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Motivated by intention to evaluate asymptotically multiple-burst-error-correcting codes on channels with memory, we will derive the following fact. Let {*Z*_{i} } be a hidden Markov process, i. e. , a functional of a Markov chain with a finite state space, and *W*_{b}(*Z*_{1}*Z*_{2}*Z*_{n}) denote the number of burst errors that appear in *Z*_{1}*Z*_{2}*Z*_{n}, where the number of burst errors is counted using Gabidulin's burst metric , 1971. As the main result, we will prove the almost sure convergence of relative burst weight *W*_{b}(*Z*_{1}*Z*_{2}*Z*_{n})/*n*, i. e. , the relative frequency of occurrence of burst errors, for a broad class of functionals { *Z*_{i} } of finite Markov chains. Functionals of Markov chains are often adopted as models of the noises on channels, especially on burst-noise channels, the most famous model of which is probably the Gilbert channel proposed in 1960. Those channel models described with Markov chains are called channels with memory (including channels with zero-memory, i. e. , memoryless ones). This work's achievement enables us to extend Gilbert's code performance evaluation in 1952, a landmark that offered the well-known Gilbert bound, discussed its relationship to the (memoryless) binary symmetric channel, and has been serving as a guide for the-Hamming-metric-based design of error-correcting codes, to the case of the-burst-metric-based codes (burst-error-correcting codes) and discrete channels with or without memory.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.10 pp.2022-2033

- Publication Date
- 1999/10/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)

- Category
- Coding Theory

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Mitsuru HAMADA, "Almost Sure Convergence of Relative Frequency of Occurrence of Burst Errors on Channels with Memory" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 10, pp. 2022-2033, October 1999, doi: .

Abstract: Motivated by intention to evaluate asymptotically multiple-burst-error-correcting codes on channels with memory, we will derive the following fact. Let {*Z*_{i} } be a hidden Markov process, i. e. , a functional of a Markov chain with a finite state space, and *W*_{b}(*Z*_{1}*Z*_{2}*Z*_{n}) denote the number of burst errors that appear in *Z*_{1}*Z*_{2}*Z*_{n}, where the number of burst errors is counted using Gabidulin's burst metric , 1971. As the main result, we will prove the almost sure convergence of relative burst weight *W*_{b}(*Z*_{1}*Z*_{2}*Z*_{n})/*n*, i. e. , the relative frequency of occurrence of burst errors, for a broad class of functionals { *Z*_{i} } of finite Markov chains. Functionals of Markov chains are often adopted as models of the noises on channels, especially on burst-noise channels, the most famous model of which is probably the Gilbert channel proposed in 1960. Those channel models described with Markov chains are called channels with memory (including channels with zero-memory, i. e. , memoryless ones). This work's achievement enables us to extend Gilbert's code performance evaluation in 1952, a landmark that offered the well-known Gilbert bound, discussed its relationship to the (memoryless) binary symmetric channel, and has been serving as a guide for the-Hamming-metric-based design of error-correcting codes, to the case of the-burst-metric-based codes (burst-error-correcting codes) and discrete channels with or without memory.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_10_2022/_p

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@ARTICLE{e82-a_10_2022,

author={Mitsuru HAMADA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Almost Sure Convergence of Relative Frequency of Occurrence of Burst Errors on Channels with Memory},

year={1999},

volume={E82-A},

number={10},

pages={2022-2033},

abstract={Motivated by intention to evaluate asymptotically multiple-burst-error-correcting codes on channels with memory, we will derive the following fact. Let {*Z*_{i} } be a hidden Markov process, i. e. , a functional of a Markov chain with a finite state space, and *W*_{b}(*Z*_{1}*Z*_{2}*Z*_{n}) denote the number of burst errors that appear in *Z*_{1}*Z*_{2}*Z*_{n}, where the number of burst errors is counted using Gabidulin's burst metric , 1971. As the main result, we will prove the almost sure convergence of relative burst weight *W*_{b}(*Z*_{1}*Z*_{2}*Z*_{n})/*n*, i. e. , the relative frequency of occurrence of burst errors, for a broad class of functionals { *Z*_{i} } of finite Markov chains. Functionals of Markov chains are often adopted as models of the noises on channels, especially on burst-noise channels, the most famous model of which is probably the Gilbert channel proposed in 1960. Those channel models described with Markov chains are called channels with memory (including channels with zero-memory, i. e. , memoryless ones). This work's achievement enables us to extend Gilbert's code performance evaluation in 1952, a landmark that offered the well-known Gilbert bound, discussed its relationship to the (memoryless) binary symmetric channel, and has been serving as a guide for the-Hamming-metric-based design of error-correcting codes, to the case of the-burst-metric-based codes (burst-error-correcting codes) and discrete channels with or without memory.

keywords={},

doi={},

ISSN={},

month={October},}

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TY - JOUR

TI - Almost Sure Convergence of Relative Frequency of Occurrence of Burst Errors on Channels with Memory

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2022

EP - 2033

AU - Mitsuru HAMADA

PY - 1999

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E82-A

IS - 10

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - October 1999

AB - Motivated by intention to evaluate asymptotically multiple-burst-error-correcting codes on channels with memory, we will derive the following fact. Let {*Z*_{i} } be a hidden Markov process, i. e. , a functional of a Markov chain with a finite state space, and *W*_{b}(*Z*_{1}*Z*_{2}*Z*_{n}) denote the number of burst errors that appear in *Z*_{1}*Z*_{2}*Z*_{n}, where the number of burst errors is counted using Gabidulin's burst metric , 1971. As the main result, we will prove the almost sure convergence of relative burst weight *W*_{b}(*Z*_{1}*Z*_{2}*Z*_{n})/*n*, i. e. , the relative frequency of occurrence of burst errors, for a broad class of functionals { *Z*_{i} } of finite Markov chains. Functionals of Markov chains are often adopted as models of the noises on channels, especially on burst-noise channels, the most famous model of which is probably the Gilbert channel proposed in 1960. Those channel models described with Markov chains are called channels with memory (including channels with zero-memory, i. e. , memoryless ones). This work's achievement enables us to extend Gilbert's code performance evaluation in 1952, a landmark that offered the well-known Gilbert bound, discussed its relationship to the (memoryless) binary symmetric channel, and has been serving as a guide for the-Hamming-metric-based design of error-correcting codes, to the case of the-burst-metric-based codes (burst-error-correcting codes) and discrete channels with or without memory.

ER -