Coding Schemes With Rate-Limited Feedback That Improve Over the No Feedback Capacity for a Large Class of Broadcast Channels

Abstract

We propose two coding schemes for the two-receiver discrete memoryless broadcast channel (BC) with rate-limited feedback from one or both receivers. They improve over the nofeedback capacity region for a large class of channels, including the class of strictly essentially less-noisy BCs that we introduce in this article. Examples of strictly essentially less-noisy BCs are the binary symmetric BC (BSBC) or the binary erasure BC (BEBC) with unequal cross-over or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously known capacity results for discrete memoryless BCs with feedback.In both our schemes, we let the receivers feed back quantization messages about their receive signals. In the first scheme, the transmitter simply relays the quantization information obtained from Receiver 1 to Receiver 2, and vice versa. This provides each receiver with a second observation of the input signal and can thus improve its decoding performance unless the BC is physically degraded. Moreover, each receiver uses its knowledge of the quantization message describing its own outputs so as to attain the same performance as if this message had not been transmitted at all.In our second scheme the transmitter first reconstructs and processes the quantized output signals, and then sends the outcome as a common update information to both receivers. A special case of our second scheme applies also to memoryless BCs without feedback but with strictly-causal state-information at the transmitter and causal state-information at the receivers. It recovers all previous achievable regions also for this setup with state-information.

Capacity Regions of Two-Receiver Broadcast Erasure Channels With Feedback and Memory

“…This section proves Theorem 4 and Theorem 5, showing that the max-weight criteria in (99) and (100) strongly stabilize all queues in the network, as defined in (10). We use Lyapunov-drift theory to prove the result.…”

Feedback and Partial Message Side-Information on the Semideterministic Broadcast Channel

“…Bracher is with at which the fresh and the feedback information are sent-we can increase the overall rates at which the messages are sent to the receivers (Example 3). From this we conclude that feedback can increase the capacity region of the SD-BC.As already mentioned, in [16] the connection between the coding idea and the BC with P-MSI is not made explicit. We make the connection explicit, and this allows us to readily extend our feedback coding scheme for the SD-BC to the case where the receivers have P-MSI.…”

“…The physically-degraded BC with parallel conferencing and the BC with conferencing and degraded message sets are studied in [9]. was later proved that feedback can, however, increase the capacity region of several BCs that are not physically degraded [11,12,13,14,15,16]; and achievable rate regions for the BC with feedback were established in [12,13,14,15,16]. An intuition for the gain due to feedback is that feedback allows the transmitter to create a common message that is useful to both receivers [11,14].…”

“…More precisely, we use the idea that the encoder can create from the feedback a new message that is useful to the deterministic receiver and can be created (and hence is known) at the stochastic receiver. A similar idea was previously used by Wu and Wigger to construct a coding scheme for the general BC with rate-limited feedback [16], though their work does not make the connection to the BC with P-MSI explicit. They use the scheme to show that feedback can increase the capacity of a large class of stochastically-(but not physically-) degraded BCs as well as the capacity of a class of BCs that consist of a binary symmetric channel and a binary erasure channel [16].…”

Exploiting Location Information to Enhance Throughput in Downlink V2I Systems

“…It turned out that if the state is known to the cloud, even with a long delay such that the state is completely outdated, such information can still increase substantially the channel capacity [3], [4], even if this outdated state information is noisy [5], [6] or rate-limited [7]. In fact, such binary state information is usually fed back to the transmitter, i.e., the cloud, with an ACK/NACK mechanism in practical communication systems, which makes the setup quite realistic.…”