Hamming code: Difference between revisions

Revision as of 15:03, 11 November 2024

Revision as of 05:11, 12 November 2024

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If the decoder does not attempt to correct errors, it can reliably detect triple bit errors. If the decoder does correct errors, some triple errors will be mistaken for single errors and "corrected" to the wrong value. Error correction is therefore a trade-off between certainty (the ability to reliably detect triple bit errors) and resiliency (the ability to keep functioning in the face of single bit errors).

This extended Hamming code was popular in computer memory systems, starting with [[IBM 7030 Stretch]] in 1961,{{sfn|Kythe|Kythe|2017|p=115}} where it is known as ''SECDED'' (or SEC-DED, abbreviated from ''single error correction, double error detection'').{{sfn|Kythe|Kythe|2017|p=95}} Server computers in 21st century, while typically keeping the SECDED level of protection, no longer use the Hamming's method, relying instead on the designs with longer codewords (128 to 256 bits of data) and modified balanced parity-check trees.{{sfn|Kythe|Kythe|2017|p=115}} The (72,64) Hamming code is still popular in some hardware designs, including [[Xilinx]] [[FPGA]] families.{{sfn|Kythe|Kythe|2017|p=115}}

==[7,4] Hamming code==