Distance increasing mapping for variable distance block code. Issue 9 (1st June 2020) - Talmale, Seema; Unnikrishnan, Srija; Lande, Bhaurao K.
Abstract : A new idea regarding the generation of a block code for a code rate of 1/2 and less than 1/2 is developed here. The minimum distance between the codewords can be maximised using a suitable transformation of the P matrix in the generator matrix G of the block code. This study gives the construction of distance increasing mapping (DIM) such that the proposed code is a variable distance modified block code with a code rate equal to 1/2. An algorithm for such DIM is developed here. The construction for distance preserving mapping (DPM) is also generalised in an algorithmic way. Further, to achieve DIM from the proposed DPM, for the established codes with a code rate less than 1/2, transformation is developed with the help of permutation arrays. The performance of the codes has also been evaluated. Decoding of this code is also simple and can be carried out using the existing techniques of decoding of block codes. The probability of undetected error is found to be better than the existing block codes.