Coding theorems for random access communication over compound channel

Zheng Wang, Jie Luo
2011 2011 IEEE International Symposium on Information Theory Proceedings  
1 Random access communication is used in practical systems to deliver bursty short messages. Because users only transmit occasionally, it is often difficult for the receiver to keep track of the time varying wireless channel states. Under this motivation, we develop channel coding theorems for random multiple access communication over compound channels with finite codeword length. Error performance bound and asymptotic error probability scaling laws are derived. We found that the results also
more » ... the results also help in deriving error performance bounds for the random multiple access system where the receiver is only interested in decoding messages from a user subset. I. INTRODUCTION In a series of recent works [1][2], information theoretic channel coding was extended to distributed random multiple access communication where users determine their codes and communication rates individually, without sharing rate information with the receiver. Due to the lack of rate coordination, reliable message recovery in random access communication is not always possible. Receiver in this case decodes the transmitted messages only if a pre-determined reliability requirement is met, otherwise the receiver reports a collision. In [1], it was shown that the fundamental performance limitation of a random multiple access system can be characterized using an achievable rate region. Asymptotically as the codeword length is taken to infinity, the receiver is able to recover the messages reliably if the communication rate vector happens to be inside the rate region, and to reliably report a collision if the rate vector happens to be outside the region. The achievable rate region was shown to coincide with the Shannon information rate region without a convex hull operation [1]. In [2], the result was further strengthened to a rate and error probability scaling law. Achievable error probability bound with finite codeword length was also obtained [2]. In both [1] and [2], state of the communication channel is assumed known at the receiver. However, because random access communication deals with bursty short messages, channel access of a user is often fractional. This makes channel estimation and tracking very difficult at the receiver. It is therefore an important task to understand the fundamental system performance when the communication channel is not perfectly known. In this paper, we illustrate how coding theorems developed in [1] [2] can be extended to random
doi:10.1109/isit.2011.6034287 dblp:conf/isit/WangL11 fatcat:jeiykidl7fbxvef2z5vghvgu2i