We establish several new results on Marton's coding scheme and its corresponding inner bound on the capacity region of the general broadcast channel. We show that unlike the Gaussian case, Marton's coding scheme without superposition coding is not optimal in general even for a degraded broadcast channel with no common message. We then establish properties of Marton's inner bound that help restrict the search space for computing the sum-rate. Next, we show that the inner bound is optimal along certain directions. Finally, we propose a coding scheme that may lead to a larger inner bound.
Achievable rate region for three user discrete broadcast channel based on coset codes
基于嵌套陪集码，我们提出了一个一般三用户离散无记忆广播信道的可达速率域。我们的特点是3至1离散广播信道，一类广播信道，其中最有名的编码技术\footnote{We henceforth refer to this as Marton's coding for three user discrete broadcast channel.}，这是通过一个自然的概括，由马顿提出的一般两个用户离散广播信道，是严格次优的。特别是，我们确定了一种新的3比1离散广播信道，其中马顿的编码被证明是严格次优的\textit{analytically}。我们提出了可实现的速率区域为一般的3比1离散广播信道，嵌套陪集码的基础上，严格扩大马顿的速率区域为上述通道。我们推广到目前的可达速率区域一般三用户离散广播信道。结合马顿的编码和这里提出的，我们提出了最知名的编码技术，一般的三个用户的离散广播信道。
For communications in the presence of eavesdroppers, random components are often used in code design to camouflage information from eavesdroppers. In broadcast channels without eavesdroppers, Marton error-correcting coding comprises random components which allow correlation between auxiliary random variables representing independent messages. In this paper, we study if Marton coding alone can ensure individual secrecy in the two-receiver discrete memoryless broadcast channel with a passive eavesdropper. Our results show that in accordance to the principle of Wyner secrecy coding, this is possi…
我们提出了两种方法来传输经典信息的量子广播信道。第一种技术是经典广播信道的叠加编码方案的量子推广。我们使用量子同时非唯一解码器，并获得[Yard et al.，IEEE Trans.Inf.Theory 57（10），2011]。我们的第二个结果是量子推广的马顿编码方案。量子马顿区域的误差分析利用了我们早期工作中的思想和Radhakrishnan等人最近在arXiv：1410.3248中提出的思想。这两个结果都利用了在量子干涉信道的背景下开发的量子同时解码的最新进展。
This paper studies the problem of secure communcation over the two-receiver discrete memoryless broadcast channel with one-sided receiver side information and with a passive eavesdropper. We proposed a coding scheme which is based upon the superposition-Marton framework. Secrecy techniques such as the one-time pad, Carleial-Hellman secrecy coding and Wyner serecy coding are applied to ensure individual secrecy. This scheme is shown to be capacity achieving for some cases of the degraded broadcast channel. We also notice that one-sided receiver side information provides the advantage of rate re…
A polar coding scheme is proposed for the Wiretap Broadcast Channel with two legitimate receivers and one eavesdropper. We consider a model in which the transmitter wishes to send different confidential (and non-confidential) information to each legitimate receiver. First, we compare two inner-bounds on the achievable region of this model from the literature, and then we design a polar coding scheme that achieves the stronger one. In the proposed scheme, the encoding uses polar-based Marton's coding, where one inner-layer must be reliably decoded by both legitimate receivers, and each receiver…
Capacity Bounds for Broadcast Channels with Confidential Messages
在本文中，我们研究了离散无记忆广播信道的容量界与机密消息。两个私人消息以及一个公共消息被传输;公共消息将由两个接收者解码，而每个私人消息仅用于其预期的接收者。此外，每个私人信息都要对非预期的接收者保密，其中保密性是通过模棱两可来衡量的。我们提出了内部和外部边界的速率模糊区域的广播信道与机密消息。建议的内界推广Csiszár和Körner的速率模糊区域的广播信道与一个单一的机密消息，刘{ \em et al}的可达速率区域的广播信道与完美的保密性，马顿和Gel'fand和Pinsker的可达速率区域的一般广播信道。我们提出的外边界，连同内边界，有助于建立几类离散无记忆广播信道的速率模糊区域的机密消息，包括少噪声，确定性和半确定性的信道。此外，专门为一般的广播信道通过删除的机密性约束，我们提出的外边界减少到新的容量外边界的离散内存广播信道。
The problem of channel coding over the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) with additive independent Gaussian states is considered. The states are known in a noncausal manner to the encoder, and it wishes to minimize the amount of information that the receivers can learn from the channel outputs about the state sequence. The state leakage rate is measured as a normalized blockwise mutual information between the state sequence and the channel outputs' sequences. We employ a new version of a state-dependent extremal inequality and show that Gaussian input maximi…
This paper focuses on $ K $-receiver discrete-time memoryless broadcast channels (DM-BCs) with private messages, where the transmitter wishes to convey $K$ private messages to $K$ receivers respectively. A general inner bound on the capacity region is proposed based on an exhaustive message splitting and a $K$-level modified Marton's coding. The key idea is to split every message into $ \sum_{j=1}^K {K\choose j} $ submessages each corresponding to a set of users who are assigned to recover them, and then send these submessages through codewords that are jointly typical with each other. To guar…
We investigate novel inner and outer bounds on the rate region of a 2-user Gaussian broadcast channel with finite, heterogeneous blocklength constraints (HB-GBC). In particular, we introduce a new, modified Sato-type outer bound that can be applied in the finite blocklength regime and which does not require the same marginal property. We then develop and analyze composite shell codes, which are suitable for the HB-GBC. Especially, to achieve a lower decoding latency for the user with a shorter blocklength constraint when successive interference cancellation is used, we derive the number of sym…
Multiple groupcasting over the broadcast channel (BC) is studied. In particular, an inner bound is obtained for the $K$-receiver discrete memoryless (DM) BC for the diamond message set which consists of four groupcast messages: one desired by all receivers, one by all but two receivers, and two more desired by all but each one of those two receivers. The inner bound is based on rate-splitting and superposition coding and is given in explicit form herein as a union over coding distributions of four-dimensional polytopes. When specialized to the so-called combination network, which is a class of…
