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 |
Note: 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) |
Note: 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).