Error correction coding method and system for near-optimal binary array

Abstract

This disclosure provides an error correction coding method and system for near-optimal binary arrays, relating to the technical field of encoders or decoders. The method includes: acquiring a binary array and preprocessing it; anchoring and locating the preprocessed binary array, transforming global location into local error correction for rows and columns; applying VT checksum constraints to the local error correction regions, introducing a main diagonal checksum equation for the array's rows / columns, enabling the recovery of symbols in missing rows or columns during decoding; recovering affected sub-blocks and determining precise deletion indices based on a VT-type signature error correction mechanism; recovering the remaining symbols in the missing rows / columns using the main diagonal checksum, thus completing the full array decoding. This disclosure approximates the information theory lower bound on redundancy as closely as possible while providing an engineering-practical coding process and complexity guarantee.

Claims

1. An error correction coding method for near-optimal binary arrays, characterized in that, include: Obtain the binary array and preprocess it; The preprocessed binary array is anchored and positioned, and the global positioning is transformed into local error correction of rows and columns; Apply VT checksum constraints to the local error correction region and introduce main diagonal check equations for the rows / columns of the array so that the symbols in the missing rows or columns can be retrieved one by one during decoding. The affected sub-blocks are recovered based on the VT-type signature error correction mechanism, and the precise deletion index is determined. The remaining symbols of the missing rows / columns are recovered with the help of the main diagonal check, thus completing the full array decoding.

2. The error correction coding method for near-optimal binary arrays as described in claim 1, characterized in that, The process of obtaining the binary array and preprocessing it includes: Obtain the binary array and divide it into several key sub-blocks according to row and column indices: U represents the first ν rows and the last (n) rows. ν) subarrays; V is the subarray of the next (n) column. ν) is a subarray of rows and the first ν columns; S is a subarray of the first µ rows and the column interval [µ+1,ν]; T is a subarray of the row interval [µ+1,ν] and the first µ columns; the remaining area is denoted as K.

3. The error correction coding method for near-optimal binary arrays as described in claim 1, characterized in that, The step of anchoring and locating the preprocessed binary array, transforming global localization into row and column local error correction, includes: Anchor bits and short alternating prefixes are preset in the first row and first column of the array. After deletion occurs, it is quickly determined whether the deletion occurred in the upper, middle or lower row interval or the corresponding column interval, thereby transforming global positioning into local error correction for sub-block U / V or S / T.

4. The error correction coding method for near-optimal binary arrays as described in claim 1, characterized in that, The application of VT checksum constraints to the local error correction region includes: Pairs of subarray U and subarray V Subarray S, Subarray T Apply the following constraints respectively: (i) Any two adjacent columns are different; (ii) Treat each column as a ν-bit or µ-bit binary vector and map it to an integer sequence, then apply VT checksum constraints to the binary signature of the integer sequence; Once a single-column deletion or a transposed single-column deletion occurs, the atomic block can be uniquely recovered and the index of the deleted column can be determined if the vector of the deleted column is known.

5. The error correction coding method for near-optimal binary arrays as described in claim 1, characterized in that, The above introduces a main diagonal parity check equation for the rows / columns of the array, enabling the symbols in the missing rows or columns to be retrieved item by item during decoding, including: For the array of the first i row or number i The column introduces a main diagonal check equation, for each i Apply the following to ∈[2,n]: ⊕_{k≠i}(A_{i,k}⊕A_{k,i})⊕A_{i,i}=p_i, where p_i is a pre-given or system-fixed parity constraint bit; take p_i=0 and let the diagonal element A_{i,i}=⊕_{k≠i}(A_{i,k}⊕A_{k,i}), thus ensuring that the equation always holds.

6. The error correction coding method for near-optimal binary arrays as described in claim 1, characterized in that, The affected sub-blocks are recovered based on the VT-type signature error correction mechanism, and the precise deletion index is determined. The remaining symbols in the missing rows / columns are recovered using main diagonal parity checking, completing the full array decoding, including: During encoding, first process the subarrays U and V... S, T Perform explicit filling to make adjacent columns distinct; then calculate subarrays U and V. The VT-type comprehensive check value a, and subarrays S and T The VT-type comprehensive check value b is obtained; the binary representations of the comprehensive check values ​​a and b are embedded into the predefined available off-diagonal positions respectively; finally, the remaining information bits are sequentially filled into the remaining off-diagonal positions, and the codeword is generated by calculating the main diagonal elements.

7. An error correction coding system for near-optimal binary arrays, characterized in that, include: The parameter acquisition module is used to acquire the binary array and preprocess it; The positioning module is used to anchor and position the preprocessed binary array, converting global positioning into local error correction of rows and columns; The verification calculation module is used to apply VT checksum constraints to the local error correction region, introduce the main diagonal check equation for the rows / columns of the array, so that the symbols in the missing rows or columns can be retrieved one by one during decoding; The decoding module is used to recover the affected sub-blocks and determine the precise deletion index based on the VT-type signature error correction mechanism, and to recover the remaining symbols of the missing rows / columns with the help of the main diagonal check, thus completing the full array decoding.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the error correction coding method for near-optimal binary arrays as described in any one of claims 1-6.

9. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement an error correction coding method for near-optimal binary arrays as described in any one of claims 1-6.

10. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement an error correction coding method for near-optimal binary arrays as described in any one of claims 1-6.

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