Achieving High Rates with Sparse Feedback Times in Binary Symmetric Channel Communication

Keskeiset käsitteet

It is possible to significantly reduce the frequency of feedback transmissions in posterior matching communication over the binary symmetric channel without noticeable loss in achievable rate.

Tiivistelmä

The paper explores how the frequency of feedback transmissions affects the achievable rate when noiseless feedback of received symbols is used for posterior-matching communication. Previous works assume that each received symbol is fed back before the next transmission, but this paper shows that the frequency of the feedback can be significantly reduced with no noticeable loss in achievable rate.
The key contributions are:

Introducing a new encoding constraint that is less restrictive and better suited for block transmissions, while still guaranteeing the performance bounds for sequential transmission.
Proposing the "look-ahead" encoding algorithm that enforces the new encoding constraints for a few transmissions in advance, to allow the transmission of a packet of symbols, while still guaranteeing a performance above the lower bounds designed for sequential transmission.
Providing simulation results that show the achievable feedback sparsity, with an average rate that exceeds the lower bounds developed for sequential transmissions.

The paper demonstrates that no feedback is required until after the initial transmission of systematic bits. After that, careful partitioning allows multiple symbols to be transmitted before feedback is required for a new partitioning step.

Tilastot

The channel capacity C is given by:
C = 1 + p log2(p) + (1 - p) log2(1 - p)
The constants C1 and C2 are defined as:
C2 = log2((1 - p) / p)
C1 = (1 - p) log2((1 - p) / p) + p log2(p / (1 - p))

Lainaukset

"Feedback cannot increase the capacity of discrete memoryless channels (DMC)."
"However, when combined with variable-length coding, feedback can help increase the decay rate of the frame error rate (FER) as a function of blocklength."

Tärkeimmät oivallukset

Feedback Communication Over the BSC with Sparse Feedback times and Causal Encoding

by Amaael Anton... klo arxiv.org 04-16-2024

https://arxiv.org/pdf/2404.09455.pdf

Syvällisempiä Kysymyksiä

How can the proposed sparse feedback scheme be extended to other channel models beyond the binary symmetric channel

The proposed sparse feedback scheme can be extended to other channel models beyond the binary symmetric channel by adapting the partitioning and encoding strategies to suit the characteristics of the specific channel. For instance, in channels with different error probabilities for different symbols or with varying noise characteristics, the partitioning of the message space into bins and the determination of feedback times may need to be adjusted. Additionally, the encoding rules and constraints may need to be modified to account for the unique features of the channel model. By customizing the scheme to the requirements of the specific channel model, the sparse feedback approach can be effectively applied to a wide range of communication scenarios.

What are the potential trade-offs between the achievable rate, feedback sparsity, and computational complexity of the "look-ahead" algorithm, and how can these be further optimized

The potential trade-offs between the achievable rate, feedback sparsity, and computational complexity of the "look-ahead" algorithm can be optimized by carefully balancing these factors based on the specific communication requirements.

Achievable Rate: The achievable rate can be optimized by fine-tuning the partitioning of the message space and the feedback intervals to maximize the information transmitted per symbol. By ensuring that the encoding constraints are met while allowing for sparse feedback, the rate can be maintained at high levels.

Feedback Sparsity: The sparsity of feedback transmissions can be optimized by adjusting the block sizes and the frequency of feedback updates. Finding the right balance between feedback sparsity and the need for timely updates can help in reducing overhead while maintaining effective communication.

Computational Complexity: The computational complexity of the algorithm can be optimized by streamlining the encoding and decoding processes, reducing redundant calculations, and optimizing the search for the optimal feedback intervals. By implementing efficient algorithms and data structures, the computational burden can be minimized without compromising performance.

To further optimize these trade-offs, iterative testing and refinement of the algorithm parameters based on performance metrics such as rate, sparsity, and complexity can help in finding the optimal configuration for a given communication scenario.

Are there any applications or scenarios where the sparse feedback communication approach could provide significant practical benefits compared to traditional posterior matching schemes

The sparse feedback communication approach could provide significant practical benefits in scenarios where real-time feedback is challenging or costly to implement. Some potential applications include:

Low-Latency Communication: In systems where immediate feedback transmission is not feasible due to latency constraints, the sparse feedback approach can offer a balance between timely updates and reduced feedback overhead. This can be beneficial in applications such as real-time control systems or interactive communication where low latency is critical.

Energy-Efficient Communication: By reducing the frequency of feedback transmissions, the sparse feedback scheme can help in conserving energy in wireless communication systems. This can be advantageous in battery-powered devices or IoT applications where energy efficiency is a key consideration.

Robust Communication in Noisy Environments: In environments with high levels of noise or interference, sparse feedback can help in improving the reliability of communication by allowing for more robust encoding and decoding strategies. This can be valuable in wireless networks or industrial settings where signal degradation is common.

Overall, the sparse feedback communication approach offers flexibility and efficiency in scenarios where traditional feedback schemes may be impractical or resource-intensive.