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.

As a generalization of Irregular Repetition Slotted ALOHA (IRSA), the probabilistic framework of coded Poisson receivers (CPR) offers a unified approach to analyze coded multiple access with successive interference cancellation (SIC). One crucial performance metric of CPRs is the stability region in which every packet can be successfully received with probability 1. In this paper, we use the potential function for convolutional Low Density Parity Check (LDPC) codes to derive the potential function for CPRs. Based on such a potential function, we derive three thresholds: the single-system threshold$G_{s}^{*}$(for the original CPRs), the potential threshold$G_{conv}^{*}$(for the convolutional CPRs), and the potential upper bound$G_{up}^{*}$. We prove that$G_{s}^{*} < G_{conv}^{*} < G_{up}^{*}$• Our numerical results show that these thresholds match very well with existing works for D-fold ALOHA.

As an abstraction and generalization of various coded random access schemes in the literature, the probabilistic framework of coded Poisson receivers (CPR) with multiple traffic classes is a tentative solution for providing differentiated services for uplink transmissions in a single network. One crucial performance metric of CPRs is the stability region in which every packet can be successfully received with probability 1. In this paper, we derive upper bounds for the stability region of CPRs when the underlying channel can be modeled by a ϕ-ALOHA receiver. Our upper bounds generalize those for the Irregular Repetition Slotted ALOHA (IRSA) protocol and can also be used for other channel models with multiple traffic classes.

Most existing works on analyzing the performance of a random ensemble of low-density parity-check (LDPC) codes assume that the degree distributions of the two ends of a randomly selected edge are independent. In the paper, we take one step further and consider ensembles of LDPC codes with degree-degree correlations. For this, we propose two methods to construct an ensemble of degree-degree correlated LDPC codes. We then derive a system of density evolution equations for such degree-degree correlated LDPC codes over a binary erasure channel (BEC). By conducting extensive numerical experiments, we show how the degree-degree correlation affects the performance of LDPC codes. Our numerical results show that LDPC codes with negative degree-degree correlation could improve the maximum tolerable erasure probability. Moreover, increasing the negative degree-degree correlation could lead to better unequal error protection (UEP) design.