The secrecy capacity region for the K-receiver degraded broadcast channel (BC) is given for confidential messages sent to the receivers and to be kept secret from an external wiretapper. Superposition coding and Wyner's random code partitioning are used to show the achievable rate tuples. Error probability analysis and equivocation calculation are also provided. In the converse proof, a new definition for the auxiliary random variables is used, which is different from either the case of the 2-receiver BC without common message or the K-receiver BC with common message, both with an external wiretapper; or the K-receiver BC without a wiretapper.The secrecy capacity region for the K-receiver degraded broadcast channel (BC) is given for confidential messages sent to the receivers and to be kept secret from an external wiretapper. Superposition coding and Wyner's random code partitioning are used to show the achievable rate tuples. Error probability analysis and equivocation calculation are also provided. In the converse proof, a new definition for the auxiliary random variables is used, which is different from either the case of the 2-receiver BC without common message or the K-receiver BC with common message, both with an external wiretapper; or the K-receiver BC without a wiretapper.

arXiv:0812.3873Dec 19, 20087 citations

1 The K-Receiver Broadcast Channel with Confidential Messages

Li-Chia Choo, Kai‐Kit Wong, Senior Member

The secrecy capacity region for the K-receiver degraded broadcast channel (BC) is given for confidential messages sent to the receivers and to be kept secret from an external wiretapper. Superposition coding and Wyner’s random code partitioning are used to show the achievable rate tuples. Error probability analysis and equivocation calculation are also provided. In the converse proof, a new definition for the auxiliary random variables is used, which is different from either the case of the 2-receiver BC without common message or the K-receiver BC with common message, both with an external wiretapper; or the K-receiver BC without a wiretapper. I.The secrecy capacity region for the K-receiver degraded broadcast channel (BC) is given for confidential messages sent to the receivers and to be kept secret from an external wiretapper. Superposition coding and Wyner’s random code partitioning are used to show the achievable rate tuples. Error probability analysis and equivocation calculation are also provided. In the converse proof, a new definition for the auxiliary random variables is used, which is different from either the case of the 2-receiver BC without common message or the K-receiver BC with common message, both with an external wiretapper; or the K-receiver BC without a wiretapper. I.

Nov 26, 20120 citations

The Three-Receiver Broadcast Channel with Degraded Message Sets and Confidential Messages

Li-Chia Choo, Kai‐Kit Wong

In this paper, bounds to the secrecy capacity region for the general 3-receiver broadcast channel with 3 degraded message sets, are presented for confidential messages sent to be kept secret from one of the receivers. This model is a more general model than 2-receiver broadcast channels with confidential messages with an external wiretapper, and recently studied 3-receiver degraded broadcast channels with confidential messages, since the conditions on the receivers are general and wiretapper receives the common message. Wyner’s code partitioning combined with double-binning is used to show achievable rate tuples. Error probability analysis and equivocation calculation are also provided. The proof for the outer bound is shown for three cases: the general case; under the condition that receiver 1 is less noisy than receiver 3, the wiretapper; and under the condition that both receivers 1 and 2 are less noisy than the wiretapper, where the inner and outer bounds coincide, giving the secrecy capacity of the special case of a 3-receiver BC with 2 degraded message sets. I.In this paper, bounds to the secrecy capacity region for the general 3-receiver broadcast channel with 3 degraded message sets, are presented for confidential messages sent to be kept secret from one of the receivers. This model is a more general model than 2-receiver broadcast channels with confidential messages with an external wiretapper, and recently studied 3-receiver degraded broadcast channels with confidential messages, since the conditions on the receivers are general and wiretapper receives the common message. Wyner’s code partitioning combined with double-binning is used to show achievable rate tuples. Error probability analysis and equivocation calculation are also provided. The proof for the outer bound is shown for three cases: the general case; under the condition that receiver 1 is less noisy than receiver 3, the wiretapper; and under the condition that both receivers 1 and 2 are less noisy than the wiretapper, where the inner and outer bounds coincide, giving the secrecy capacity of the special case of a 3-receiver BC with 2 degraded message sets. I.

Mar 3, 20091 citation

3-Receiver Broadcast Channels with Common and Confidential Messages

Yeow-Khiang Chia, Abbas El Gamal

This paper establishes inner bounds on the secrecy capacity regions for the general 3-receiver broadcast channel with one common and one confidential message sets. We consider two setups. The first is when the confidential message is to be sent to two receivers and kept secret from the third receiver. Achievability is established using indirect decoding, Wyner wiretap channel coding, and the new idea of generating secrecy from a publicly available superposition codebook. The inner bound is shown to be tight for a class of reversely degraded broadcast channels and when both legitimate receivers are less noisy than the third receiver. The second setup investigated in this paper is when the confidential message is to be sent to one receiver and kept secret from the other two receivers. Achievability in this case follows from Wyner wiretap channel coding and indirect decoding. This inner bound is also shown to be tight for several special cases.This paper establishes inner bounds on the secrecy capacity regions for the general 3-receiver broadcast channel with one common and one confidential message sets. We consider two setups. The first is when the confidential message is to be sent to two receivers and kept secret from the third receiver. Achievability is established using indirect decoding, Wyner wiretap channel coding, and the new idea of generating secrecy from a publicly available superposition codebook. The inner bound is shown to be tight for a class of reversely degraded broadcast channels and when both legitimate receivers are less noisy than the third receiver. The second setup investigated in this paper is when the confidential message is to be sent to one receiver and kept secret from the other two receivers. Achievability in this case follows from Wyner wiretap channel coding and indirect decoding. This inner bound is also shown to be tight for several special cases.

arXiv:0910.1407Oct 8, 20092 citations

Three-Receiver Broadcast Channels With Common and Confidential Messages

Yeow-Khiang Chia, Abbas El Gamal

This paper establishes inner bounds on the secrecy capacity regions for the general three-receiver broadcast channel with one common and one confidential message sets. We consider two setups. The first is when the confidential message is to be sent to two receivers and kept secret from the third receiver. Achievability is established using indirect decoding, Wyner wiretap channel coding, and the new idea of generating secrecy from a publicly available superposition codebook. The inner bound is shown to be tight for a class of reversely degraded broadcast channels and when both legitimate receivers are less noisy than the third receiver. The second setup investigated in this paper is when the confidential message is to be sent to one receiver and kept secret from the other two receivers. Achievability in this case follows from Wyner wiretap channel coding and indirect decoding. This inner bound is also shown to be tight for several special cases.This paper establishes inner bounds on the secrecy capacity regions for the general three-receiver broadcast channel with one common and one confidential message sets. We consider two setups. The first is when the confidential message is to be sent to two receivers and kept secret from the third receiver. Achievability is established using indirect decoding, Wyner wiretap channel coding, and the new idea of generating secrecy from a publicly available superposition codebook. The inner bound is shown to be tight for a class of reversely degraded broadcast channels and when both legitimate receivers are less noisy than the third receiver. The second setup investigated in this paper is when the confidential message is to be sent to one receiver and kept secret from the other two receivers. Achievability in this case follows from Wyner wiretap channel coding and indirect decoding. This inner bound is also shown to be tight for several special cases.

IEEE Transactions on Information TheoryJan 31, 201264 citations

The Secrecy Rate Region of the Broadcast Channel

Ghadamali Bagherikaram, Seyed Abolfazl Motahari, Amir Keyvan Khandani

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as Secret Superposition Scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma. Finally, we assume that the channels are Additive White Gaussian Noise (AWGN) and show that secret superposition scheme with Gaussian codebook is optimal. The converse proof is based on the generalized entropy power inequality.In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as Secret Superposition Scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma. Finally, we assume that the channels are Additive White Gaussian Noise (AWGN) and show that secret superposition scheme with Gaussian codebook is optimal. The converse proof is based on the generalized entropy power inequality.

arXiv:0806.4200Jun 25, 200833 citations

Another Proof for the Secrecy Capacity of the

K

-Receiver Broadcast Channel With Confidential Messages