Cyclic and Linear Block Codes Questions and Answers for Viva

Answer-1: A block code is a coding scheme that divides data into fixed-length blocks and encodes each block separately.

Answer-2: A linear block code is a block code in which the code words form a linear subspace of the vector space over the finite field.

Answer-3: Linear block codes are represented by generator and parity-check matrices, which define the linear relationship between the code words.

Answer-4: The key property of linear block codes is linearity, meaning that the sum of any two valid codewords is also a valid codeword.

Answer-5: Linear block codes have simple encoding and decoding algorithms, and their linearity allows for efficient error detection and correction.

Answer-6: A cyclic code is a special type of linear block code with the property that cyclically shifting any codeword results in another codeword in the code.

Answer-7: Cyclic codes can be represented using generator polynomials or parity-check polynomials, which define the code properties and structure.

Answer-8: A generator polynomial is a polynomial whose roots correspond to the cyclic code's codewords when evaluated at specific field elements.

Answer-9: Cyclic codes are generated by selecting a generator polynomial and constructing codewords by polynomial division.

Answer-10: A parity-check polynomial is a polynomial that satisfies the property that the sum of its coefficients times the corresponding codeword symbols equals zero.

Answer-11: The generator matrix in cyclic codes is a matrix representation of the generator polynomial, used for encoding data into codewords.

Answer-12: The parity-check matrix in cyclic codes is a matrix representation of the parity-check polynomial, used for error detection and decoding.

Answer-13: Systematic codes are linear block codes in which a portion of the codeword directly represents the input data, making it easier to decode.

Answer-14: Systematic cyclic codes are constructed using generator polynomials that have a factor of (x + 1), allowing for easy encoding and decoding.

Answer-15: Systematic cyclic codes simplify the encoding and decoding process, as the original data can be directly extracted from the codeword.

Answer-16: CRC is an error-detecting code commonly used in data transmission, where a short sequence of redundant bits is appended to the data to detect errors.

Answer-17: CRC works by dividing the message and appended CRC bits by a predetermined polynomial. The remainder obtained after division is transmitted along with the message. At the receiver's end, the remainder is recalculated, and if it doesn't match the expected value, an error is detected.

Answer-18: Cyclic codes are widely used in telecommunications, data storage systems, error correction in digital communication, and various other digital communication applications.

Answer-19: The Hamming distance in cyclic codes is the minimum number of positions at which any two distinct codewords differ. It determines the error detection and correction capability of the code.

Answer-20: Errors in cyclic codes can be corrected using algorithms such as the Syndrome Decoding algorithm, which utilizes the parity-check matrix to determine and correct errors in the received codeword.