Random Coding Error Exponents for the Two-User Interference Channel

This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, etc.). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. Also, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive single-letter formulas for the random coding error exponents. We compare our results with the best known lower bound on the error exponent, and show that our exponents can be strictly better. Then, in the second part of this paper, we consider more complicated coding ensembles, and find a lower bound on the error exponent associated with the celebrated Han-Kobayashi (HK) random coding ensemble, which is based on superposition coding.Comment: accepted IEEE Transactions on Information Theor

Channel Detection in Coded Communication

We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to detect the set which contains the prevailing channel. We begin with the simplified case where each of the sets is a singleton. For any given code, we derive the optimum detection/decoding rule in the sense of the best trade-off among the probabilities of decoding error, false alarm, and misdetection, and also introduce sub-optimal detection/decoding rules which are simpler to implement. Then, various achievable bounds on the error exponents are derived, including the exact single-letter characterization of the random coding exponents for the optimal detector/decoder. We then extend the random coding analysis to general sets of channels, and show that there exists a universal detector/decoder which performs asymptotically as well as the optimal detector/decoder, when tuned to detect a channel from a specific pair of channels. The case of a pair of binary symmetric channels is discussed in detail.Comment: Submitted to IEEE Transactions on Information Theor

A Rate-Splitting Approach To Robust Multiuser MISO Transmission

For multiuser MISO systems with bounded uncertainties in the Channel State Information (CSI), we consider two classical robust design problems: maximizing the minimum rate subject to a transmit power constraint, and power minimization under a rate constraint. Contrary to conventional strategies, we propose a Rate-Splitting (RS) strategy where each message is divided into two parts, a common part and a private part. All common parts are packed into one super common message encoded using a shared codebook and decoded by all users, while private parts are independently encoded and retrieved by their corresponding users. We prove that RS-based designs achieve higher max-min Degrees of Freedom (DoF) compared to conventional designs (NoRS) for uncertainty regions that scale with SNR. For the special case of non-scaling uncertainty regions, RS contrasts with NoRS and achieves a non-saturating max-min rate. In the power minimization problem, RS is shown to combat the feasibility problem arising from multiuser interference in NoRS. A robust design of precoders for RS is proposed, and performance gains over NoRS are demonstrated through simulations.Comment: To appear in ICASSP 201