Real-time Binary Posterior Matching

Lalitha, Anusha; Khina, Anatoly; Javidi, Tara; Kostina, Victoria

doi:10.1109/isit.2019.8849479

Cited by 8 publications

(21 citation statements)

References 9 publications

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“…3, we plot the rate R n ( ) = n E[λn] achieved by the instantaneous SED code in comparison with the existing schemes as a function of message length n, for a fixed error probability . The instantaneous SED code achieves a significantly larger rate than either Naghshvar et al' block encoding scheme [11] or Lalitha et al's instantaneous encoding scheme [15]. Note that the simulation Fig.…”

Section: A the Instantaneous Sed Code: Algorithmmentioning

confidence: 80%

“…Our bound outperforms the achievability bounds derived from Burnashev's [8] and Naghshvar et al's [11] schemes with block encoding. Furthermore, simulations show that the instantaneous SED code achieves a significantly larger rate than Naghshvar et al's [11] and Lalitha et al's [15] schemes.…”

Section: Introductionmentioning

confidence: 87%

“…where (15) holds since Y t −X t −(B * t , Y t−1 ) is a Markov chain. Since the encoder knows Y t through the noiseless feedback, the posterior in (15) is also available at the encoder.…”

Section: A the Instantaneous Sed Code: Algorithmmentioning

confidence: 99%

“…While the schemes in [2]- [14] use block encoding, one existing work that considered instantaneous encoding is Lalitha et al [15]. Their scheme operates as follows.…”

Section: Introductionmentioning

confidence: 99%

“…The encoder finds the interval that contains the median of the posterior of the message, and transmits a bit describing whether the n-bit representation of the message is above or below a randomly chosen boundary of this interval. Lalitha et al [15] proved that their scheme achieves the probability of erroneously decoding the first n bits at time t that decays exponentially in t, and derived a lower bound on the maximum rate that leads to a vanishing error probability.…”

Section: Introductionmentioning

confidence: 99%

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Instantaneous SED coding over a DMC

Guo

Kostina

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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In this paper, we propose a novel code for transmitting a sequence of n message bits in real time over a discretememoryless channel (DMC) with noiseless feedback, where the message bits stream into the encoder one by one at random time instants. Similar to existing posterior matching schemes with block encoding, the encoder in our work takes advantage of the channel feedback to form channel inputs that contain the information the decoder does not yet have, and that are distributed close to the capacity-achieving input distribution, but dissimilar to the existing posterior matching schemes, the encoder performs instantaneous encoding -it immediately weaves the new message bits into a continuing transmission. A posterior matching scheme by Naghshvar et al. partitions the source messages into groups so that the group posteriors have a small-enough difference (SED) to the capacity-achieving distribution, and transmits the group index that contains the actual message. Our code adopts the SED rule to apply to the evolving message alphabet that contains all the possible variable-length strings that the source could have emitted up to that time. Our instantaneous SED code achieves better delay-reliability tradeoffs than existing feedback codes over 2-input DMCs: we establish this dominance both by simulations and via an analysis comparing the performance of the instantaneous SED code to Burnashev's reliability function.Due to the message alphabet that grows exponentially with time t, the complexity of the instantaneous SED code is doubleexponential in t. To overcome this complexity barrier to practical implementation, we design a low-complexity code for binary symmetric channels that we name the instantaneous type set SED code. It groups the message strings into sets we call type sets and tracks their prior and posterior probabilities jointly, resulting in the reduction of complexity from double-exponential to O(t 4 ). Simulation results show that the gap in performance between the instantaneous SED code and the instantaneous type-set SED code is negligible.

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Section: A the Instantaneous Sed Code: Algorithmmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 87%

Section: A the Instantaneous Sed Code: Algorithmmentioning

confidence: 99%

“…While the schemes in [2]- [14] use block encoding, one existing work that considered instantaneous encoding is Lalitha et al [15]. Their scheme operates as follows.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Instantaneous SED coding over a DMC

Guo

Kostina

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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Reliability function for streaming over a DMC with feedback

Guo¹,

Kostina²

2022

2022 IEEE International Symposium on Information Theory (ISIT)

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Conventionally, posterior matching is investigated in channel coding and block encoding contexts -the source symbols are equiprobably distributed and are entirely known by the encoder before the transmission. In this paper, we consider a streaming source, whose symbols progressively arrive at the encoder at a sequence of deterministic times. We derive the joint source-channel coding (JSCC) reliability function for streaming over a discrete memoryless channel (DMC) with feedback. We propose a novel instantaneous encoding phase that operates during the symbol arriving period and that achieves the JSCC reliability function for streaming when followed by a block encoding scheme that achieves the JSCC reliability function for a classical source whose symbols are fully accessible before the transmission. During the instantaneous encoding phase, the evolving message alphabet is partitioned into groups whose priors are close to the capacity-achieving distribution, and the encoder determines the group index of the actual sequence of symbols arrived so far and applies randomization to exactly match the distribution of the transmitted index to the capacity-achieving one. Surprisingly, the JSCC reliability function for streaming is equal to that for a fully accessible source, implying that the knowledge of the entire symbol sequence before the transmission offers no advantage in terms of the reliability function. For streaming over a symmetric binary-input DMC, we propose a one-phase instantaneous small-enough difference (SED) code that not only achieves the JSCC reliability function, but also, thanks to its single-phase time-invariant coding rule, can be used to stabilize an unstable linear system over a noisy channel. For equiprobably distributed source symbols, we design low complexity algorithms to implement both the instantaneous encoding phase and the instantaneous SED code. The algorithms group the source sequences into sets we call types, which enable the encoder and the decoder to track the priors and the posteriors of source sequences jointly, leading to a log-linear complexity in time. While the reliability function is derived for non-degenerate DMCs, i.e., DMCs whose transition probability matrix has all positive entries, for degenerate DMCs we design a code with instantaneous encoding that achieves zero error for all rates below Shannon's joint source-channel coding limit.

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Real-Time Variable-to-Fixed Lossless Source Coding of Randomly Arriving Symbols

Abend

Khina

2021

2020 IEEE Information Theory Workshop (ITW)

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We address the recently suggested problem of causal lossless coding of a randomly arriving source samples. We construct variable-to-fixed coding schemes and show that they outperform the previously considered fixed-to-variable schemes when traffic is high both in terms of delay and Age of Information by appealing to tools from queueing theory. We supplement our theoretical bounds with numerical simulations.

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Real-time Binary Posterior Matching

Cited by 8 publications

References 9 publications

Instantaneous SED coding over a DMC

Instantaneous SED coding over a DMC

Reliability function for streaming over a DMC with feedback

Real-Time Variable-to-Fixed Lossless Source Coding of Randomly Arriving Symbols

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