Chen Feng

A Unified Discretization Approach to Compute–Forward: From Discrete to Continuous Inputs

Chen Feng, Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore

Compute–forward is a coding technique that enables receiver(s) in a network to directly decode one or more linear combinations of the transmitted codewords. Initial efforts focused on Gaussian channels and derived achievable rate regions via nested lattice codes and single-user (lattice) decoding as well as sequential (lattice) decoding. Recently, these results have been generalized to discrete memoryless channels via nested linear codes and joint typicality coding, culminating in a simultaneous-decoding rate region for recovering one or more linear combinations from K users. Using a discretization approach, this paper translates this result into a simultaneous-decoding rate region for a wide class of continuous memoryless channels, including the important special case of Gaussian channels. Additionally, this paper derives a single, unified expression for both discrete and continuous rate regions via an algebraic generalization of Rényi’s information dimension.

2022

Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations

Chen Feng, Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore

Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations of codewords can sometimes be decoded more efficiently than codewords themselves. The present work further develops this framework by studying the simultaneous decoding of multiple messages. Specifically, consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with "single-user" or sequential decoding can yield better achievable rates. For instance, the compute-forward problem examines the scenario of recovering L

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Towards an Algebraic Network Information Theory: Distributed Lossy Computation of Linear Functions

Chen Feng, Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore

Consider the important special case of the K-user distributed source coding problem where the decoder only wishes to recover one or more linear combinations of the sources. The work of Körner and Marton demonstrated that, in some cases, the optimal rate region is attained by random linear codes, and strictly improves upon the best-known achievable rate region established via random i.i.d. codes. Recent efforts have sought to develop a framework for characterizing the achievable rate region for nested linear codes via joint typicality encoding and decoding. Here, we make further progress along this direction by proposing an achievable rate region for simultaneous joint typicality decoding of nested linear codes. Our approach generalizes the results of Körner and Marton to computing an arbitrary number of linear combinations and to the lossy computation setting.

2019

A Joint Typicality Approach to Compute–Forward

Chen Feng, Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore

This paper presents a joint typicality framework for encoding and decoding nested linear codes in 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 a linear combination 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, our framework provides some valuable insights on establishing the optimal decoding rate region for compute–forward by considering joint decoders, progressing beyond most previous works that consider successive cancellation decoding. Specifically, this paper establishes an achievable rate region for simultaneously decoding two linear combinations of nested linear codewords from K senders.

2018

Towards an algebraic network information theory: Simultaneous joint typicality decoding

Chen Feng, Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore

Recent work has employed joint typicality encoding and decoding of nested linear code ensembles to generalize the compute-forward strategy to discrete memoryless multiple-access channels (MACs). An appealing feature of these nested linear code ensembles is that the coding strategies and error probability bounds are conceptually similar to classical techniques for random i.i.d. code ensembles. In this paper, we consider the problem of recovering K linearly independent combinations over a K-user MAC, i.e., recovering the messages in their entirety via nested linear codes. While the MAC rate region is well-understood for random i.i.d. code ensembles, new techniques are needed to handle the statistical dependencies between competing codeword K-tuples that occur in nested linear code ensembles.

2017

A joint typicality approach to compute-forward

Chen Feng, Michael Christoph Gastpar, Sung Hoon Lim

A general framework for analyzing linear codes with joint typicality encoders and decoders is presented. Using this approach, we provide a new perspective on the compute-forward framework. In particular, an achievable rate region for computing the weighted sum of nested linear codewords over a discrete memoryless multiple access channel (MAC) is established. When specialized to the Gaussian MAC, we recover the lattice-based compute-forward rate region by Nazer and Gastpar, providing a unified treatment over both discrete memoryless and Gaussian networks. By further utilizing simultaneous joint typicality decoders, we provide a joint decoding rate region for computing two linear combinations of nested linear codewords from K-senders. Our result provides some insight on one of the main open problems in the compute-forward framework, the joint decoding rate region of compute-forward.

2015

Near-Infrared Guided Color Image Dehazing

Chen Feng, Sabine Süsstrunk

Near-infrared (NIR) light has stronger penetration capability than visible light due to its long wavelength, thus being less scattered by particles in the air. This makes it desirable for image dehazing to unveil details of distant objects in landscape photographs. In this paper, we propose an improved image dehazing scheme using a pair of color and NIR images, which effectively estimates the airlight color and transfers details from the NIR. A two-stage dehazing method is proposed by exploiting the dissimilarity between RGB and NIR for airlight color estimation, followed by a dehazing procedure through an optimization framework. Experiments on captured haze images show that our method can achieve substantial improvements on the detail recovery and the color distribution over the existing image dehazing algorithms.

2013