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Sparse Regression Codes for Non-coherent SIMO channels

Sai Dinesh Kancharana, Madhusudan Kumar Sinha, Arun Pachai Kannu

TL;DR

The paper tackles short-blocklength communication over non-coherent flat-fading SIMO channels by leveraging SPARCs with no pilot symbols. It introduces a non-coherent ML-based decoder (MLMP) and a parallel variant (P-MLMP), along with a rigorous sparsity-based recovery bound, and complements these with a SPARC-AMP decoder (SAMP) backed by MMSE denoising and state evolution. The study demonstrates that MLMP/P-MLMP outperform existing sparse-recovery methods and that SPARC-based schemes surpass pilot-based polar codes and non-coherent polar codes in BLER at relevant code rates. The results highlight the practical viability of pilotless SPARC-based coding for HRLLC scenarios and point to future work extending to MIMO frequency-selective settings.

Abstract

Motivated by hyper-reliable low-latency communication in 6G, we consider error control coding for short block lengths in multi-antenna fading channels. In general, the channel fading coefficients are unknown at both the transmitter and receiver, which is referred to as non-coherent channels. Conventionally, pilot symbols are transmitted to facilitate channel estimation, causing power and bandwidth overhead. Our paper considers sparse regression codes (SPARCs) for non-coherent flat-fading channels without using pilots. We develop a novel greedy decoder for SPARC using maximum likelihood principles, referred to as maximum likelihood matching pursuit (MLMP). MLMP works based on successive combining principles as opposed to conventional greedy algorithms, which are based on successive cancellation. We also obtain the noiseless perfect recovery condition for our successive combining algorithm. In addition, we develop an approximate message passing (AMP) SPARC decoder for the non-coherent flat fading model. Using simulation studies, we show that the MLMP decoder for SPARC outperforms AMP and other greedy decoders. Also, SPARC with MLMP decoder outperforms polar codes employing pilot-based channel estimation and polar codes with non-coherent decoders.

Sparse Regression Codes for Non-coherent SIMO channels

TL;DR

The paper tackles short-blocklength communication over non-coherent flat-fading SIMO channels by leveraging SPARCs with no pilot symbols. It introduces a non-coherent ML-based decoder (MLMP) and a parallel variant (P-MLMP), along with a rigorous sparsity-based recovery bound, and complements these with a SPARC-AMP decoder (SAMP) backed by MMSE denoising and state evolution. The study demonstrates that MLMP/P-MLMP outperform existing sparse-recovery methods and that SPARC-based schemes surpass pilot-based polar codes and non-coherent polar codes in BLER at relevant code rates. The results highlight the practical viability of pilotless SPARC-based coding for HRLLC scenarios and point to future work extending to MIMO frequency-selective settings.

Abstract

Motivated by hyper-reliable low-latency communication in 6G, we consider error control coding for short block lengths in multi-antenna fading channels. In general, the channel fading coefficients are unknown at both the transmitter and receiver, which is referred to as non-coherent channels. Conventionally, pilot symbols are transmitted to facilitate channel estimation, causing power and bandwidth overhead. Our paper considers sparse regression codes (SPARCs) for non-coherent flat-fading channels without using pilots. We develop a novel greedy decoder for SPARC using maximum likelihood principles, referred to as maximum likelihood matching pursuit (MLMP). MLMP works based on successive combining principles as opposed to conventional greedy algorithms, which are based on successive cancellation. We also obtain the noiseless perfect recovery condition for our successive combining algorithm. In addition, we develop an approximate message passing (AMP) SPARC decoder for the non-coherent flat fading model. Using simulation studies, we show that the MLMP decoder for SPARC outperforms AMP and other greedy decoders. Also, SPARC with MLMP decoder outperforms polar codes employing pilot-based channel estimation and polar codes with non-coherent decoders.
Paper Structure (34 sections, 2 theorems, 50 equations, 7 figures, 1 table, 1 algorithm)

This paper contains 34 sections, 2 theorems, 50 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Existing literature on SPARCs
  3. Our contribution
  4. Outline of the paper
  5. Notations
  6. Background/Preliminaries
  7. SPARC encoding
  8. MUB Matrices
  9. SPARC for unknown fading channel
  10. Maximum likelihood matching pursuit
  11. Maximum Likelihood Detector
  12. Maximum Likelihood Matching Pursuit
  13. Parallel-MLMP
  14. Performance Guarantees of MLMP Algorithm
  15. Modified Block-OMP (MBOMP)
  16. ...and 19 more sections

Key Result

Lemma 1

For the non-coherent SIMO flat fading channel, the MLMP coincides with the maximum likelihood detector for SPARCs when sparsity $K=1$.

Figures (7)

  • Figure 1: Comparison of state evolution parameters and empirical MSE for (256,124) SPARCs at Eb/N0 = 18 dB.
  • Figure 2: Comparison of MLMP with existing sparse recovery algorithms
  • Figure 3: Parallel-MLMP at different code rates
  • Figure 4: Performance of SAMP at increasing code rate
  • Figure 5: Performance of SAMP with online SE
  • ...and 2 more figures

Theorems & Definitions (5)

  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • proof