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Error Recovery Properties and Soft Decoding of QuasiArithmetic Codes
, 2008
"... This paper first introduces a new set of aggregated state models for softinput decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding perfor ..."
Abstract

Cited by 4 (0 self)
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This paper first introduces a new set of aggregated state models for softinput decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding performance and complexity. It is shown that closetooptimal decoding performance can be obtained with low values of the aggregation parameter, that is, with a complexity which is significantly reduced with respect to optimal QA bit/symbol models. The choice of the aggregation parameter depends on the synchronization recovery properties of the QA codes. This paper thus describes a method to estimate the probability mass function (PMF) of the gain/loss of symbols following a single bit error (i.e., of the difference between the number of encoded and decoded symbols). The entropy of the gain/loss turns out to be the average amount of information conveyed by a length constraint on both the optimal and aggregated state models. This quantity allows us to choose the value of the aggregation parameter that will lead to closetooptimal decoding performance. It is shown that the optimum position for the length constraint is not the last time instant of the decoding process. This observation leads to the introduction of a new technique for robust decoding of QA codes with redundancy which turns out to outperform techniques based on the concept of forbidden symbol.
Using the Fourier Transform to Compute the Weight Distribution of a Binary Linear Block Code
, 2001
"... An analytical technique is presented to compute the weight distribution of a linear block code by performing a Fourier analysis involving certain matrices obtained from the code trellis. The proposed method is general, easy to implement, and can be used without having to traverse the trellis or carr ..."
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An analytical technique is presented to compute the weight distribution of a linear block code by performing a Fourier analysis involving certain matrices obtained from the code trellis. The proposed method is general, easy to implement, and can be used without having to traverse the trellis or carry out tedious analytical work. The introduced technique can be used as a flexible analytical tool to capture the weight structure of the code with application to problems involving analysis and/or design.
doi:10.1155/2008/752840 Research Article Error Recovery Properties and Soft Decoding of QuasiArithmetic Codes
, 2007
"... This paper first introduces a new set of aggregated state models for softinput decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding perfor ..."
Abstract
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This paper first introduces a new set of aggregated state models for softinput decoding of quasi arithmetic (QA) codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding performance and complexity. It is shown that closetooptimal decoding performance can be obtained with low values of the aggregation parameter, that is, with a complexity which is significantly reduced with respect to optimal QA bit/symbol models. The choice of the aggregation parameter depends on the synchronization recovery properties of the QA codes. This paper thus describes a method to estimate the probability mass function (PMF) of the gain/loss of symbols following a single bit error (i.e., of the difference between the number of encoded and decoded symbols). The entropy of the gain/loss turns out to be the average amount of information conveyed by a length constraint on both the optimal and aggregated state models. This quantity allows us to choose the value of the aggregation parameter that will lead to closetooptimal decoding performance. It is shown that the optimum position for the length constraint is not the last time instant of the decoding process. This observation leads to the introduction of a new technique for robust decoding of QA codes with redundancy which turns out to outperform techniques based on the concept of forbidden symbol. Copyright © 2008 Simon Malinowski et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.