Abstracts of brief communications (posters) are incorporated during this book. they're prepared alphabetically part by way of part. Abstracts bought among may perhaps sixteen, 1994 and should 22, 1994 look less than past due abstracts. these bought after may possibly 22, 1994 should not incorporated.
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Note that the RS (Reed-Solomon) codes are nonbinary BCH codes, which has the largest possible minimum distance for any linear code with the same message size K and codeword length N , yielding the error correcting capability of dc = ( N − K ) / 2 . 4 Convolutional Coding and Viterbi Decoding In the previous sections, we discussed the block coding that encodes every K -bit block of message sequence independently of the previous message block (vector). In this section, we are going to see the convolutional coding that converts a K -bit message vector into an N -bit channel input sequence dependently of the previous ( L − 1) K -bit message vector ( L : constraint length).
3 Cyclic Coding A cyclic code is a linear block code having the property that a cyclic shift (rotation) of any codeword yields another codeword. Due to this additional property, the encoding and decoding processes can be implemented more efficiently using a feedback shift register. 25) into an N -bit codeword represented by an ( N − 1) th-degree polynomial is as follows: 1. Divide x N − K m(x) by the generator polynomial g (x) to get the remainder polynomial rm ( x ) . 2. 26) + m0 x N −K + m1 x N − K +1 + " + mK −1 x N −1 which has the generator polynomial g(x) as a (multiplying) factor.
2. 26) + m0 x N −K + m1 x N − K +1 + " + mK −1 x N −1 which has the generator polynomial g(x) as a (multiplying) factor. Then the first ( N − K ) coefficients constitute the parity vector and the remaining K coefficients make the message vector. Note that all the operations involved in the polynomial multiplication, division, addition, and subtraction are not the ordinary arithmetic ones, but the modulo-2 operations. 1) find the codeword for a message vector m = [1 0 1 1]. 2) to get the remainder polynomial rm ( x ) = 1 and add it to x N − K m ( x ) = x 3m ( x ) to make the codeword polynomial as c ( x ) = rm ( x ) + x 3 m ( x ) = 1 + 0 ⋅ x + 0 ⋅ x 2 + 1 ⋅ x 3 + 0 ⋅ x 4 + 1 ⋅ x 5 + 1 ⋅ x 6 → c = [1 0 parity 0 1 | 0 1 1] message The codeword made in this way has the N − K = 3 parity bits and K = 4 message bits.