Single parity check code A single-parity-check code uses a single-parity bit to generate codeword with an even or odd parity, i.e. an even or odd number of nonzero bits respectively. Then, and for an even-parity code, parity-check sum: Parity-check matrix and generator matrix are trivial: Decode...
T ransmission of encoded information through DMC Source messages are encoded in M codewords : where the codeword letter is a letter of input alphabet : , In DMC, noise sequences (error patterns) : are added to codewords, producing output sequences : where the output sequence letter is a letter o...
Variable length binary codes Codeword length . Average number of code letters (bits) per source symbol ( average length of a codeword): , for binary code: . If then, By proper selection of codeword lengths, the minimum distance of one bit from absolute minimum (4.2.2) can be achieved. Distance ...
Decimal to binary conversion Step 1. Set j = n . Divide a decimal number by 2, set the reminder into the right most bit . Step 2. Set . Divide the last obtained result by 2, set the reminder into the j -th bit Step 3. If the last obtained result is 1, then set and GO TO Step 4, otherwise GO TO St...
Hamming code Hamming codes are the primary class of single-error-correcting codes. Number of nonzero syndromes of an block code is: . Number of single-error patterns is n . Then, to correct every single error inequality (6.4.1) has to be fulfilled: In general, number of all errors up to errors is:...
Measurement test treated as data transmission through DMC If are data generated by a source (channel input), the measured data - System Under Test (SUT) states, and are the received data (channel output), measurements - SUT states clustered in ambiguity sets then, the acquired mutual informatio...
Product code A single-parity-check code has no error-correction capability, it can only detect occurrence of odd number of errors. Error correction can be achieved by combining two single-parity-check codes and , in a form of rectangular array. The code parameters are: ; , Then, such product code ...
Source with memory Consider a sequence of messages of a discrete memoryless source X , of the length L : where is any element of X . Total of all sequences: A discrete memoryless source X described by sequences (2.2.1) is called the L -the extens...
S ymmetric Channel (SC) A DMC is defined to be symmetric if set of outputs can be partitioned into subsets in such a way that for each subset , each row of the corresponding submatrix is a permutation of each other row and each column is a permutation of each other column. Example SC transition p...
Classification of transmissions Total: . Error less: M . Erroneous: . Non detectable errors: when any of M codewords becomes any other codeword. Detectable errors: , when any of M code words becomes any of redundant sequences. Correctable errors: , as each of redundant sequences (words) can ...
