Information-theoretic arguments focus on modeling the reliability of information transmission, assuming availability of infinite data at sources, thus ignoring randomness in message generation times at the respective sources. However, in information transport networks, not only is reliable transmission important, but also stability, i.e., finiteness of mean delay in- curred by messages from the time of generation to the time of successful reception. Usually, delay analysis is done separately using queueing-theoretic arguments, whereas reliable information transmission is studied using information theory. In this thesis, we investigate these two important aspects of data communication jointly by suitably combining models from these two fields. In particular, we model scheduled communication of messages , that arrive in a random process, (i) over multiaccess channels, with either independent decoding or joint decoding, and (ii) over degraded broadcast channels. The scheduling policies proposed permit up to a certain maximum number of messages for simultaneous transmission. In the first part of the thesis, we develop a multi-class discrete-time processor-sharing queueing model, and then investigate the stability of this queue. In particular, we model the queue by a discrete-time Markov chain defined on a countable state space, and then establish (i) a sufficient condition for c-regularity of the chain, and hence positive recurrence and finiteness of stationary mean of the function c of the state, and (ii) a sufficient condition for transience of the chain. These stability results form the basis for the conclusions drawn in the thesis. The second part of the thesis is on multiaccess communication with random message arrivals. In the context of independent decoding, we assume that messages can be classified into a fixed number of classes, each of which specifies a combination of received signal power, message length, and target probability of decoding error. Each message is encoded independently and decoded independently. In the context of joint decoding, we assume that messages can be classified into a fixed number of classes, each of which specifies a message length, and for each of which there is a message queue. From each queue, some number of messages are encoded jointly, and received at a signal power corresponding to the queue. The messages are decoded jointly across all queues with a target probability of joint decoding error. For both independent decoding and joint decoding, we derive respective discrete- time multiclass processor-sharing queueing models assuming the corresponding information-theoretic models for the underlying communication process. Then, for both the decoding schemes, we (i) derive respective outer bounds to the stability region of message arrival rate vectors achievable by the class of stationary scheduling policies, (ii) show for any mes- sage arrival rate vector that satisfies the outer bound, that there exists a stationary “state-independent” policy that results in a stable system for the corresponding message arrival process, and (iii) show that the stability region of information arrival rate vectors, in the limit of large message lengths, equals an appropriate information-theoretic capacity region for independent decoding, and equals the information-theoretic capacity region for joint de-coding. For independent decoding, we identify a class of stationary scheduling policies, for which we show that the stability region in the limit of large maximum number of simultane-ous transmissions is independent of the received signal powers, and each of which achieves a spectral efficiency of 1 nat/s/Hz in the limit of large message lengths. In the third and last part of the thesis, we show that the queueing model developed for multiaccess channels with joint decoding can be used to model communication over degraded broadcast channels, with superposition encoding and successive decoding across all queues. We then show respective results (i), (ii), and (iii), stated above.

A Broadcast Channel is a communication path between a single source and two or more receivers or users. The source intends to communicate independent information to the users. A particular case of interest is the Gaussian Broadcast Channel (GBC) where the noise at each user is additive white Gaussian noise (AWGN). The capacity region of GBC is well known and the input to the channel is distributed as Gaussian. The capacity region of another special case of GBC namely Fading Broadcast Channel (FBC)was given in [Li and Goldsmith, 2001]and was shown that superposition of Gaussian codes is optimal for the FBC (treated as a vector degraded Broadcast Channel). The capacity region obtained when the input to the channel is distributed uniformly over a finite alphabet(Constellation)is termed as Constellation Constrained(CC) capacity region [Biglieri 2005]. In this thesis the CC capacity region for two-user GBC and the FBC are obtained. In case of GBC the idea of superposition coding with input from finite alphabet and CC capacity was explored in [Hupert and Bossert, 2007]but with some limitations. When the participating individual signal sets are nearly equal i.e., given total average power constraint P the rate reward α (also the power sharing parameter) is approximately equal to 0.5, we show via simulation that with rotation of one of the signal sets by an appropriate angle the CC capacity region is maximally enlarged. We analytically derive the expression for optimal angle of rotation. In case of FBC a heuristic power allocation procedure called finite-constellation power allocation procedure is provided through which it is shown (via simulation)that the ergodic CC capacity region thus obtained completely subsumes the ergodic CC capacity region obtained by allocating power using the procedure given in[Li and Goldsmith, 2001].It is shown through simulations that rotating one of the signal sets by an optimal angle (obtained by trial and error method)for a given α maximally enlarges the ergodic CC capacity region when finite-constellation power allocation is used. An expression for determining the optimal angle of rotation for the given fading state, is obtained. And the effect of rotation is maximum around the region corresponding to α =0.5. For both GBC and FBC superposition coding is done at the transmitter and successive decoding is carried out at the receivers.