1. Layered Decoding and Secrecy Over Degraded Broadcast Channel
Shaofeng Zou, Yingbin Liang, Lifeng Lai, Shlomo Shamai (Shitz)
Department of EECS, Syracuse University College of Engineering & Computer Science
Introduction
A K-receiver degraded broadcast channel with layered decoding and secrecy constraints is investigated, in which receivers are ordered by their channel quality. Each receiver is required to decode one more message compared to the receiver with one level worse channel quality, and this message should be kept secure from all receivers with worse channel quality. For both the discrete memoryless channel and the Gaussian channel, the secrecy capacity region is characterized. The achievability scheme is based on stochastic encoding and superposition coding schemes. Novel generalization of the analysis of leakage rates and of the proof of the converse is developed for the K-receiver scenario.
Channel Model
The channel we study is degraded broadcast channel including discrete memoryless channel (DMC) and Gaussian channel.
The channel transition probability function is given by , where X is the channel input and Yi is the output at the i-th receiver.
The Gaussian broadcast channel is defined by where Zk is a zero mean Gaussian noise with variance N. We assume that
It is assumed that the receivers have degraded outputs, i.e., they satisfy the following Markov chain condition, Hence the quality of the channel decreased from YK to Y1
Secrecy Capacity Result
The capacity region is defined to be union of all achievable rate tuples satisfying the system constraints.
To claim a region is a capacity region, we need to give a corresponding scheme to achieve all the rate points inside the region and prove that all points outside this region are not achievable.
For the discrete memoryless channel we have the following secrecy capacity region, for some PU1U2…UK-1X such that the following Markov chain holds
We also get the capacity region for the Gaussian broadcast channel.
Problem
We study a model of the degraded broadcast channel with layered decoding and secrecy constraints.
The receivers are ordered by the quality of the channel from the transmitter to the receivers.
Depending on the order of the receiver, it can decode certain messages, and all other messages are secured from this receiver.
Basic idea of How to Achieve the Capacity Region
We use a combination of superposition and random binning.
The message is the bin number. The message we actually transmit is the node number.
The receiver that are required to decode the message can decode the node number, hence it can easily locate which bin the node is in. While the low privilege receivers can not determine which bin the node is in, hence the message is secured from them.
Performance Measurement
We want to characterize all the possible transmission rate tuples (R1,R2,…RK) such that decoder i can decode message M1,M2,…Mi, and messages Mi+1,…,MK are secured from it.
We define the probability of decoding error to be Pe, and the information leakage rate to be Rl.
A secrecy rate tuple (R1,R2,…RK) is said to be achievable, if there exists an encoding and decoding scheme, such that both Pe and Rl goes to zero as n goes to infinity.

2. Layered Decoding and Secrecy Over Degraded Broadcast Channel
Shaofeng Zou, Yingbin Liang, Lifeng Lai, Shlomo Shamai (Shitz)
Department of EECS, Syracuse University College of Engineering & Computer Science

3. Layered Decoding and Secrecy Over Degraded Broadcast Channel
Shaofeng Zou, Yingbin Liang, Lifeng Lai, Shlomo Shamai (Shitz)
Department of EECS, Syracuse University College of Engineering & Computer Science

4. Layered Decoding and Secrecy Over Degraded Broadcast Channel
Shaofeng Zou, Yingbin Liang, Lifeng Lai, Shlomo Shamai (Shitz)
Department of EECS, Syracuse University College of Engineering & Computer Science

5. Layered Decoding and Secrecy Over Degraded Broadcast Channel
Shaofeng Zou, Yingbin Liang, Lifeng Lai, Shlomo Shamai (Shitz)
Department of EECS, Syracuse University College of Engineering & Computer Science

6. Layered Decoding and Secrecy Over Degraded Broadcast Channel
Shaofeng Zou, Yingbin Liang, Lifeng Lai, Shlomo Shamai (Shitz)
Department of EECS, Syracuse University College of Engineering & Computer Science