Gray code In this code, two code words that encode consecutive digital numbers differ in only one bit. Step 1. Perform decimal to binary conversion. The word is obtained. Step 2. Shift binary word into the right by one bit, i.e. delete the least w...
A prefix condition code A prefix condition code is defined as a code in which no codeword is the prefix of any other codeword. For the given integers assigned to a prefix condition codewords, the minimum alphabet length D can be found. This length can be determined from equation (4.1.1) or can be...
Binary Markov source of the second order For such source: M =2, L =2, and the source N =4 states are: . The source is defined (modeled) by probability assignment of four states: and eight conditional probabilities: . To find the source entropy, at first, joint probabilities have to be calculated...
CYCLIC CODES In general, encoding and decoding of linear block codes can be concisely described in terms of matrix algebra, generator or parity-check matrix. A subclass of linear codes can be extracted, the so called cyclic codes. Such codes are usually described in terms of polynomial algebra, gen...
Entropy of individual source Entropy H ( X ) is measure of information generated by a memoryless source X , It expresses the expected quantity of information contained in a single message, measured in [bit/message of X ] or simply [bit]. ...
Error control limits Error detection limit : the maximum number of errors that a block code can detect. To detect every single error, from the total of n single errors, . To detect every single and double error, . To detect all errors up to , ...
Fixed length binary information codes A decimal number L of l digits is considered. This number is encoded in the fixed-length binary information code: . Four codes are considered (see Fig.4.1.2). Codeword index i is omitted, for simplicity of description. ...
Binary Coded Decimal to BCD (8421) code Each decimal digit is encoded in four bit binary word, word with weights: 8421. Then, . Find BCD codeword. Four digits 1979 encoded in the binary code 8421 give: 1 9 7 9 ...
Binary to decimal conversion For the binary codeword of the length n : the decimal number: It can be viewed, that (4.3.1) is the weighed sum, bits of a binary codeword are the weights. ...
D eterministic Channel Example channel transition probabilities and transition probability diagram: 0 021 1 1 1 1 ...
