Bounds on the maximum coding rate of multiple-access channels and feedback channels

Licentiatavhandling, 2016

We provide upper and lower bounds on the coding rate of multiple-access channels (MACs) and feedback channels. Traditional MACs have been extensively studied under the assumption of availability of perfect channel state information (CSI). In Paper A we relax this assumption for a Rayleigh block-fading MAC and provide bounds on the sum-rate capacity. The upper bound relies on a dual formula for channel capacity and on the assumption that the users can cooperate perfectly. The lower bound is derived assuming a noncooperative scenario where each user employs unitary space-time modulation (independently from the other users). Numerical results show that the gap between the upper and the lower bound is small already at moderate SNR values. Motivated by the growth of machine-type communication, in Paper B we present a finite-blocklength analysis of the throughput and the average delay achievable in a wireless system where i) several uncoordinated users transmit short coded packets, ii) interference is treated as noise, and iii) 1-bit feedback from the intended receivers enables the use of a simple automatic repeat request protocol. Our analysis exploits the recent results on the characterization of the maximum coding rate at finite blocklength and finite block-error probability by Polyanskiy, Poor, and Verd\'u (2010), and by Yang \emph{et al.} (2014). For a given number of information bits, we determine the coded-packet size that maximizes the per-user throughput and minimizes the average delay. Finally, in Paper C, we present nonasymptotic achievability and converse bounds on the maximum coding rate (for a fixed average error probability and a fixed average blocklength) of variable-length full-feedback (VLF) and variable-length stop-feedback (VLSF) codes operating over a binary erasure channel (BEC). For the VLF setup, the achievability bound relies on a scheme that maps each message onto a variable-length Huffman codeword and then repeats each bit of the codeword until it is received correctly. The converse bound is inspired by the meta-converse framework by Polyanskiy, Poor, and Verd\'u (2010) and relies on binary sequential hypothesis testing. For the case of zero error probability, our achievability and converse bounds match. For the VLSF case, we provide achievability bounds that exploit the following feature of BEC: the decoder can assess the correctness of its estimate by verifying whether the chosen codeword is the only one that is compatible with the erasure pattern.