RU2006141316A - METHOD FOR SYNDROME DECODING OF CYCLIC LINEAR BLOCK CODE AND DEVICE FOR ITS IMPLEMENTATION - Google Patents

Claims (9)

1. A syndromic decoding method with a “tough” solution of a cyclic linear block code, comprising the sequential execution of the following procedures: calculating the syndrome for the received distorted code implementation, selecting the syndrome from the preformed correspondence table — the leader of the adjacent error class of the corresponding correction vector, mod2 addition of the received distorted code implementations with the selected correction vector and highlighting the systematic part of the corrected codeword as decoded information, ayuschiysya that code for the received distorted implementation b⊕e _kc perfect code calculated syndrome advanced s, at any position of a nonzero element which line numbers are determined in the extended check matrix H _{n, n,} which comprise a gap is also non-zero element, then each of of these lines is added in pairs in mod2 with the extended syndrome s, as a result of which the current syndromes s _{1, i of the} first step of the iteration of the presentation of the extended syndrome are calculated in the form of linear combinations of the rows of the extended test mat eggs H _{n, n} , in addition, each current syndrome s _{1, i} is associated with a vector N _{1, i} , in which the row number of the expanded check matrix H _{n, n} is entered _, which participated in the formation of the current syndrome s _{1, i} , and if one of the current syndromes s _{1, i} = 0, then the minimum weight error vector is found, and the codeword element distorted in the communication channel is indicated in N _{1, i} , then after the correction (inversion) of the distorted element, the corrected systematic part of the code is selected as decoded information words, and if all the current synd ohms s _{1, i} ≠ 0 then go to the next step of the iteration, that is, for each current syndrome previous m-order iteration step s _{m, i} are calculated pair of vectors s _{m + 1, i,} N _{m + 1, i,} as well as and during the first step of the iteration, if we replace each time the extended syndrome s with the current syndrome s _{m, i} , now if one of the current syndromes s _{m + 1, i} = 0, then the error vector of the minimum weight is found, and the elements distorted in the communication channel the code word is indicated in N _{m + 1, i} , then after correction (inversion) of the distorted elements, the decoded information is selected from the corrected systematic part of the codeword, and if all the current syndromes are s _{m + 1, i} ≠ 0, then we proceed to the next step of the iteration, the number of which cannot be more than t (t is the multiplicity of corrected errors), etc., up to until the current syndrome, which is a zero vector, is formed, then after the correction (inversion) of the distorted elements, the corrected systematic part of the code word is selected as decoded information. 2. The method according to claim 1, characterized in that when decoding imperfect codes with a “hard” solution, if a syndrome that is a zero vector is not found in the t-th iteration step, then it is necessary to refuse to correct this distorted codeword, since the weight of the correction vector exceeds the multiplicity of the corrected errors of the (n, k) code and is equal to t + 1, however, if it is necessary to correct the corrected t + 1-fold errors of the imperfect code, then it is necessary to completely t + 1 iterate, moreover, if at t + 1th iteration, only one syndrome is defined rum, which is a zero vector, then a correctable t + 1-fold error is found, the distorted elements of which are given by the vector N _{t + 1, i} , and if several syndromes that are zero vectors are defined at the t + 1st iteration, then an uncorrectable t + 1-time error and correction should be discarded. 3. The method according to claim 1, characterized in that in the case of decoding extended codes with a “hard” decision, before the decoding, the extension element is removed from the possibly distorted code word received through the communication channel. 4. The method according to claim 1, characterized in that in the case of decoding shortened codes with a “hard” solution, before decoding, zero elements are added to the beginning of a possibly distorted code word received over the communication channel, the number of which is equal to the shortening value. 5. The method according to claim 1, characterized in that in the case of decoding perfect, imperfect and extended codes with a “soft” solution for each pair of vectors s _{m, i} and N _{m, i} , a modified metric is calculated

or

where p (for _j / b _{j, c} ) is the conditional probability that the value of _{j is} obtained at the output of the demodulator when transmitting the code word of the _ith symbol over the communication channel at the jth position, e _{i, j} is the jth element of the ith error vector e _i belonging to the adjacent error class of the syndrome s _{m, i} and those elements of the distorted codeword received from the communication channel that are specified by the vector N _{m, i} for which s _{m, i} = 0 and the metric m _{m, i is} maximal. 6. The method according to claim 1, characterized in that in the case of decoding shortened codes with a “soft” solution, before decoding, zero elements with conditional probabilities p (for _j / b _{j, 0} ) are added to the beginning of a possibly distorted code word received through the communication channel = 1 and p (for _j / b _{j, 1} ) = 0. 7. The method according to claim 1, characterized in that in order to reduce the computational complexity of decoding, the current syndromes s _{m, i} , in which in the vector N _{m, i the} positions of the distorted elements are repeated, are excluded from consideration. 8. The method according to claim 1, characterized in that to reduce the computational complexity of the decoding from the consideration, the repeating current syndromes s _{m, i} are excluded. 9. The syndromic decoding device of a cyclic linear block code for implementing the method according to any one of claims 1 to 8, characterized by a syndrome calculation unit, a current information storage and updating unit, a reading unit, a nonzero element search unit, an expanded check matrix search unit, an calculation unit current information, a corrected codeword correction unit, a decoded information generation unit.