Achievable rate region for three user discrete broadcast channel based on coset codes

We present an achievable rate region for the general three user discrete memoryless broadcast channel, based on nested coset codes. We characterize 3-to-1 discrete broadcast channels, a class of broadcast channels for which the best known coding technique\footnote{We henceforth refer to this as Marton's coding for three user discrete broadcast channel.}, which is obtained by a natural generalization of that proposed by Marton for the general two user discrete broadcast channel, is strictly sub-optimal. In particular, we identify a novel 3-to-1 discrete broadcast channel for which Marton's coding is \textit{analytically} proved to be strictly suboptimal. We present achievable rate regions for the general 3-to-1 discrete broadcast channels, based on nested coset codes, that strictly enlarge Marton's rate region for the aforementioned channel. We generalize this to present achievable rate region for the general three user discrete broadcast channel. Combining together Marton's coding and that proposed herein, we propose the best known coding technique, for a general three user discrete broadcast channel.Comment: A non-additive 3-user discrete broadcast channel is identified for which achievable rate region based on coset codes is analytically proven to be strictly larger than that achievable using unstructured iid codes. This version is submitted to IEEE Transactions on Information Theor

An Algebraic Framework for Multi-Terminal Communication.

We consider the problem of developing coding techniques and characterizing information-theoretic achievable rate regions for the following three multi-terminal communication channels. Firstly, we study an interference channel with three transmitter receiver pairs (3-IC). Secondly, we consider a broadcast channel with three receivers (3-BC), wherein three independent information streams are to be communicated to the three receivers. Thirdly, we consider a two user multiple access channel (MAC) with channel state information distributed at the transmitters (MAC-DSTx). The above channels are assumed discrete, memoryless and used without feedback. Current known coding technique for a general instance of these channels are based on independent unstructured codes. Recognizing the need for codes endowed with algebraic closure properties, we identify three ensembles of coset codes. We propose coding techniques based on these ensembles that exploit their algebraic closure property. We develop tools to characterize information-theoretic performance of the proposed coding techniques. These enable us derive achievable rate regions for a general instance of the above channels. The current known achievable rate regions can be enlarged by gluing together current known coding techniques and the ones proposed herein. Moreover, such an enlargement, as indicated below, is proven to be strict for certain instances. We identify additive and non-additive instances of 3-IC for which the derived achievable rate region is analytically proven to be strictly larger than current known largest. Moreover, for these channels, the proposed coding techniques based on coset codes is capacity achieving. We also identify a vector 3-BC for which the achievable rate region derived herein is analytically proven to be strictly larger than the current known largest. This vector 3-BC is the first known broadcast channel, for which superposition and binning of unstructured independent codes, proposed over three decades ago, can be strictly improved upon. We also identify non-additive and non-symmetric instances of MAC-DSTx for which the proposed coding technique is verified, through computation, to yield strictly larger achievable rate regions. Finally, we develop a coding technique based on nested coset codes to characterize a weaker set of sufficient conditions for the problem of computing sum of sources over a discrete memoryless MAC.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107264/1/arunpr_1.pd

Distributed Structure: Joint Expurgation for the Multiple-Access Channel

In this work we show how an improved lower bound to the error exponent of the memoryless multiple-access (MAC) channel is attained via the use of linear codes, thus demonstrating that structure can be beneficial even in cases where there is no capacity gain. We show that if the MAC channel is modulo-additive, then any error probability, and hence any error exponent, achievable by a linear code for the corresponding single-user channel, is also achievable for the MAC channel. Specifically, for an alphabet of prime cardinality, where linear codes achieve the best known exponents in the single-user setting and the optimal exponent above the critical rate, this performance carries over to the MAC setting. At least at low rates, where expurgation is needed, our approach strictly improves performance over previous results, where expurgation was used at most for one of the users. Even when the MAC channel is not additive, it may be transformed into such a channel. While the transformation is lossy, we show that the distributed structure gain in some "nearly additive" cases outweighs the loss, and thus the error exponent can improve upon the best known error exponent for these cases as well. Finally we apply a similar approach to the Gaussian MAC channel. We obtain an improvement over the best known achievable exponent, given by Gallager, for certain rate pairs, using lattice codes which satisfy a nesting condition.Comment: Submitted to the IEEE Trans. Info. Theor

Secure Compute-and-Forward in a Bidirectional Relay

We consider the basic bidirectional relaying problem, in which two users in a wireless network wish to exchange messages through an intermediate relay node. In the compute-and-forward strategy, the relay computes a function of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes in a Gaussian multiple access (MAC) channel, and the computed function value is forwarded to the user nodes in an ensuing broadcast phase. In this paper, we study the problem under an additional security constraint, which requires that each user's message be kept secure from the relay. We consider two types of security constraints: perfect secrecy, in which the MAC channel output seen by the relay is independent of each user's message; and strong secrecy, which is a form of asymptotic independence. We propose a coding scheme based on nested lattices, the main feature of which is that given a pair of nested lattices that satisfy certain "goodness" properties, we can explicitly specify probability distributions for randomization at the encoders to achieve the desired security criteria. In particular, our coding scheme guarantees perfect or strong secrecy even in the absence of channel noise. The noise in the channel only affects reliability of computation at the relay, and for Gaussian noise, we derive achievable rates for reliable and secure computation. We also present an application of our methods to the multi-hop line network in which a source needs to transmit messages to a destination through a series of intermediate relays.Comment: v1 is a much expanded and updated version of arXiv:1204.6350; v2 is a minor revision to fix some notational issues; v3 is a much expanded and updated version of v2, and contains results on both perfect secrecy and strong secrecy; v3 is a revised manuscript submitted to the IEEE Transactions on Information Theory in April 201