A Comparison of Superposition Coding Schemes

There are two variants of superposition coding schemes. Cover's original superposition coding scheme has code clouds of the identical shape, while Bergmans's superposition coding scheme has code clouds of independently generated shapes. These two schemes yield identical achievable rate regions in several scenarios, such as the capacity region for degraded broadcast channels. This paper shows that under the optimal maximum likelihood decoding, these two superposition coding schemes can result in different rate regions. In particular, it is shown that for the two-receiver broadcast channel, Cover's superposition coding scheme can achieve rates strictly larger than Bergmans's scheme.Comment: 5 pages, 3 figures, 1 table, submitted to IEEE International Symposium on Information Theory (ISIT 2013

Multiple Access Channels with Generalized Feedback and Confidential Messages

This paper considers the problem of secret communication over a multiple access channel with generalized feedback. Two trusted users send independent confidential messages to an intended receiver, in the presence of a passive eavesdropper. In this setting, an active cooperation between two trusted users is enabled through using channel feedback in order to improve the communication efficiency. Based on rate-splitting and decode-and-forward strategies, achievable secrecy rate regions are derived for both discrete memoryless and Gaussian channels. Results show that channel feedback improves the achievable secrecy rates.Comment: To appear in the Proceedings of the 2007 IEEE Information Theory Workshop on Frontiers in Coding Theory, Lake Tahoe, CA, September 2-6, 200

Empirical Coordination with Channel Feedback and Strictly Causal or Causal Encoding

In multi-terminal networks, feedback increases the capacity region and helps communication devices to coordinate. In this article, we deepen the relationship between coordination and feedback by considering a point-to-point scenario with an information source and a noisy channel. Empirical coordination is achievable if the encoder and the decoder can implement sequences of symbols that are jointly typical for a target probability distribution. We investigate the impact of feedback when the encoder has strictly causal or causal observation of the source symbols. For both cases, we characterize the optimal information constraints and we show that feedback improves coordination possibilities. Surprisingly, feedback also reduces the number of auxiliary random variables and simplifies the information constraints. For empirical coordination with strictly causal encoding and feedback, the information constraint does not involve auxiliary random variable anymore.Comment: 5 pages, 6 figures, presented at IEEE International Symposium on Information Theory (ISIT) 201

Posterior Matching Scheme for Gaussian Multiple Access Channel with Feedback

Posterior matching is a method proposed by Ofer Shayevitz and Meir Feder to design capacity achieving coding schemes for general point-to-point memoryless channels with feedback. In this paper, we present a way to extend posterior matching based encoding and variable rate decoding ideas for the Gaussian MAC with feedback, referred to as time-varying posterior matching scheme, analyze the achievable rate region and error probabilities of the extended encoding-decoding scheme. The time-varying posterior matching scheme is a generalization of the Shayevitz and Feder's posterior matching scheme when the posterior distributions of the input messages given output are not fixed over transmission time slots. It turns out that the well-known Ozarow's encoding scheme, which obtains the capacity of two-user Gaussian channel, is a special case of our extended posterior matching framework as the Schalkwijk-Kailath's scheme is a special case of the point-to-point posterior matching mentioned above. Furthermore, our designed posterior matching also obtains the linear-feedback sum-capacity for the symmetric multiuser Gaussian MAC. Besides, the encoding scheme in this paper is designed for the real Gaussian MAC to obtain that performance, which is different from previous approaches where encoding schemes are designed for the complex Gaussian MAC. More importantly, this paper shows potential of posterior matching in designing optimal coding schemes for multiuser channels with feedback.Comment: submitted to the IEEE Transactions on Information Theory. A shorter version has been accepted to IEEE Information Theory Workshop 201

Multiple Access Channels with States Causally Known at Transmitters

It has been recently shown by Lapidoth and Steinberg that strictly causal state information can be beneficial in multiple access channels (MACs). Specifically, it was proved that the capacity region of a two-user MAC with independent states, each known strictly causally to one encoder, can be enlarged by letting the encoders send compressed past state information to the decoder. In this work, a generalization of the said strategy is proposed whereby the encoders compress also the past transmitted codewords along with the past state sequences. The proposed scheme uses a combination of long-message encoding, compression of the past state sequences and codewords without binning, and joint decoding over all transmission blocks. The proposed strategy has been recently shown by Lapidoth and Steinberg to strictly improve upon the original one. Capacity results are then derived for a class of channels that include two-user modulo-additive state-dependent MACs. Moreover, the proposed scheme is extended to state-dependent MACs with an arbitrary number of users. Finally, output feedback is introduced and an example is provided to illustrate the interplay between feedback and availability of strictly causal state information in enlarging the capacity region.Comment: Accepted by IEEE Transactions on Information Theory, November 201