<p>In this article, our objective is to propose an alternative algorithm to the single parity check algorithm that exhibits improved capabilities. To achieve this, we introduce a function for symmetrizing binary codes with an error resilience capability. Additionally, we present the symmetry check algorithm for error detection and provide a theoretical proof that the error detection bits of the symmetry check algorithm not only identify errors but also enable the recovery of a portion of the original binary code bits. The symmetry check algorithm has the ability to recover a portion of the data in any channel, regardless of the level of noise present, in proportion to the introduced noise. By implementing the symmetry check algorithm on a group of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7305_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">$512 \times 512$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>512</mn> <mo>×</mo> <mn>512</mn> </mrow> </math></EquationSource> </InlineEquation> grayscale images with a <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7305_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$20\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>20</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> error probability, we observed a <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7305_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$25\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>25</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> increase in the peak signal-to-noise ratio. This feature is not present in the single parity check algorithm. One of our key achievements is that in the event of data loss in the original image, the symmetry check algorithm can detect it using the symmetry bits and recover the lost image as a black and white image, while still performing error control.</p>

An alternative proposed single error detection algorithm for the single parity check algorithm

期刊论文
发表日期：

2025年5月10日

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Parviz Gharehbagheri,
Hamid Haj Seyyed Javadi,
Nader Jafari Rad,
Hamidreza Bakhshi

摘要

In this article, our objective is to propose an alternative algorithm to the single parity check algorithm that exhibits improved capabilities. To achieve this, we introduce a function for symmetrizing binary codes with an error resilience capability. Additionally, we present the symmetry check algorithm for error detection and provide a theoretical proof that the error detection bits of the symmetry check algorithm not only identify errors but also enable the recovery of a portion of the original binary code bits. The symmetry check algorithm has the ability to recover a portion of the data in any channel, regardless of the level of noise present, in proportion to the introduced noise. By implementing the symmetry check algorithm on a group of $512 \times 512$ $512 \times 512$ grayscale images with a $20\%$ $20 %$ error probability, we observed a $25\%$ $25 %$ increase in the peak signal-to-noise ratio. This feature is not present in the single parity check algorithm. One of our key achievements is that in the event of data loss in the original image, the symmetry check algorithm can detect it using the symmetry bits and recover the lost image as a black and white image, while still performing error control.