Convolutional Coded Poisson Receivers

TL;DR

This paper introduces convolutional coded Poisson receivers (CCPRs) that integrate spatial coupling techniques, expanding the stability region for packet decoding in multi-class traffic channels and approaching theoretical bounds.

Contribution

The paper develops a new CCPR framework with spatial coupling, derives stability bounds, and demonstrates improved stability regions through density evolution analysis.

Findings

Stability region of CCPRs is larger than CPRs.

CCPRs approach outer bounds with large window sizes.

Multiclass CCPRs have a recursively evaluable stability boundary.

Abstract

In this paper, we present a framework for convolutional coded Poisson receivers (CCPRs) that incorporates spatially coupled methods into the architecture of coded Poisson receivers (CPRs). We use density evolution equations to track the packet decoding process with the successive interference cancellation (SIC) technique. We derive outer bounds for the stability region of CPRs when the underlying channel can be modeled by a $\phi$-ALOHA receiver. The stability region is the set of loads that every packet can be successfully received with a probability of 1. Our outer bounds extend those of the spatially-coupled Irregular Repetition Slotted ALOHA (IRSA) protocol and apply to channel models with multiple traffic classes. For CCPRs with a single class of users, the stability region is reduced to an interval. Therefore, it can be characterized by a percolation threshold. We study the potential threshold by the potential function of the base CPR used for constructing a CCPR. In addition, we prove that the CCPR is stable under a technical condition for the window size. For the multiclass scenario, we recursively evaluate the density evolution equations to determine the boundaries of the stability region. Numerical results demonstrate that the stability region of CCPRs can be enlarged compared to that of CPRs by leveraging the spatially-coupled method. Moreover, the stability region of CCPRs is close to our outer bounds when the window size is large.