accurate, however, UB (12) provides a better approximation of the minimum achievable WER at relatively high SNRs. We also show the Hamming weight distribution of the PR code with k = 32 at different block lengths in Fig. 7. As can be seen the PR code with a properly chosen primitive polynomial has a weight distribution that can be well approximated by (9), therefore the union bound in (12) can well approximate the WER at relatively high ...
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... Coding sequences have been devised for massive access, including Walsh sequences and decorrelated sequences [40], or almost affinely disjoint subspaces [41], where it is possible to characterize the Hamming weight distribution of pseudorandom sequences [42], and Khachatrian-Martirossian construction to enable K > n users signal in n dimensions simultaneously, where K ≈ 1 2 n log 2 n is the optimal scaling [2, Slides 57-59]. Furthermore, it has been shown that when the inputs are constrained to ±1, it is possible to have K n. ...
The fifth-generation of wireless communication networks is required to support a range of use cases such as enhanced mobile broadband (eMBB), ultra-reliable, low-latency communications (URLLC), massive machine-type communications (mMTCs), with heterogeneous data rate, delay, and power requirements. The 4G LTE air interface uses extra overhead to enable scheduled access, which is not justified for small payload sizes. We employ a random access communication model with retransmissions for multiple users with small payloads at the low spectral efficiency regime. The radio resources are split non-orthogonally in the time and frequency dimensions. Retransmissions are combined via Hybrid Automatic Repeat reQuest (HARQ) methods, namely Chase Combining and Incremental Redundancy with a finite buffer size constraint $C_{\sf buf}$. We determine the best scaling for the spectral efficiency (SE) versus signal-to-noise ratio (SNR) per bit and for the user density versus SNR per bit, for the sum-optimal regime and when the interference is treated as noise, using a Shannon capacity approximation. Numerical results show that the scaling results are applicable over a range of $\eta$, $T$, $C_{\sf buf}$, $J$, at low received SNR values. The proposed analytical framework provides insights for resource allocation in general random access systems and specific 5G use cases for massive URLLC uplink access.
