Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bounds for Joint Detection and Decoding on the Binary-Input AWGN Channel

Simon Obermüller, Jannis Clausius, Marvin Geiselhart, Stephan ten Brink

TL;DR

This work establishes finite-blocklength bounds for joint detection and decoding (JDD) on the binary-input AWGN channel, analyzing two schemes: decoder-aided detection (DAD) and hybrid preamble and energy detection (HyPED). It derives both achievability and converse bounds for the information rate and a general blocklength bound for JDD, showing that DAD can rapidly approach the rate of synchronous transmission, outperforming preamble-based detection and distribution-based bounds. The results are supported by numerical bounds and simulations of practical codes, demonstrating substantial gains in inclusive error rate and suggesting practical design trade-offs between detection and decoding performance. The findings contribute to a deeper theoretical understanding of asynchronous JDD limits and guide the design of low-overhead receivers for IoT, mMTC, and URLLC.

Abstract

For asynchronous transmission of short blocks, preambles for packet detection contribute a non-negligible overhead. To reduce the required preamble length, joint detection and decoding (JDD) techniques have been proposed that additionally utilize the payload part of the packet for detection. In this paper, we analyze two instances of JDD, namely hybrid preamble and energy detection (HyPED) and decoder-aided detection (DAD). While HyPED combines the preamble with energy detection for the payload, DAD also uses the output of a channel decoder. For these systems, we propose novel achievability and converse bounds for the rates over the binary-input additive white Gaussian noise (BI-AWGN) channel. Moreover, we derive a general bound on the required blocklength for JDD. Both the theoretical bound and the simulation of practical codebooks show that the rate of DAD quickly approaches that of synchronous transmission.

Bounds for Joint Detection and Decoding on the Binary-Input AWGN Channel

TL;DR

This work establishes finite-blocklength bounds for joint detection and decoding (JDD) on the binary-input AWGN channel, analyzing two schemes: decoder-aided detection (DAD) and hybrid preamble and energy detection (HyPED). It derives both achievability and converse bounds for the information rate and a general blocklength bound for JDD, showing that DAD can rapidly approach the rate of synchronous transmission, outperforming preamble-based detection and distribution-based bounds. The results are supported by numerical bounds and simulations of practical codes, demonstrating substantial gains in inclusive error rate and suggesting practical design trade-offs between detection and decoding performance. The findings contribute to a deeper theoretical understanding of asynchronous JDD limits and guide the design of low-overhead receivers for IoT, mMTC, and URLLC.

Abstract

For asynchronous transmission of short blocks, preambles for packet detection contribute a non-negligible overhead. To reduce the required preamble length, joint detection and decoding (JDD) techniques have been proposed that additionally utilize the payload part of the packet for detection. In this paper, we analyze two instances of JDD, namely hybrid preamble and energy detection (HyPED) and decoder-aided detection (DAD). While HyPED combines the preamble with energy detection for the payload, DAD also uses the output of a channel decoder. For these systems, we propose novel achievability and converse bounds for the rates over the binary-input additive white Gaussian noise (BI-AWGN) channel. Moreover, we derive a general bound on the required blocklength for JDD. Both the theoretical bound and the simulation of practical codebooks show that the rate of DAD quickly approaches that of synchronous transmission.
Paper Structure (14 sections, 2 theorems, 26 equations, 3 figures)

This paper contains 14 sections, 2 theorems, 26 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System Model and Performance Metrics
  4. Decoder-aided Detection and Decoding
  5. Heuristic Hybrid Preamble and Energy Detection
  6. Distribution-based Detection Bounds for Finite Length
  7. Joint Detection and Decoding Schemes and their Bounds
  8. Converse Bound on the Required Blocklength
  9. Achievability Bound for Decoder-aided Detection
  10. Preamble-Energy Detection
  11. Numerical Results
  12. Bounds
  13. Performance of Actual Systems
  14. Conclusion and Outlook

Key Result

Theorem 1

For a system with noise variance $\sigma^2$ and required error rates $P_\mathrm{FA} \leq \epsilon_\mathrm{FA}$ and $P_\mathrm{MD} \leq \epsilon_\mathrm{MD}$, the blocklength $n$ is lower bounded by

Figures (3)

  • Figure 1: Frame structure for conventional, separate detection and decoding (top) and JDD (bottom).
  • Figure 2: Achievability (dashed) and converse (solid) bounds on the rate $R$ for $E_\mathrm{S}/N_0=-3\,\mathrm{dB}$, $\epsilon_\mathrm{FA}=10^{-4}$, $\epsilon_\mathrm{MD}=10^{-4}$, and $\epsilon_\mathrm{IE}=10^{-3}$ for different detection schemes. Performances of DAD achieved in Monte Carlo simulation are marked by \ref{['plt:system']}.
  • Figure 3: $P_\mathrm{IE}$ over SNR of achievability (dashed) and converse (solid) bounds and simulated systems (dotted) for $\epsilon_\mathrm{FA}=\epsilon_\mathrm{MD}= 10^{-4}$ and blocklength $n=84$ and $k=12$. The simulated plots are marked by \ref{['plt:pie_dad']} for DAD, \ref{['plt:pie_hyped']} for HyPED and \ref{['plt:pie_preamble']} for preamble-based detection.

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2