An Efficient Feedback Coding Scheme With Low Error Probability for Discrete Memoryless Channels

Q: What is the need for the circular shift of the intervals?

2) To explain the need for the circular shift of the intervals via Ui , note that if the authors map a point on the interval directly to the input symbol, the chosen symbol would depend on both the position and the length of the interval corresponding to the correct message.

Q: What is the error probability of the sphere packing bound?

As the authors discussed, to analyze the error probability of their scheme, it suffices to study how Si increases from S0 = e−nR to Sn > 1/2.

Question

1. What contributions have the authors mentioned in the paper "An efficient feedback coding scheme with low error probability for discrete memoryless channels" ?

2. What is the probability of the message being recovered?

3. What is the reason the authors use the maximal information gain rule in (3) to select Vi?

4. What is the DT bound for a binary symmetric channel?

Accepted Answer

This paper introduces a new fixed-length feedback coding scheme which achieves the capacity for all discrete memoryless channels, has an error exponent that approaches the sphere packing bound as the rate approaches the capacity, and has O ( n log n ) coding complexity.

Accepted Answer

Since the pseudo posterior probabilities of all the messages sum up to one, if the pseudo posterior probability of the transmitted message Sn = sn(m, Y n, Un) > 1/2, the authors can be sure that the message is recovered correctly.

Accepted Answer

3) The reason the authors use the maximal information gain rule in (3) to select Vi is that it yields a better bound on the error exponent than the simpler rule of selecting Vi uniformly at random.

Accepted Answer

3) The dependence-testing (DT) bound [16], which is the error exponent for random coding without feedback when a threshold decoder is used.

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The actualmoment generating function is ψs(ρ) = pα + qβ, where q = 1 − p, andα=⎧ ⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩(2 p)−ρ (1 − 2s + 4sp (ρ − 1)(q − p) ) + 2s ρ − 1 s ≤ 1 2 ,(2s − 1)(2q − q − p s )−ρ− 2s(1 − (2q − (q − p)/s) 1−ρ)(ρ − 1)(q − p) s > 1 2 ,β =⎧ ⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩(2q)−ρ (1 − 2s − 4sq (ρ − 1)(q − p) ) + 2s ρ − 1 s ≤ 1 2 ,(2s − 1)(2 p + q − p s )−ρ+ 2s(1 − (2 p − (q − p)/s) 1−ρ)(ρ − 1)(q − p) s > 1 2 .The value of ' can be found approximately using dynamic programming.

Accepted Answer

Lemma 2 (Ending Phase MGF): For any DMC p(y|x), there exists 0 < Send < 1, γ > 0 and 'end < 1 such that when s ≥ Send,ψs ( γ (1 − s)−1 ) ≤ 'end.

Accepted Answer

2) To explain the need for the circular shift of the intervals via Ui , note that if the authors map a point on the interval directly to the input symbol, the chosen symbol would depend on both the position and the length of the interval corresponding to the correct message.

Accepted Answer

As the authors discussed, to analyze the error probability of their scheme, it suffices to study how Si increases from S0 = e−nR to Sn > 1/2.

Accepted Answer

The maximal information gain rule always selects the input symbol whose probability interval has the larger overlapping area with the message interval.

Accepted Answer

As a result of these differences, their scheme can achieve good error exponent over the entire rate range using a simpler error probability analysis.

Accepted Answer

In this section, the authors briefly discuss the implementation of their coding algorithm and show that its computational complexity for DMCs is O (n log n) and its memory complexity is O (n).

Accepted Answer

Although there are enR possible messages, most of them share the same pseudo posterior probability, so instead of storing the pseudo posterior probabilities of the messages separately, the authors store intervals of message points with the same pseudo posterior probability.

An Efficient Feedback Coding Scheme With Low Error Probability for Discrete Memoryless Channels

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Most frequently asked questions

1. What contributions have the authors mentioned in the paper "An efficient feedback coding scheme with low error probability for discrete memoryless channels" ?

2. What is the probability of the message being recovered?

3. What is the reason the authors use the maximal information gain rule in (3) to select Vi?

4. What is the DT bound for a binary symmetric channel?

5. What is the value of'in the sphere packing bound?

6. What is the proof of the lemma?

7. What is the need for the circular shift of the intervals?

8. What is the error probability of the sphere packing bound?

9. What is the maximum information gain rule for a binary symmetric channel?

10. what is the simplest way to estimate the posterior probability of a message?

11. What is the coding algorithm for DMCs?

12. What is the enR probability of the messages?

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Citations

国際会議参加報告:2014 IEEE International Symposium on Information Theory

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References

Channel Coding Rate in the Finite Blocklength Regime

The zero error capacity of a noisy channel

Self-adjusting binary search trees

A coding scheme for additive noise channels with feedback--I: No bandwidth constraint

Sequential transmission using noiseless feedback

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