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Understanding Hamming Code for Error Detection and Correction

Explore examples of Hamming codes with parity bit flip, single-bit errors, double-bit errors, and error correction techniques. Learn how Hamming code methods can detect and correct errors efficiently.

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Understanding Hamming Code for Error Detection and Correction

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  1. Figure 5.5Hamming Example – 8 bit Data(No Errors – ED[0:12] is Encoded(d01…d08)) Data even parity Data odd parity (p03=1) ED odd parity (so pW=1) Check bits: No difference pW2 == pW (as expected) Check-Bits == 0 AND pW == pW2 => NO ERRORS  Sam Siewert 1

  2. Figure 5.6Hamming Example (Data SBE in Data ED[5]) SBE, bit-flipped (d02 from 1 to 0) SYN encodes bit position (flip ED[5] to restore) pW2 != pW (parity error) Check-Bits != 0 AND pW != pW2 => SBE, CAN CORRECT  Sam Siewert 2

  3. Figure 5.7Hamming Example (Data MBE) MBE, 2 bits-flipped (d02 and d05 both) SYN encodes MBE (out of range for ECC) pW != pW2 (double MBE) Check-Bits != 0 AND pW == pW2 => DOUBLE MBE DETECTED  Sam Siewert 3

  4. Figure 5.8Hamming Example (Parity SBE in Encoded Data) SBE, bit-flipped (p04 from 1 to 0) SYN encodes bit position (flip ED[8] to restore) pW2 != pW (parity error) Check-Bits != 0 AND pW != pW2 => Parity SBE, CAN CORRECT  Sam Siewert 4

  5. Figure 5.9Hamming Example(pW flip – Simple Parity Error, No ED error!) SYN indicates no error (pW flip only possibility) pW2 != pW (parity error) Check-Bits == 0 AND pW != pW2 => pW ERROR  Sam Siewert 5

  6. Figure 5.10FS LB to PB Mapping Example #1 - Start #2 #3 #4 #5 #6 #7 #1 – All blocks FREE #2 – Erase S0 & S1, Write LB 0, 1, 2, 3 #3 – Read LB 0, 2, Modify, Write LB 0, 2 #4 – Read LB 1, 3, Modify, Write LB 1, 3 #5 – Read LB 0, 2, Modify and Cache #6 – Buffer LB 0, 1, 2, Erase S0 #7 – Write-back LB 0, 1, 2 to S0 11 Writes, 3 Sector Erases Write Amplification = 11 / 10 = 1.1 Start State from End State #7 Above #8- Read LB 1, 3, Modify and Cache #9 – Erase S1 #10 – Write-back LB 1, 3 to S1 #11 – Read LB 0, 2, Modify, Write LB 0, 2 #12 – Read LB 1, 3, Modify and Cache #13 – Erase S0 #14 – Write-back LB 1, 3 6 Writes, 2 Sector Erases Write Amplification = 17 / 16 = 1.0625 #8 #9 #10 #11 #12 #13 #14  Sam Siewert 6

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