errors. However, by using minimum distance decoding, final n-k symbols of C are referred to as parity symbols. where the received word is decoded to a nearest code- The performance of a block code is often measured by word, a linear code of minimum distance t allows the the number of errors that it can correct or the amount of correction of up to 1121 errors. It can be shown that Channel protection fundamentals CHAPTER 3.4 function of a syndrome decoder is to first compute the syndrome of the received vector and then subtract the = codeword corresponding error vector from the received vector. correct decoding Another way of viewing syndrome decoding is through region a standard array [36]. A standard array of a binary code is formed by setting aside a 2n-k X 2k array and popu- lating the first row of the array with all 2k possible codewords with the all-zero codeword occupying the first column of the first row. Next, we generate all pos- sible weight 1 error vectors and add each error vector to the first row to generate another row. This process is Figure 3.4-2 Example of a codebook that consists of several continued by increasing the weight of the error vector and codewords with a minimum distance of dmin- The correct decoding regions are shown as spheres centered around the filling the rows until the entire array is populated as in codewords with a radius of dmin/2. Table 3.4-1. If the result of an addition of an error vector with the first row equals a row that is already in the a linear code of minimum distance t can simultaneously standard array, then the error vector is skipped and the correct errors and detect ejerrors if lected<t - 1 with next error vector is used to generate further rows. The ecked. Moreover, it can correct ee erasures and ec errors result will be an array, where each row corresponds a shift simultaneously if ee+2ec-t-1. of all of the codewords by an error vector. The first column The minimum distance of an (n, k) linear code must will contain the error vectors and each row may be be les