Table I
Two-Filter Output
Table II
Decoding Table for the (n,k) = (7,4) Hamming Code
| Syndrome s | Bit in error | Coset Leader e |
|---|
| 000 | 0 | 0000000 |
| 100 | 1 | 1000000 |
| 010 | 2 | 0100000 |
| 001 | 3 | 0010000 |
| 110 | 4 | 0001000 |
| 011 | 5 | 0000100 |
| 111 | 6 | 0000010 |
| 101 | 7 | 0000001 |
Table III
Nonerror-Correcting Output with Training Set (No Noise), F = 4, L = 2
| Letter | Code word | Letter | Code word |
|---|
| A | 0000 | a | 1000 |
| B | 0001 | b | 1001 |
| C | 0010 | c | 1010 |
| D | 0011 | d | 1011 |
| E | 0100 | e | 1100 |
| F | 0101 | f | 1101 |
| G | 0110 | g | 1110 |
| H | 0111 | h | 1111 |
Table IV
Reference Key Vector Images and Associated Output Code Words from the (7,4) Hamming Coded Associative Processor with F = 7, L = 2 and No Noise
| Letter | Code word | Letter | Code word |
|---|
| A | 0000000 | a | 1010001 |
| B | 1101000 | b | 0111001 |
| C | 0110100 | c | 1100101 |
| D | 1011100 | d | 0001101 |
| E | 1110010 | e | 0100011 |
| F | 0011010 | f | 1001011 |
| G | 1000110 | g | 0010111 |
| H | 0101110 | h | 1111111 |
Table V
Performance of 4-Bit vs 7-bit Hamming Code Associative Processors for Various Levels of the Noise Variance σ2 (the Total Number of Images is 16)
| σ2 Noise | No error correction 4-bit code percent correct (number of errors) | Hamming code percent correct (number of errors) | Number of corrected errors in Hamming code processor |
|---|
| 0.15 | 81% (3) | 100% (0) | 7 |
| 0.20 | 50% (8) | 81% (3) | 9 |
| 0.25 | 50% (8) | 62% (6) | 3 |
| 0.40 | 38% (10) | 56% (7) | 4 |
| 0.50 | 38% (10) | 44% (9) | 6 |
| 0.60 | 31% (11) | 31% (11) | 5 |
Table VI
Output from σ2 = 0.2 Output Noise Tests
| Letter | 4-Bit code output | (7,4) Hamming code output | Corrected Hamming code |
|---|
| A | 0010* | 0000001** | 0000000 |
| B | 0001 | 0111000* | |
| C | 0010 | 0110110** | 0110100 |
| D | 0011 | 1011001* | |
| E | 1100* | 1110010 | |
| F | 0001* | 0001011* | |
| G | 1011* | 1010110** | 1000110 |
| H | 0111 | 0101100** | 0101110 |
| a | 0000* | 1010011** | 1010001 |
| b | 1001 | 1111001** | 0111001 |
| c | 1000* | 1101101** | 1100101 |
| d | 1001 | 0001101 | |
| e | 1100 | 0000011** | 0100011 |
| f | 1100* | 1001011 | |
| g | 1110 | 0010011 | |
| h | 1111 | 0111111** | 1111111 |
For the 4-bit code result the
* indicates error; for the 7-bit (
7,4) Hamming code result the
* indicates uncorrectable error; the
** indicates correctable error.
Table VII
Estimated Probability p of an Output Bit Transition Error for Input Images with Various Noise σ2
| Noise variance σ2 | Bit error probability p | 4-Bit output (number of errors) | Hamming code(number of errors) |
|---|
| 0.4 | 0.02 | 89% (18) | 93% (10) |
| 0.5 | 0.04 | 81% (34) | 95% (8) |
| 0.6 | 0.08 | 73% (44) | 91% (15) |
| 0.7 | 0.10 | 65% (45) | 85% (20) |
| 0.8 | 0.11 | 63% (59) | 80% (32) |
| 1.0 | 0.13 | 54% (73) | 69% (50) |
| 1.3 | 0.18 | 43% (92) | 63% (59) |
: Each
p estimate is based on ten runs. The percentage of the total 160 images for each
σ2 value correctly classified for the 4-bit Hamming code schemes are listed (with the number or images mis-classified given in parenthesis).
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