(Perfect) Integer Codes Correcting Single Errors

Integer codes correcting single asymmetric errors

“…In this paper, we have restricted ourselves to values of b less than or equal to 12. The reason for this is twofold: first, the number of the C i 's roughly doubles with the increase of b (Tables 1 and 2), and second, for the mentioned values of b the proposed codes are fully comparable with those presented in [15].…”

“…The error correction procedure for the presented codes is very similar to those described in [15], [16]. In short, if S ≠ 0, the decoder will lookup the syndrome table (ST) to find the entry with the error correction data.…”

“…To illustrate this, in Fig. 2, they are compared with codes from [14] and [15]. As we can see, for practical data lengths up to 4096 bits, the proposed codes require the same number of check-bits as the best systematic SAECCs [14] and one check-bit less than integer single error correcting (SEC) codes [15].…”

“…2. Comparison of information-bit lengths and check-bit lengths of the best systematic SAECCs[14], the proposed codes and integer SEC codes[15].…”

Integer Codes Correcting Single Errors within Two Bytes

“…The first step in the construction of the proposed codes is to determine the integer values of single errors corrupting one and two b-bit bytes. For that purpose, we will rely on the analysis from [22]. In that paper, it was shown that the integer value of a single error is equal to ei = ± 2 r , where 0 ≤ r ≤ b -1 and 1 ≤ i ≤ k + 1.…”