Multiple Access Channels with Combined Cooperation and Partial Cribbing

In this paper we study the multiple access channel (MAC) with combined cooperation and partial cribbing and characterize its capacity region. Cooperation means that the two encoders send a message to one another via a rate-limited link prior to transmission, while partial cribbing means that each of the two encoders obtains a deterministic function of the other encoder's output with or without delay. Prior work in this field dealt separately with cooperation and partial cribbing. However, by combining these two methods we can achieve significantly higher rates. Remarkably, the capacity region does not require an additional auxiliary random variable (RV) since the purpose of both cooperation and partial cribbing is to generate a common message between the encoders. In the proof we combine methods of block Markov coding, backward decoding, double rate-splitting, and joint typicality decoding. Furthermore, we present the Gaussian MAC with combined one-sided cooperation and quantized cribbing. For this model, we give an achievability scheme that shows how many cooperation or quantization bits are required in order to achieve a Gaussian MAC with full cooperation/cribbing capacity region. After establishing our main results, we consider two cases where only one auxiliary RV is needed. The first is a rate distortion dual setting for the MAC with a common message, a private message and combined cooperation and cribbing. The second is a state-dependent MAC with cooperation, where the state is known at a partially cribbing encoder and at the decoder. However, there are cases where more than one auxiliary RV is needed, e.g., when the cooperation and cribbing are not used for the same purposes. We present a MAC with an action-dependent state, where the action is based on the cooperation but not on the cribbing. Therefore, in this case more than one auxiliary RV is needed

Successive Refinement with Decoder Cooperation and its Channel Coding Duals

We study cooperation in multi terminal source coding models involving successive refinement. Specifically, we study the case of a single encoder and two decoders, where the encoder provides a common description to both the decoders and a private description to only one of the decoders. The decoders cooperate via cribbing, i.e., the decoder with access only to the common description is allowed to observe, in addition, a deterministic function of the reconstruction symbols produced by the other. We characterize the fundamental performance limits in the respective settings of non-causal, strictly-causal and causal cribbing. We use a new coding scheme, referred to as Forward Encoding and Block Markov Decoding, which is a variant of one recently used by Cuff and Zhao for coordination via implicit communication. Finally, we use the insight gained to introduce and solve some dual channel coding scenarios involving Multiple Access Channels with cribbing.Comment: 55 pages, 15 figures, 8 tables, submitted to IEEE Transactions on Information Theory. A shorter version submitted to ISIT 201

Cooperative Binning for Semi-deterministic Channels with Non-causal State Information

The capacity of the semi-deterministic relay channel (SD-RC) with non-causal channel state information (CSI) only at the encoder and decoder is characterized. The capacity is achieved by a scheme based on cooperative-bin-forward. This scheme allows cooperation between the transmitter and the relay without the need to decode a part of the message by the relay. The transmission is divided into blocks and each deterministic output of the channel (observed by the relay) is mapped to a bin. The bin index is used by the encoder and the relay to choose the cooperation codeword in the next transmission block. In causal settings the cooperation is independent of the state. In \emph{non-causal} settings dependency between the relay's transmission and the state can increase the transmission rates. The encoder implicitly conveys partial state information to the relay. In particular, it uses the states of the next block and selects a cooperation codeword accordingly and the relay transmission depends on the cooperation codeword and therefore also on the states. We also consider the multiple access channel with partial cribbing as a semi-deterministic channel. The capacity region of this channel with non-causal CSI is achieved by the new scheme. Examining the result in several cases, we introduce a new problem of a point-to-point (PTP) channel where the state is provided to the transmitter by a state encoder. Interestingly, even though the CSI is also available at the receiver, we provide an example which shows that the capacity with non-causal CSI at the state encoder is strictly larger than the capacity with causal CSI

Channels with Cooperation Links that May Be Absent

It is well known that cooperation between users in a communication network can lead to significant performance gains. A common assumption in past works is that all the users are aware of the resources available for cooperation, and know exactly to what extent these resources can be used. Unfortunately, in many modern communication networks the availability of cooperation links cannot be guaranteed a priori, due to the dynamic nature of the network. In this work a family of models is suggested where the cooperation links may or may not be present. Coding schemes are devised that exploit the cooperation links if they are present, and can still operate (although at reduced rates) if cooperation is not possible.Comment: Accepted for publication in the IEEE transaction on Information Theory, June 201