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Low-Complexity Block-Based Decoding Algorithms for Short Block Channels

Mody Sy, Raymond Knopp

TL;DR

The paper tackles the challenge of decoding very short block-length transmissions in 5G NR, where ML-based decoding of Reed-Muller codes paired with DMRS is computationally intensive. It introduces a block-based encoding/decoding framework using First-Order Reed-Muller codes $RM(1,m)$ and decodes via Fast Hadamard Transform to achieve quasi-linear complexity $O(N'\log N')$, significantly reducing processing time. A key enhancement is adaptive DMRS/data power adjustment, characterized by a parameter $\beta$, which narrows the performance gap to ML, achieving gains up to several dB in practical scenarios and improving benefits with more receive antennas. Overall, the approach offers a viable, low-latency path for short-packet decoding in 5G/6G URLLC contexts while maintaining near-ML performance under realistic channel conditions.

Abstract

This paper presents low-complexity block-based encoding and decoding algorithms for short block length channels. In terms of the precise use-case, we are primarily concerned with the baseline 3GPP Short block transmissions in which payloads are encoded by Reed-Muller codes and paired with orthogonal DMRS. In contemporary communication systems, the short block decoding often employs the utilization of DMRS-based least squares channel estimation, followed by maximum likelihood decoding. However, this methodology can incur substantial computational complexity when processing long bit length codes. We propose an innovative approach to tackle this challenge by introducing the principle of block/segment encoding using First-Order RM Codes which is amenable to low-cost decoding through block-based fast Hadamard transforms. The Block-based FHT has demonstrated to be cost-efficient with regards to decoding time, as it evolves from quadric to quasi-linear complexity with a manageable decline in performance. Additionally, by incorporating an adaptive DMRS/data power adjustment technique, we can bridge/reduce the performance gap and attain high sensitivity, leading to a good trade-off between performance and complexity to efficiently handle small payloads.

Low-Complexity Block-Based Decoding Algorithms for Short Block Channels

TL;DR

The paper tackles the challenge of decoding very short block-length transmissions in 5G NR, where ML-based decoding of Reed-Muller codes paired with DMRS is computationally intensive. It introduces a block-based encoding/decoding framework using First-Order Reed-Muller codes and decodes via Fast Hadamard Transform to achieve quasi-linear complexity , significantly reducing processing time. A key enhancement is adaptive DMRS/data power adjustment, characterized by a parameter , which narrows the performance gap to ML, achieving gains up to several dB in practical scenarios and improving benefits with more receive antennas. Overall, the approach offers a viable, low-latency path for short-packet decoding in 5G/6G URLLC contexts while maintaining near-ML performance under realistic channel conditions.

Abstract

This paper presents low-complexity block-based encoding and decoding algorithms for short block length channels. In terms of the precise use-case, we are primarily concerned with the baseline 3GPP Short block transmissions in which payloads are encoded by Reed-Muller codes and paired with orthogonal DMRS. In contemporary communication systems, the short block decoding often employs the utilization of DMRS-based least squares channel estimation, followed by maximum likelihood decoding. However, this methodology can incur substantial computational complexity when processing long bit length codes. We propose an innovative approach to tackle this challenge by introducing the principle of block/segment encoding using First-Order RM Codes which is amenable to low-cost decoding through block-based fast Hadamard transforms. The Block-based FHT has demonstrated to be cost-efficient with regards to decoding time, as it evolves from quadric to quasi-linear complexity with a manageable decline in performance. Additionally, by incorporating an adaptive DMRS/data power adjustment technique, we can bridge/reduce the performance gap and attain high sensitivity, leading to a good trade-off between performance and complexity to efficiently handle small payloads.
Paper Structure (7 sections, 13 equations, 5 figures, 1 table)

This paper contains 7 sections, 13 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Block-based Channel Coding For Short Data
  4. Block-based Encoding Principle
  5. Block-based Decoding via FHT
  6. Numerical Results
  7. Conclusion

Figures (5)

  • Figure 1: General resource mapping
  • Figure 2: Block-based RM(1, M) encoding of Short block -length :Transmitter end.
  • Figure 3: Block-based Hadamard/Fast Hadamard Transform based decoding: Receiver end.
  • Figure 4: Block Error Rate, 11 bits, 2 PRB(16 REs=data, 8 REs=DMRS), Block-based decoding via HT & FHT based decoders vs ML decoder, Adaptative DMRS/data Power Adjustment, Unknown Channel State Information (CSI), nRx = 2,4, 8, Rayleigh Fading Channel.
  • Figure 5: Block Error Rate, 11 bits, 2 PRB(16 REs=data, 8 REs=DMRS), Block-based decoding via HT & FHT based decoders vs ML decoder, Adaptative DMRS/data Power Adjustment, Unknown Channel State Information (CSI), ( $4\times4$) MIMO, Rayleigh Fading Channel.