Zero-Error Capacity of $ P $ -ary Shift Channels and FIFO Queues

Kovačević, Mladen; Stojaković, Miloš; Tan, Vincent Y. F.

doi:10.1109/tit.2017.2756667

Cited by 12 publications

(4 citation statements)

References 26 publications

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“…In recent years, studies have been done towards determining the zeroerror capacity of special channels with memory. In [21], the zero-error capacity of special symbol shift channels is determined. In [22], Cao et.…”

Section: Introductionmentioning

confidence: 99%

Bounded State Estimation over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity

Saberi,

Farokhi,

Nair

2020

Preprint

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We investigate bounded state estimation of linear systems over finitestate erasure and additive noise channels in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the topological entropy of the channel dynamics. Some examples are introduced and separate capacity bounds based on their specific features are derived and compared with bounds from topological entropy. Necessary and sufficient conditions for linear state estimation with bounded errors via such channels are then obtained, by extending previous results for nonstochastic memoryless channels to finite-state channels. These estimation conditions bring together the topological entropies of the linear system and the discrete channel.

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Section: Introductionmentioning

confidence: 99%

Bounded State Estimation over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity

Saberi,

Farokhi,

Nair

2020

Preprint

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“…In this context one may also be interested in codes correcting all possible patterns of shifts such that each shift is bounded by s. Such (zero-error) codes have been studied in several related settings: bit-shift channels [27], [38], timing channels [22], [23], skew-tolerant parallel asynchronous communications [9], [21], etc. In many cases, the optimal codes have been found and the zero-error capacity of the corresponding channel determined.…”

Section: Discussionmentioning

confidence: 99%

Runlength-Limited Sequences and Shift-Correcting Codes: Asymptotic Analysis

Kovačević

2019

IEEE Trans. Inform. Theory

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This work is motivated by the problem of error correction in bit-shift channels with the so-called (d, k) input constraints (where successive 1's are required to be separated by at least d and at most k zeros, 0 ≤ d < k ≤ ∞). Bounds on the size of optimal (d, k)-constrained codes correcting a fixed number of bit-shifts are derived, with a focus on their asymptotic behavior in the large block-length limit. The upper bound is obtained by a packing argument, while the lower bound follows from a construction based on a family of integer lattices. Several properties of (d, k)-constrained sequences that may be of independent interest are established as well; in particular, the exponential growth-rate of the number of (d, k)-constrained constant-weight sequences is characterized. The results are relevant for magnetic and optical information storage systems, reader-to-tag RFID channels, and other communication models where bit-shift errors are dominant and where (d, k)-constrained sequences are used for modulation.

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“…In data center storage systems, the automatic treatment a large amount of data imposes reliability constraints which do not support any positive probability of error, even if arbitrarily small. In [5], Kovačević investigated the zero-error capacity, for the duplication channels in DNA-based data storage systems, and in [6], [7], for the timing channels in molecular communication.…”

Section: A Motivationsmentioning

confidence: 99%

Variable-Length Coding for Zero-Error Channel Capacity

Charpenay,

Treust

2020

Preprint

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The zero-error channel capacity is the maximum asymptotic rate that can be reached with error probability exactly zero, instead of a vanishing error probability. The nature of this problem, essentially combinatorial rather than probabilistic, has led to various researches both in Information Theory and Combinatorics. However, the zero-error capacity is still an open problem, for example the capacity of the noisy-typewriter channel with 7 letters is unknown.In this article, we propose a new approach to construct optimal zero-error codes, based on the concatenation of words of variable-length, taken from a generator set. Three zero-error variable-length coding schemes, referred to as "variable-length coding", "intermingled coding" and "automata-based coding", are under study. We characterize their asymptotic performances via linear difference equations, in terms of simple properties of the generator set, e.g. the roots of the characteristic polynomial, the spectral radius of an adjacency matrix, the inverse of the convergence radius of a generator series. For a specific example, we construct an "intermingled" coding scheme that achieves asymptotically the zero-error capacity.

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Zero-Error Capacity of $ P $ -ary Shift Channels and FIFO Queues

Cited by 12 publications

References 26 publications

Bounded State Estimation over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity

Bounded State Estimation over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity

Runlength-Limited Sequences and Shift-Correcting Codes: Asymptotic Analysis

Variable-Length Coding for Zero-Error Channel Capacity

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