Homologous Codes for Multiple Access Channels

Building on recent development by Padakandla and Pradhan, and by Lim, Feng, Pastore, Nazer, and Gastpar, this paper studies the potential of structured nested coset coding as a complete replacement for random coding in network information theory. The roles of two techniques used in nested coset coding to generate nonuniform codewords, namely, shaping and channel transformation, are clarified and illustrated via the simple example of the two-sender multiple access channel. While individually deficient, the optimal combination of shaping and channel transformation is shown to achieve the same performance as traditional random codes for the general two-sender multiple access channel. The achievability proof of the capacity region is extended to the multiple access channels with more than two senders, and with one or more receivers. A quantization argument consistent with the construction of nested coset codes is presented to prove achievability for their Gaussian counterparts. These results open up new possibilities of utilizing nested coset codes with the same generator matrix for a broader class of applications

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

Capacity, Error Exponent, and Structural Results for Communication Networks

In various multi-terminal communication scenarios, contrary to point-to-point communication, characterization of fundamental limits such as capacity and error exponent is still an open problem. We study such fundamental limits and the structure of optimality achieving codes. This thesis consists of two parts: in the first part, we investigate the role of algebraic structures in multi-terminal communications. We show the necessity of various types of algebraic structure in capacity achieving codes and argue that the lack of such structures in the conventional random codes leads to their sub-optimality. We develop a new class of partially structured codes called quasi-structured code (QSC). Such codes span the spectrum from completely structured to completely unstructured codes. It is shown that the application of QSCs leads to improvements over the current coding strategies for many problems including distributed source coding and multiple-access channel (MAC) with feedback. In the second part of the thesis, we study the optimal error exponent in various multi-terminal communication scenarios. We derive a lower and upper bound on the error exponent of discrete memoryless MAC with noiseless feedback and variable-length codes (VLCs). The bounds increase linearly with respect to a specific Euclidean distance measure defined between the transmission rate pair and the capacity boundary. The bounds are shown to be tight for specific classes of MACs.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149959/1/mohsenhd_1.pd

Group, Lattice and Polar Codes for Multi-terminal Communications.

We study the performance of algebraic codes for multi-terminal communications. This thesis consists of three parts: In the rst part, we analyze the performance of group codes for communications systems. We observe that although group codes are not optimal for point-to-point scenarios, they can improve the achievable rate region for several multi-terminal communications settings such as the Distributed Source Coding and Interference Channels. The gains in the rates are particularly signicant when the structure of the source/channel is matched to the structure of the underlying group. In the second part, we study the continuous alphabet version of group/linear codes, namely lattice codes. We show that similarly to group codes, lattice codes can improve the achievable rate region for multi-terminal problems. In the third part of the thesis, we present coding schemes based on polar codes to practically achieve the performance limits derived in the two earlier parts. We also present polar coding schemes to achieve the known achievable rate regions for multi-terminal communications problems such as the Distributed Source Coding, the Multiple Description Coding, Broadcast Channels, Interference Channels and Multiple Access Channels.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108876/1/ariaghs_1.pd