Bike Xie

Optimal exchange of packets for universal recovery in broadcast networks

Consider an arbitrarily connected broadcast network of N nodes that all wish to recover k desired packets. Each node begins with a subset of the desired packets and broadcasts messages to its neighbors. For the case where nodes must transmit an integer number of packets, this paper provides necessary and sufficient conditions which characterize the set of all transmission schemes that permit universal recovery (in which every node learns all k packets). By relaxing the integer transmission constraint, this paper gives a computable lower-bound on the amount of information required to be broadcast to achieve universal recovery. Furthermore, a network-coding-based scheme (computable in polynomial time) can always achieve this lower bound if packet splitting is permitted. In this way, packet splitting can provide a significant reduction in the amount of communication required for universal recovery. For cliques with N nodes, this paper shows that splitting the packet into N - 1 chunks allows the lower bound to be achieved with high probability.

A mutual information invariance approach to symmetry in discrete memoryless channels

There are numerous notions of symmetry for discrete memoryless channels. A common goal of these various definitions is that the capacity may be easily computed once the channel is declared to be symmetric. In this paper we focus on a class of definitions of symmetry characterized by the invariance of the channel mutual information over a group of permutations of the input distribution. For definitions of symmetry within this class, we give a simple proof of the optimality of the uniform distribution. The fundamental channels are all symmetric with a general enough definition of symmetry. This paper provides a definition of symmetry that covers these fundamental channels along with a proof that is simple enough to find itself on the chalkboard of even the most introductory class in information theory.

Optimal Transmission Strategy and Explicit Capacity Region for Broadcast Z Channels

This paper provides an explicit expression for the capacity region of the two-user broadcast Z channel and proves that the optimal boundary can be achieved by independent encoding of each user. Specifically, the information messages corresponding to each user are encoded independently and the OR of these two encoded streams is transmitted. Nonlinear turbo codes that provide a controlled distribution of ones and zeros are used to demonstrate a low-complexity scheme that operates close to the optimal boundary.

Optimal natural encoding scheme for discrete multiplicative degraded broadcast channels

Certain degraded broadcast channels (DBCs) have the property that the boundary of the capacity region can be achieved by an encoder that combines independent codebooks (one for each receiver) using the same single-letter function that adds distortion to the channel. We call this the natural encoder for the DBC. Natural encoders are known to achieve the capacity region boundary of the broadcast Gaussian channel, and the broadcast binary-symmetric channel. Recently, they have also been shown to achieve the capacity region of the broadcast Z channel. This paper shows that natural encoding achieves the capacity region boundary for discrete multiplicative DBCs. The optimality of the natural encoder also leads to a relatively simple expression for the capacity region for discrete multiplicative DBCs.

Optimal Transmission Strategy and Capacity Region for Broadcast Z Channels

This paper presents an optimal transmission strategy, with simple encoding and decoding, for the two-user broadcast Z channel. This paper provides an explicit-form expression for the capacity region and proves that the optimal surface can be achieved by independent encoding. Specifically, the information messages corresponding to each user are encoded independently and the OR of these two streams is transmitted. Nonlinear turbo codes that provide a controlled distribution of ones and zeros are used to demonstrate a low-complexity scheme that works close to the optimal surface.

Minimizing weighted sum finish time for one-to-many file transfer in peer-to-peer networks

This paper considers the problem of transfer ring a file from one source node to multiple receivers in a peer-to-peer (P2P) network. The objective is to minimize the weighted sum finish time (WSFT) for the one-to-many file transfer where peers have both uplink and downlink bandwidth constraints specified. The static scenario is a file-transfer scheme in which the constructed network topology and the network resource (link throughput) allocation remains static until all receivers finish downloading. This paper first shows that the static scenario can be optimized in polynomial time by convex optimization, and the associated optimal static WSFT can be achieved by linear network coding. This paper also proposes a static rateless-coding-based scheme which has almost-optimal empirical performance. The dynamic scenario is a file transfer scheme which can re-construct the network topology and re-allocate the network resource during the file transfer. This paper proposes a dynamic rateless-coding based scheme, which provides significantly smaller WSFT than the optimal static scheme does.

Optimal independent-encoding schemes for input-symmetric degraded broadcast channels

An input-symmetric (IS) degraded broadcast channel (DBC) is a discrete DBC whose component channels are input-symmetric and the intersection of their input-symmetry groups is transitive. The discrete additive DBC and the group-additive DBC are IS-DBCs. This paper introduces an independent encoding scheme which employs permutation functions of the independent codes. This permutation encoding approach for the group-additive DBC is to employ group additions of the independent codes. This paper shows that the permutation encoding approach achieves the boundary of the capacity region for IS-DBCs, and yields a simple characterization of that capacity region.

WLC21-5: Universal Space-Time Serially Concatenated Trellis Coded Modulations

In this paper, we propose serially concatenated trellis coded modulations (SCTCMs) that perform consistently close to the available mutual information for the 2-by-2 compound matrix channel. The proposed SCTCMs use universal SCTCMs for the period-2 periodic fading channel in order to deliver consistent performance over eigenvalue skew. Within the family of channels having the same eigenvalue skew, a time-varying linear transformation (TVLT) is used to mitigate the performance variation over different eigenvectors. The proposed SCTCMs of 1, 2 and 3 bits per transmission require excess mutual information in the ranges 0.11- 0.15, 0.23-0.26 and 0.35-0.53 bits per antenna, respectively. Because of their consistent performance over all channels, the proposed codes will have good frame-error-rate (FER) performance over any quasi- static fading distribution. In particular, the codes provide competitive FER performance in quasi-static Rayleigh fading.