Performance Analysis of Rateless Codes in an ALOHA Wireless Ad Hoc Network

In this paper, we study the performance of rateless error correction codes in a wireless ad hoc network (WANET). The salient features of a WANET are Rayleigh fading, constant power transmission, pure ALOHA as the channel access protocol, and the nodes being modeled by a homogeneous space-time Poisson point process. For such a WANET, this paper quantifies the rate density (RD) and the dynamic variations of the packet transmission time by deriving an upper bound on the CCDF of the packet transmission time. The performance of rateless codes is compared with two benchmarks, i.e., the ergodic RD (ERD) and the RD of fixed-rate codes. The proposed rateless coding scheme does not require time diversity as each packet is transmitted within a single coherence time. Yet, it is shown that the RD can be up to 76% and 50% of the ERD in noise- and interference-limited regimes, respectively. Thus, the presented network nearly achieves the ERD while requiring significantly shorter delays. This paper shows that a low-complexity Gaussian receiver with a nearest neighbor decoder has almost the performance of an ideal matched receiver. We also show that power control in the form of channel thresholding leads to a 72% gain in the RD relative to a constant power transmission.