A Joint Typicality Approach to Algebraic Network Information Theory

Abstract

This paper presents a joint typicality framework for encoding and decoding nested linear codes for multi-user networks. This framework provides a new perspective on compute-forward within the context of discrete memoryless networks. In particular, it establishes an achievable rate region for computing the weighted sum of nested linear codewords over a discrete memoryless multiple-access channel (MAC). When specialized to the Gaussian MAC, this rate region recovers and improves upon the lattice-based compute-forward rate region of Nazer and Gastpar, thus providing a unified approach for discrete memoryless and Gaussian networks. Furthermore, this framework can be used to shed light on the joint decoding rate region for compute-forward, which is considered an open problem. Specifically, this work establishes an achievable rate region for simultaneously decoding two linear combinations of nested linear codewords from K senders.

69 pages, 11 figures, submitted to the IEEE Transactions on Information Theory

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• Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations
• Gaussian Multiple Access via Compute-and-Forward
• Coded Network Function Virtualization: Fault Tolerance via In-Network Coding
• How to Compute Modulo Prime-Power Sums
• Communication versus Computation: Duality for multiple access channels and source coding
• Homologous Codes for Multiple Access Channels
• Rate-Diverse Gaussian Multiple Access: Efficient Encoder and Decoder Designs