Silas L. Fong

Variable-Rate Linear Network Coding

We introduce variable-rate linear network coding for single-source finite acyclic network. In this problem, the source of a network transmits messages at different rates in different time sessions and every nonsource node in the network decodes the messages if possible. We propose two efficient algorithms for implementing variable-rate linear network coding under different circumstances.

Non-Asymptotic Achievable Rates for Energy-Harvesting Channels Using Save-and-Transmit

This paper investigates the information-theoretic limits of energy-harvesting (EH) channels in the finite blocklength regime. The EH process is characterized by a sequence of i.i.d. random variables with finite variances. We use the save-andtransmit strategy proposed by Ozel and Ulukus (2012) together with Shannons non-asymptotic achievability bound to obtain lower bounds on the achievable rates for both additive white Gaussian noise channels and discrete memoryless channels under EH constraints. The first-order terms of the lower bounds of the achievable rates are equal to C and the second-order (backoff from capacity) terms are proportional to -√log n/n, where n denotes the blocklength and C denotes the capacity of the EH channel, which is the same as the capacity without the EH constraints. The constant of proportionality of the backoff term is found and qualitative interpretations are provided.

Asymptotic expansions for the AWGN channel with feedback under a peak power constraint

This paper investigates the asymptotic expansion for the size of block codes defined for the additive white Gaussian noise (AWGN) channel with feedback under the following setting: A peak power constraint is imposed on every transmitted codeword (i.e., maximum per-codeword power constraint), and the average error probability of decoding the transmitted message is non-vanishing as the blocklength increases. It is well-known that the presence of feedback does not increase the first-order asymptotics (i.e., capacity) in the asymptotic expansion for the AWGN channel. The main contribution of this paper is proving an upper bound on the asymptotic expansion for the AWGN channel with feedback. Combined with existing achievability results for the AWGN channel, our result implies that the presence of feedback does not improve the second- and third-order asymptotics.

Strong converse theorems for classes of multimessage multicast networks: A Rényi divergence approach

This paper establishes that the strong converse holds for some classes of discrete memoryless multimessage multicast networks (DM-MMNs) whose corresponding cut-set bounds are tight, i.e., coincide with the set of achievable rate tuples. The strong converse for these classes of DM-MMNs implies that all sequences of codes with rate tuples belonging to the exterior of the cut-set bound have average error probabilities that tend to one. Examples in the classes of DM-MMNs include wireless erasure networks, DM-MMNs consisting of independent discrete memoryless channels (DMCs), and single-destination DM-MMNs consisting of independent DMCs with destination feedback. Our proof technique leverages the properties of the Rényi divergence.

Practical network coding on three-node point-to-point relay networks

We study the three-node point-to-point relay network which consists of two terminal nodes and one relay node between them and investigate practical network coding schemes for the network. The rate region achievable by the practical network coding schemes is obtained, and a procedure for constructing the linear network codes that achieve the rate pairs in the achievable rate region is presented. In addition, we show that the use of network coding rather than routing alone enlarges the achievable rate region, in particular increases the maximum equal-rate throughput.

Two-Hop Interference Channels: Impact of Linear Schemes

We consider the two-hop interference channel (IC), which consists of two source-destination pairs communicating with each other via two relays. We analyze the degrees of freedom (DoF) of this network when the relays are restricted to perform linear schemes, and the channel gains are constant (i.e., slow fading). We show that, somewhat surprisingly, by using vector-linear strategies at the relays, it is possible to achieve 4/3 sum-DoF when the channel gains are real. The key achievability idea is to alternate relaying coefficients across time, to create different end-to-end interference structures (or topologies) at different times. Although each of these topologies has only 1 sum-DoF, we manage to achieve 4/3 by coding across them. Furthermore, we develop a novel outer bound that matches our achievability, hence characterizing the sum-DoF of two-hop ICs with linear schemes. We also generalize the result to the multi-antenna setting, where each node has M antennas, and the relays are restricted to one-shot linear schemes. We further extend the result to the case of complex channel gains, by intuitively viewing each complex node with M antennas as a real node with 2M antennas, and characterize the sum-DoF to be 2M - 1/3.

Cut-set bound for generalized networks

In a network, a node is said to incur a delay if its encoding of each transmitted symbol involves only its received symbols obtained before the time slot in which the transmitted symbol is sent (hence the transmitted symbol sent in a time slot cannot depend on the received symbol obtained in the same time slot). A node is said to incur no delay if its received symbol obtained in a time slot is available for encoding its transmitted symbol sent in the same time slot. In the classical discrete memoryless network (DMN), every node incurs a delay. A well-known result for the classical DMN is the cut-set outer bound. In this paper, we generalize the model of the DMN in such a way that some nodes may incur no delay, and we obtain the cut-set outer bound for the generalized DMN.

Capacity bounds for full-duplex two-way relay channel with feedback

We consider a two-way relay channel (TRC) in which two terminals exchange their messages with the help of a relay between them. The two terminals transmit messages to the relay through the Multiple Access Channel (MAC) and the relay transmits messages to the two terminals through the Broadcast Channel (BC). We assume that the MAC and the BC do not interfere with each other, and each terminal receives signals only from the relay but not the other terminal. All the nodes are assumed to be full-duplex, which means that they can transmit and receive information at the same time. We present with detailed proofs an outer bound on the capacity region of each of the discrete memoryless TRC with feedback and the Gaussian TRC with feedback. We show that the outer bound for the discrete memoryless TRC with feedback is loose for some TRC.

On the Scaling Exponent of Polar Codes for Binary-Input Energy-Harvesting Channels

This paper investigates the scaling exponent of polar codes for binary-input energy-harvesting (EH) channels with infinite-capacity batteries. The EH process is characterized by a sequence of independent and identically distributed random variables with finite variances. The scaling exponent μ of polar codes for a binary-input memoryless channel (BMC) qY|X with capacity C(qY|X) characterizes the closest gap between the capacity and the non-asymptotic achievable rates in the following way. For a fixed average error probability e ∈ (0, 1), the closest gap between the capacity C(qY|X) and a non-asymptotic achievable rate Rn for a length-n polar code scales as n-1/μ, i.e., min{|C(qY|X) - Rn|} = O(n-1/μ). It has been shown that the scaling exponent μ for any binary-input memoryless symmetric channel with C(qY|X) ∈ (0, 1) lies between 3.579 and 4.714, where the upper bound 4.714 was shown by an explicit construction of polar codes. Our main result shows that 4.714 remains to be a valid upper bound on the scaling exponent for any binary-input EH channel, i.e., a BMC subject to additional EH constraints. Our result thus implies that the EH constraints do not worsen the rate of convergence to capacity if polar codes are employed. An auxiliary contribution of this paper is that the upper bound on μ holds for binary-input memoryless asymmetric channels.

Cut-set bound for generalized networks with positive delay

In a network, a node is said to incur a delay if its encoding of each transmitted symbol involves only its received symbols obtained before the time slot in which the transmitted symbol is sent (hence the transmitted symbol sent in a time slot cannot depend on the received symbol obtained in the same time slot). A node is said to incur no delay if its received symbol obtained in a time slot is available for encoding its transmitted symbol sent in the same time slot. In this paper, we investigate the generalized discrete memoryless network (DMN) where some nodes may incur no delay. We call the capacity region of the generalized DMN under the constraint that every node incurs a delay the positive-delay region. We establish the cut-set outer bound on the positive-delay region. In addition, we use our cut-set outer bound to show that in some two-node generalized DMN, the positive-delay region is strictly smaller than the capacity region.