Ordered statistical decoding method and device

Abstract

The invention provides an ordered statistical decoding method and device, and relates to the technical field of communication. The ordered statistical decoding method comprises the following steps: carrying out confidence attenuation on local bits in a receiving sequence to obtain a local attenuation sequence; determining reliable bits in the target sequence; the target sequence is the attenuation sequence; performing a re-coding operation based on the reliable bits and a generated matrix to obtain a decoding codeword candidate list; and determining a decoding result corresponding to the target sequence based on the decoding codeword candidate list. According to the method, the confidence of the receiving sequence is locally attenuated, the confidence of error bits with large confidence is also attenuated, and then the error bits are removed from recoded reliable bits, so that the decoding performance is improved.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and in particular, to an ordered statistic decoding method and apparatus. Background Art

[0002] The ordered statistic (OSD) decoding algorithm is a general decoding algorithm applicable to various linear block codes. Its main decoding steps can be divided into three steps: First, the received codeword symbols and the generator matrix are rearranged according to the magnitude of their log-likelihood ratios. Gaussian elimination is performed on the rearranged generator matrix to obtain a new systematic form generator matrix. The reliable bits are changed into information bits, and the error pattern and the sorted reliable information bits are re-encoded together to obtain a list of candidate decoded codewords. The codeword with the smallest Euclidean distance in the list of candidate codewords is selected as the decoded codeword. However, due to the existence of error bits with high confidence, it affects the re-encoding to obtain the correct decoded codeword, thereby affecting the decoding performance. Summary of the Invention

[0003] The present invention provides an ordered statistic decoding method and apparatus to solve the defect in the prior art that the correct decoded codeword cannot be selected due to error bits with high confidence, and improve the decoding performance.

[0004] The present invention provides an ordered statistic decoding method, including the following steps.

[0005] Attenuate the confidence of local bits in the received sequence to obtain a local attenuation sequence; Determine the reliable bits in the target sequence; the target sequence is the attenuation sequence; Perform a re-encoding operation based on the reliable bits and the generator matrix to obtain a list of candidate decoded codewords; Based on the list of candidate decoded codewords, determine the decoding result corresponding to the target sequence.

[0006] According to the ordered statistic decoding method provided by the present invention, performing a re-encoding operation based on the reliable bits and the generator matrix includes: Based on the reliable bits and the original systematic generator matrix, use Gaussian elimination to generate a re-encoded systematic form generator matrix; Perform a re-encoding operation based on the systematic form generator matrix.

[0007] According to the ordered statistic decoding method provided by the present invention, performing a re-encoding operation based on the reliable bits and the generator matrix includes: Construct a permutation function polynomial with the position coordinates of the reliable bits in the target sequence as independent variables and the position coordinates of the information bits in the target sequence as dependent variables; Based on the permutation function polynomial, perform permutation adjustment on the coordinate positions of each bit in the target sequence to obtain a target permutation sequence; Based on a given systematic generation matrix, perform re-encoding operation on the target sequence to obtain a list of candidate decoded codewords.

[0008] According to the ordered statistic decoding method provided by the present invention, the permutation function polynomial is an affine permutation polynomial.

[0009] According to the ordered statistic decoding method provided by the present invention, construct a permutation function polynomial with the position coordinates of the reliable bits in the target sequence as independent variables and the position coordinates of the information bits in the target sequence as dependent variables, including: Respectively use the position coordinates of different partial reliable bits in the target sequence as independent variables and the position coordinates of the information bits in the target sequence as dependent variables to construct permutation function polynomials, and obtain a plurality of permutation function polynomials.

[0010] According to the ordered statistic decoding method provided by the present invention, based on the permutation function polynomial, perform permutation adjustment on the coordinate positions of each bit in the target sequence, including: Respectively perform permutation adjustment on the coordinate positions of each bit in the target sequence based on each permutation function polynomial to obtain a plurality of permutation sequences; Based on the confidence levels of the information bit bits in each permutation sequence, select the target permutation sequence from the permutation sequences.

[0011] According to the ordered statistic decoding method provided by the present invention, before determining the reliable bits in the target sequence, it further includes: Perform multi-directional derivation on the local attenuation sequence to obtain derivative sequences in each direction of the local attenuation sequence; Use each derivative sequence as a target sequence, jump to the step of determining the reliable bits in the target sequence, and obtain the decoding results corresponding to each derivative sequence; Reconstruct the decoded sequence based on the decoding results corresponding to each derivative sequence.

[0012] According to the ordered statistic decoding method provided by the present invention, after reconstructing the decoded sequence based on the decoding results corresponding to each derivative sequence, it further includes: Use a parity-check matrix to check the decoded sequence; If the check passes, output the decoding result based on the decoded sequence; If the check fails, jump to the multi-directional derivation step to perform multi-directional derivation on the decoded sequence.

[0013] According to the ordered statistic decoding method provided by the present invention, when the check is not passed and the convergence direction of the decoder is incorrect, the local bits with attenuated confidence in the received sequence are adjusted, and the local attenuation sequence is updated.

[0014] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the ordered statistic decoding method described above is implemented.

[0015] The present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the ordered statistic decoding method, the ordered statistic joint decoding method, the ordered statistic decoding method based on local attenuation, or the ordered statistic joint decoding method based on local attenuation described above is implemented.

[0016] The present invention also provides a computer program product, including a computer program. When the computer program is executed by a processor, the ordered statistic decoding method described above is implemented.

[0017] An ordered statistic decoding method and device provided by the present invention attenuate the confidence of the received sequence locally. The confidence of the wrong bits with large confidence will also be attenuated. Therefore, when selecting a codeword based on the Euclidean distance in the codeword candidate list, it will not be affected by the wrong bits with large confidence. Furthermore, the correct decoded codeword can be selected from the decoded codeword candidate list, ensuring the decoding performance. Description of the Drawings

[0018] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0019] Figure 1 It is a schematic flowchart of the OSD decoding method based on local attenuation of confidence provided by an embodiment of the present invention.

[0020] Figure 2 It is a schematic flowchart of the original OSD joint decoding method with local attenuation of confidence provided by an embodiment of the present invention.

[0021] Figure 3 It is one of the simulation result diagrams of the decoding effect provided by an embodiment of the present invention.

[0022] Figure 4 It is a schematic flowchart of the permutation OSD joint decoding method with local attenuation of confidence provided by an embodiment of the present invention.

[0023] Figure 5 It is a schematic flow chart of the permutation-based OSD decoding method provided by an embodiment of the present invention.

[0024] Figure 6 It is the second simulation result diagram of the decoding effect of an embodiment of the present invention.

[0025] Figure 7 It is a schematic structural diagram of an electronic device provided by an embodiment of the present invention. Detailed implementation manners

[0026] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0027] The following combines Figures 1-7 to describe the ordered statistic decoding method of the present invention.

[0028] Figure 1 It is a schematic flow chart of the OSD decoding method based on confidence local attenuation provided by an embodiment of the present invention. As Figure 1 shown, the method includes the following: Step 101: Attenuate the confidence of local bits in the received sequence to obtain a local attenuation sequence.

[0029] Step 102: Determine the reliable bits in the target sequence; the target sequence is the attenuation sequence or the transformed sequence of the attenuation sequence.

[0030] Step 103: Perform a re-encoding operation based on the reliable bits and the generator matrix to obtain a list of candidate decoded codewords.

[0031] Step 104: Determine the decoded result corresponding to the target sequence based on the list of candidate decoded codewords.

[0032] In the embodiment of the present invention, the confidence of the local bits in the received sequence is attenuated, and a re-encoding operation is performed based on the locally attenuated sequence. The decoded result is selected based on the list of candidate decoded codewords, and the decoded result is verified. If the verification fails, the bits whose confidence is attenuated are replaced (i.e., the local position changes), and the updated attenuation sequence is obtained. Steps 101 to 104 are continued to be repeated until a decoded result that satisfies the verification relationship is obtained.

[0033] In the embodiments of the present invention, the decoding operation in step 103 may adopt the OSD decoding method based on Gaussian elimination in the prior art (i.e., the original OSD decoding method), or may adopt the permutation-based OSD decoding method provided in the following embodiments of the present invention (which will be introduced in detail below). Of course, other decoding methods in the prior art may also be adopted.

[0034] When decoding using the OSD decoding method based on Gaussian elimination, the confidence of bits in different parts of the received sequence is attenuated respectively to obtain multiple locally attenuated sequences. The decoding method based on Gaussian elimination is used to decode each locally attenuated sequence, and the codeword with the smallest Euclidean distance is selected from the codeword candidate lists corresponding to all locally attenuated sequences as the final decoding result.

[0035] In some embodiments of the present invention, as Figure 2 shown, the confidence local attenuation, derivative decoding, and the OSD decoding based on Gaussian elimination are combined for decoding. Specifically, after the confidence of bits in a part of the original received sequence is attenuated, the locally attenuated sequence is differentiated in multiple directions. Then, the decoding method based on Gaussian elimination is used to decode each differentiated sequence, and the codeword is reconstructed based on the decoding result of each differentiated sequence (in this embodiment, the codeword reconstruction can be performed by using a voting method, that is, the confidence of relevant bit positions in the differentiation process is used to assign weights to the votes to form soft information voting, and the reconstructed codeword is obtained according to the hard decision of the soft information voting result. This is an existing reconstruction method and will not be elaborated herein). The reconstructed codeword is verified. If the verification is passed, the codeword is output. If the verification fails, the differentiated sequence is used as the target sequence to jump to the multi-directional differentiation step to perform multi-directional differentiation on the codeword, and the iteration continues. If the verification fails and converges to the wrong result, the locally attenuated bits are adjusted. For example, the confidence attenuation of the first 10 bits is adjusted to the confidence attenuation of the 5th to 14th bits. Then, the multi-directional differentiation is performed on the updated locally attenuated sequence, and the above loop iteration continues.

[0036] It should be noted that the selection of the part can be made as needed, which can be a continuous selection, such as the selection method in the above example, or an interval selection.

[0037] In some embodiments of the present invention, the local attenuation of the confidence can be realized by using a sliding window and attenuating the confidence of bits within the sliding window.

[0038] When decoding the received sequence of an additive white Gaussian noise channel, we calculate the log-likelihood ratio of the derivative sequence corresponding to the received sequence (this log-likelihood ratio is used to evaluate the confidence of bits). The received sequence The corresponding log-likelihood ratio is: , where is the received bit log-likelihood ratio, I where is the coordinate of the received sequence. The calculation formula of is: where Pr( |0) represents the probability that the received symbol is after passing through the channel when the transmitted bit is 0, and Pr( |1) represents the probability that the received symbol is

[0039] The log-likelihood ratio corresponding to the received sequence is , which reduces the confidence of local bits (such as reducing the confidence of all bits within the sliding window ). The reduced local log-likelihood ratio is , where is the attenuation factor. Specifically, taking the sliding window operation on the received sequence as an example, the confidence of the bits in the window is reduced to obtain multiple sequences with adjusted confidence, such as , , , , , , …, , , , , , , , , , , , , …, , , , , , , , , , , , , , , …, , , , …, , , , , , , , , …, , ……, , , …, , , , , , , . When contains an error bit, the confidence of the error bit in the sliding window after local attenuation will also decrease accordingly. In this way, the reliable bits after removing the error bits and re-encoding can be obtained, changing the error pattern of the OSD decoding, making it possible that the error pattern that could not be decoded and corrected originally can be decoded and corrected by the OSD, that is, making it possible to select the correct decoded codeword from the list. It should be noted that in this embodiment, the log-likelihood ratio is used to characterize the confidence.

[0040] As Figure 2 shown, this decoding scheme is mainly divided into four steps: (1) Calculate the directional derivative sequences of the received sequence; (2) Perform OSD decoding based on Gaussian elimination on the derivative sequences; (3) Reconstruct the original sequence using the decoding results of the derivative sequences; (4) When the reconstructed codeword does not satisfy the parity-check relationship of the H matrix and converges to the error result, adjust the local bits with attenuated confidence in the original received sequence, and repeat steps (1)-(3); when the reconstructed codeword satisfies the parity-check relationship of the H matrix, output the decoding result.

[0041] Specifically, taking the additive white Gaussian noise channel as an example, the received sequence corresponds to the log-likelihood ratio .

[0042] Let be any element in B, that is, refers to any differentiation direction, and its log-likelihood ratio is . Perform OSD decoding based on Gaussian elimination in multiple directions on the derivative sequences to obtain candidate codewords in multiple directions. Reconstruct the original sequence using the candidate codewords after OSD decoding of the derivative sequences in each direction. The sign bit of the log-likelihood ratio can be selected as the decoding result v .

[0043] If v satisfies the parity-check relationship of the H matrix, output the decoding result. Otherwise, change the log-likelihood ratio values in the sliding window, recalculate the log-likelihood ratios in each differentiation direction, and perform OSD decoding based on Gaussian elimination in each direction again, reconstruct the decoding result, and continue to iterate (large loop iteration). If the decoding resultv If the parity-check relationship of the H matrix is satisfied, the decoding result is output.

[0044] For example, the received sequence whose corresponding log-likelihood ratio is attenuates the confidence of the local bits of the received sequence (for example, windowing the local part of the received sequence and reducing the confidence of the bits in the window). For example, the resulting sequence is , , , , , , , …, , and then perform multi-directional derivatives on , , , , , , , …, . Perform OSD decoding based on Gaussian elimination on each multi-directional derivative sequence. Each derivative sequence corresponds to a candidate codeword list. For each derivative sequence, select the candidate codeword with the smallest Euclidean distance from its corresponding candidate codeword list as its decoding result. Then, reconstruct the decoding sequence based on the decoding results corresponding to each direction derivative sequence (the reconstruction method can choose the voting method). Select the sign bit of the log-likelihood ratio of the decoding sequence as the decoding result v , and judge whether the decoding result v satisfies the parity-check relationship of the H matrix. If it is satisfied, output the decoding result v . If it is not satisfied, perform multi-directional derivatives on the reconstructed decoding sequence and continue to iterate (small-loop iteration). If the small-loop iteration fails the parity check for the reconstructed codeword and detects an incorrect decoding convergence direction, adjust the local bits with attenuated confidence in the received sequence to obtain an updated local attenuation sequence. For example, obtain the sequence , , , , , , , , , , , …, , and then based on the updated local attenuation sequence , , , , , , , , , , , …, perform multi-directional derivatives. Repeat the above steps for small-loop iteration. If the small-loop iteration fails the parity check for the reconstructed codeword and detects an incorrect decoding convergence direction, adjust the locally decayed bits in the received sequence to obtain an updated locally decayed sequence, such as obtaining the sequence , , , , , , , , , , , , , …, . Then, for , , , , , , , , , , , , , …, perform multi-directional derivatives. Repeat the above steps until a decoding result that satisfies the parity check relationship of the H matrix is output v .

[0045] It should be noted that when using windowing operations to decay the confidence of local bits, adjusting the locally decayed bits in the received sequence can be achieved by moving a sliding window with a set step size (and decaying the confidence of the bits in the new window). If the sliding window reaches the end and still fails to output a reconstructed result that satisfies the parity check relationship, after adjusting the sliding window size, the starting position of the interval, and the value of the decay factor, the loop iteration can be restarted.

[0046] Next, the decoding effect of the decoding method based on local decay provided by the embodiments of the present invention is simulated. For the (256, 37) eBCH code decoding, as Figure 3As shown, the eDD-OSD(1) curve is the simulation effect curve of the original OSD (i.e., the OSD based on Gaussian elimination) joint decoding scheme with low-order local attenuation, and the OSD(3) and OSD(4) curves are the simulation effect curves of the high-order original OSD (i.e., the OSD based on Gaussian elimination) decoding scheme. It can be seen that the low-order local attenuation OSD joint decoding scheme has a gain of more than 1 dB compared with the high-order original OSD.

[0047] As Figure 4 shown, the decoding method in the above embodiment can also be applied to the permutation OSD decoding method (i.e., replacing the OSD decoding based on Gaussian elimination with the OSD decoding based on permutation). Specifically, the confidence of bits in different parts of the received sequence is attenuated respectively to obtain multiple locally attenuated sequences, and the permutation OSD decoding method is used to decode each locally attenuated sequence. The codeword with the minimum Euclidean distance is selected from the codeword candidate lists corresponding to all locally attenuated sequences as the final decoding result.

[0048] The permutation-based OSD decoding method provided by the embodiments of the present invention will be introduced in detail below.

[0049] As Figure 5 shown, the permutation-based OSD decoding method includes the following steps: Step 501: Construct a permutation function polynomial with the position coordinates of the reliable bits in the target sequence as independent variables and the position coordinates of the information bits in the target sequence as dependent variables.

[0050] Step 502: Based on the permutation function polynomial, permute and adjust the coordinate positions of each bit in the target sequence to obtain a target permutation sequence.

[0051] Step 503: Based on a given systematic generator matrix, perform a recoding operation on the target permutation sequence to obtain a decoding codeword candidate list.

[0052] Step 504: Based on the decoding codeword candidate list, determine the decoding result corresponding to the target sequence.

[0053] It should be noted that the target sequence in steps 501 to 504 is the locally attenuated sequence described above. The given systematic generator matrix in step 503 is an arbitrarily given systematic generator matrix, and there is no requirement for the position of the information bits in the systematic form matrix, that is, the information bits are not necessarily in the first several positions, and any position is acceptable. Just set it in advance during decoding.

[0054] The above reliable bits are generally selected based on the confidence level. Specifically, the bits in the target sequence are sorted according to the confidence level from large to small, and then the kA linear independent information bit is used as a reliable bit. In this embodiment, the confidence level is determined according to the absolute value of the received bit.

[0055] Since the codeword will be affected by channel noise during channel transmission, it is necessary to decode the received sequence. The existing original OSD decoding (i.e., the OSD decoding based on Gaussian elimination described above) is to determine the first k most reliable linearly independent bits in the received sequence as information bits, that is, to generate a matrix After sorting in descending order according to the sequence and then generating a new generating matrix through Gaussian elimination (transforming the columns corresponding to the reliable bits in the generating matrix into the form of unit vectors) for subsequent re-encoding operations and other decoding operations. However, due to the complexity of the Gaussian elimination operation and the characteristics of serial execution, its efficiency is relatively low. In response to this, the embodiment of the present invention proposes a completely different processing method from the above method (i.e., the OSD decoding method based on permutation), which directly permutes the reliable bits in the received sequence to the information positions, without operating on the generating matrix, thereby avoiding the complexity and low decoding efficiency caused by the Gaussian elimination operation. Specifically, the embodiment of the present invention introduces a permutation function , which satisfies a condition that the codeword vector after permutation still belongs to the original codeword. Briefly speaking, the permutation function can realize the permutation of the positions of each bit in the received sequence. Through this permutation function, the reliable bits are permuted to the information positions, and then a given systematic form generating matrix can be directly used for re-encoding operations. In the re-encoding operation and subsequent decoding operations, the OSD decoding based on permutation is the same as the original OSD decoding method (i.e., the OSD decoding method based on Gaussian elimination).

[0056] The permutation function mentioned above needs to be constructed, and the construction will be introduced below.

[0057] Since the purpose of the permutation function is to permute the coordinate positions of the reliable bits to the information positions, in the embodiment of the present invention, when constructing the permutation function, as described in step 501, the position coordinates of the reliable bits in the target sequence are used as independent variables, and the position coordinates of the information positions in the target sequence are used as dependent variables to construct the permutation function polynomial, that is, the known position coordinates of the reliable bits and the target coordinates (the coordinates of the information positions) to which they want to be permuted are used as the independent and dependent variables of the polynomial respectively, and the coefficients and parameters in the polynomial are solved. After obtaining the solution results of the coefficients and parameters in the polynomial, the permutation function polynomial is obtained.

[0058] Specifically, taking the position coordinates of different partial reliable bits in the target sequence as independent variables and the position coordinates of the information bits in the target sequence as dependent variables, a permutation function polynomial is constructed to obtain multiple permutation function polynomials. Based on each permutation function polynomial, the coordinate positions of each bit in the target sequence are permutationally adjusted to obtain multiple permutation sequences; based on the confidence levels of the information bit bits in each permutation sequence, the target permutation sequence is selected from the permutation sequences.

[0059] For example, in the target sequence sorted in descending order of confidence level, the l ( l > number of information bits, for example l = 20) bits have coordinates 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 、 , if there are, for example, 10 unknown coefficients in the permutation function polynomial (the number of information bits > the number of unknown coefficients in the affine permutation function polynomial, and the number of information bits is, for example, 15), then 10 are randomly selected from the 20 reliable bits to solve for the unknown coefficients. Among them, there are multiple combination ways for the random selection. For example, ([[]] 、 、 、 、 、 、 、 、 、 、 ), ([[]] 、 、 、 、 、 、 、 、 、 ), ([[]] 、 、 、 , , , , , , ), ( , , , , , , , , , ), and so on. Taking the position coordinates in each of the above combinations as independent variables and the coordinates of the first 10 information bits as dependent variables, the unknown coefficients in the permutation function polynomial are solved, and thus multiple permutation function polynomials can be obtained. Based on each permutation function polynomial, permutation operations are performed on the positions of the bits in the target sequence, and multiple alternative permutation sequences can be obtained. Select an alternative permutation sequence with the best effect as the target permutation sequence. The evaluation criterion for the permutation effect can be to select the alternative permutation sequence with the largest sum of the confidence levels of the information bit bits in the alternative permutation sequence as the target sequence. The evaluation criterion for the permutation effect can also be that the intersection of the reliable bits in the information bits of the alternative permutation sequence and the reliable bits included in the information bits after sorting the information bits in descending order of confidence level (from largest to smallest) is the largest. Specifically, the number of information bits is 15. After the target sequence is sorted in descending order of bit confidence level, the bits in the information bits are A1, A2,... A15. Determine the intersection size between the bits of the information bits of each alternative permutation sequence and A1, A2,... A15, and select the alternative permutation sequence with the largest intersection as the target sequence.

[0060] In some embodiments of the present invention, the above permutation function may be an affine permutation polynomial.

[0061] The above permutation-based OSD decoding method will be described below with specific examples.

[0062] The form of the affine permutation polynomial is as follows: Among them, the polynomial coefficients are all elements of the finite field and e is divisible by m , and we can obtain the permuted bit coordinates. By backtracking the permutation polynomial from some reliable bits . From the perspective of the matrix form, the permutation polynomial is expressed as , which is determined by the vector composed of the parameters and multiplied by a transformation matrix. That is, , where the transformation matrix is: is a primitive element of the finite field. The transformation matrix is a Vandermonde matrix after deleting the all-zero column in the first column , according to the invertibility of the Vandermonde matrix, the affine permutation function can be inversely transformed, that is where is the first permutation results. According to the partial permutation results and the inverse matrix of the sub-transformation matrix the parameters of the affine permutation polynomial can be determined and , that is, according to the first reliable position permutation results and the reverse affine permutation , the partial reliable positions can be permuted in descending order. The inverse matrix of the sub-transformation matrix will not change during the decoding process and can be calculated offline before decoding. The affine permutation constructed in this way can permute some reliable bits with high confidence to the re-encoded information bits, and the permutation of the remaining bits is determined by the affine permutation function obtained by the inverse transformation . Determine the intersection size of the reliable bits contained in the information bits of each permuted codeword and the reliable bits contained in the information bits after descending order sorting, and select the permutation with the largest intersection in the affine permutation group , that is, the most reliable affine permutation . The affine permutation constructed in this way takes into account both affine invariance and descending order effect, and the permuted codeword still belongs to the original codeword, and the original system form of the generator matrix can be used for re-encoding.

[0063] Next, the decoding effect of the joint decoding method based on confidence local attenuation and permutation-based OSD provided by the embodiments of the present invention is simulated. For the (256, 93) RM code decoding, as Figure 6 shown, the eOSSDD(1) (square) curve is the simulation effect curve of the permutation OSD joint decoding scheme with low-order local attenuation, the OSD(3) (star) curve is the simulation effect curve of the high-order original OSD decoding scheme, and the ML curve is the maximum likelihood decoding performance. It can be seen that the permutation OSD joint decoding scheme with low-order local attenuation has a gain of more than 1 dB compared with the high-order original OSD.

[0064] It should be noted that the OSD decoding based on Gaussian elimination gradually achieves the optimal decoding performance by increasing the order of the error pattern. However, as the decoding order increases, the decoding complexity also increases exponentially, and each decoding requires Gaussian elimination with high complexity and serial implementation. The OSD approaching the maximum likelihood decoding performance requires a high order and Gaussian elimination, but the complexity of both seriously affects the decoding efficiency. To improve the above decoding efficiency problem, in some embodiments of the present invention, the above target sequence can directly be the received sequence, that is, directly apply the permutation-based OSD decoding method provided by the embodiments of the present invention to the received sequence to avoid the need for Gaussian elimination with high complexity and serial implementation during OSD decoding. That is to say, in some embodiments of the present invention, instead of performing local confidence attenuation on the received sequence, the permutation-based OSD decoding method provided by the embodiments of the present invention is directly used for decoding, that is, reliable bits are permuted to information bits through affine permutation, thereby avoiding the process of Gaussian elimination transforming reliable bits into information bits, thus reducing the decoding complexity and latency.

[0065] For the permutation-based OSD decoding method, in order to enhance the decoding performance, in some embodiments of the present invention, other decoding methods are also combined with the permutation-based OSD decoding method. Specifically, the derivative decoding method is combined with the permutation-based OSD decoding method to achieve decoding with balanced performance and complexity. This decoding scheme mainly includes three steps: (1) Calculate the derivative sequences in each direction of the received sequence or the locally attenuated sequence; (2) Perform permutation-based OSD decoding on the derivative sequences; (3) Reconstruct the original sequence with the decoding results of the derivative sequences to obtain the final decoding result.

[0066] First, perform multi-directional derivation on the received sequence to obtain the derivative sequences in each direction of the received sequence. Then, perform the operations of steps 501 to 504 in the above embodiments on each derivative sequence to obtain the decoding result corresponding to each derivative sequence. It should be noted that the derivative sequences in this embodiment are the target sequences described above. After obtaining the decoding results corresponding to each derivative sequence, reconstruct the decoding sequence based on the decoding results corresponding to each derivative sequence (the reconstruction method can use the voting method mentioned above).

[0067] After completion of the reconstruction, select the sign bit of the log-likelihood ratio as the decoding result . Let the parity-check matrix of the original codeword be H. If v satisfies the parity-check relationship of the H matrix, then output the decoding result . Otherwise, perform derivation in each direction on the reconstructed decoding sequence and continue the iteration until the maximum number of iterations.

[0068] It should be noted that after the above-mentioned re-encoding operation is performed based on each derivative sequence, a candidate codeword list corresponding to each derivative sequence will be obtained, and the codeword with the smallest Euclidean distance is selected from the candidate codeword list as the decoding result corresponding to each derivative sequence.

[0069] In the above text, a permutation operation and a re-encoding operation are performed on each derivative sequence, but it is also possible to only select valuable derivative sequences for subsequent permutation operations and re-encoding operations. In some embodiments of the present invention, some worthless derivative sequences can be filtered out based on a certain criterion. Specifically, the criterion can be the size of the intersection between the reliable bits determined based on the derivative sequence and the reliable bits in the information bits after the received sequence is sorted in descending order of confidence. For example, the derivative sequence with the largest intersection can be selected for subsequent permutation operations and re-encoding operations, or multiple derivative sequences with the most forward intersection amounts can be selected for subsequent permutation operations and re-encoding operations.

[0070] The following introduces the joint decoding method based on permutation and derivation according to the embodiments of the present invention with specific examples.

[0071] Taking an additive white Gaussian noise channel as an example, assume the received sequence is . First, perform a derivation calculation on the received sequence to obtain the corresponding sequence of affine invariant derivative codes. In this example, some non-zero elements in the finite field are used as the derivation directions, and the set composed of these non-zero elements is denoted as B.

[0072] Let be any element in B, that is, represents any derivation direction. The log-likelihood ratio of the directional derivative sequence is where , is the log-likelihood ratio of the th, th bit of the received sequence and satisfies the relationship .

[0073] Then, decode the derivative sequence. Select the first reliable bits according to the magnitude of the log-likelihood ratio and calculate the affine permutation according to . In order to further include more reliable bits in the information bits, we can obtain a set of different through random permutations of the first permutations, and then obtain a set of affine permutation polynomials . Define a selection metric, that is, the size of the intersection between the reliable bits included in the information bits of each permuted codeword and the reliable bits included in the information bits after sorting in descending order, and select the affine permutation group The permutation with the largest intersection in the middle, that is, the most reliable affine permutation , using the permuted the first k hard decision information is used for the re-encoding operation to obtain candidate codewords. A metric can also be selected as the direction selection metric. Set a threshold, and directions with an intersection less than the threshold are regarded as unreliable directions and no subsequent decoding is performed.

[0074] Finally, the original sequence is reconstructed using the decoding results of the derivative sequences. The decoding results of the derivative sequences in all directions are used for reconstruction to obtain the reconstructed sequence. For the i th element of the reconstructed sequence, that is, the reconstruction result of the log-likelihood ratio corresponding to the i th bit of the original received sequence . After the reconstruction is completed, we can choose to take the sign bit of the log-likelihood ratio as the decoding result . Let the parity-check matrix of the original codeword be H. If satisfies the parity-check relationship of the H matrix, the decoding result is output. Otherwise, the reconstructed decoding result is used for multi-directional derivation and the iteration continues until the maximum number of iterations.

[0075] The ordered statistical decoding device provided by the present invention is described below. The ordered statistical decoding device described below can be correspondingly referred to the ordered statistical decoding method described above. The ordered statistical decoding device includes: A confidence attenuation module for attenuating the confidence of local bits in the received sequence to obtain a local attenuation sequence.

[0076] A reliable bit determination module for determining reliable bits in the target sequence; the target sequence is the attenuation sequence.

[0077] A re-encoding module for performing a re-encoding operation based on the reliable bits and the generator matrix to obtain a list of candidate decoded codewords.

[0078] A decoding result screening module for determining the decoding result corresponding to the target sequence based on the list of candidate decoded codewords.

[0079] For how each module in this device specifically works, it can be correspondingly referred to the content of the ordered statistical decoding method embodiment described above, and will not be elaborated here.

[0080] Figure 7 An entity structure diagram of an electronic device is exemplified, as Figure 7As shown, the electronic device may include: a processor 710, a communications interface 720, a memory 730, and a communication bus 740. Among them, the processor 710, the communications interface 720, and the memory 730 communicate with each other through the communication bus 740. The processor 710 can call the logical instructions in the memory 730 to execute the ordered statistics decoding method, which includes: attenuating the confidence of local bits in the received sequence to obtain a local attenuation sequence; determining the reliable bits in the target sequence; the target sequence is the attenuation sequence; performing a re-encoding operation based on the reliable bits and the generator matrix to obtain a list of candidate decoded codewords; and determining the decoding result corresponding to the target sequence based on the list of candidate decoded codewords. For more specific methods, reference can be made to the ordered statistics decoding method described above, which will not be elaborated here.

[0081] In addition, when the logical instructions in the above-mentioned memory 730 are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes. For more specific methods, reference can be made to the ordered statistics decoding method described above, which will not be elaborated here.

[0082] On the other hand, the present invention also provides a computer program product. The computer program product includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the ordered statistics decoding method provided by the above-mentioned various methods. The method includes: attenuating the confidence of local bits in the received sequence to obtain a local attenuation sequence; determining the reliable bits in the target sequence; the target sequence is the attenuation sequence; performing a re-encoding operation based on the reliable bits and the generator matrix to obtain a list of candidate decoded codewords; and determining the decoding result corresponding to the target sequence based on the list of candidate decoded codewords. For more specific methods, reference can be made to the ordered statistics decoding method described above, which will not be elaborated here.

[0083] In another aspect, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements an ordered statistic decoding method provided by the above-mentioned various methods. The method includes: attenuating the confidence of local bits in the received sequence to obtain a local attenuation sequence; determining reliable bits in the target sequence; the target sequence is the attenuation sequence; performing a re-encoding operation based on the reliable bits and the generation matrix to obtain a list of candidate decoded codewords; and determining a decoded result corresponding to the target sequence based on the list of candidate decoded codewords. As for a more specific method, reference may be made to the ordered statistic decoding method described above, which will not be elaborated here.

[0084] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0085] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An ordered statistical decoding method, characterized in that: include: Perform confidence attenuation on local bits in the received sequence to obtain a local attenuated sequence; determining reliable bits in a target sequence; The target sequence is the attenuation sequence; Perform a re-encoding operation based on the reliable bits and the generator matrix to obtain a decoding codeword candidate list; Based on the decoding codeword candidate list, a decoding result corresponding to the target sequence is determined.

2. The ordered statistical decoding method according to claim 1, characterized in that: The re-encoding operation is performed based on the reliable bits and the generator matrix, including: Based on the reliable bits and the original system generator matrix, a re-encoded system form generator matrix is ​​generated by using Gaussian elimination method; A re-encoding operation is performed based on the systematic form generation matrix.

3. The ordered statistical decoding method according to claim 1, characterized in that: The re-encoding operation is performed based on the reliable bits and the generator matrix, including: Constructing a permutation function polynomial using the position coordinates of the reliable bits in the target sequence as independent variables and the position coordinates of the information bits in the target sequence as dependent variables; Performing permutation adjustment on the coordinate position of each bit in the target sequence based on the permutation function polynomial to obtain a target permutation sequence; The target sequence is re-encoded based on a given system generation matrix to obtain a decoding codeword candidate list.

4. The ordered statistical decoding method according to claim 3, characterized in that: The permutation function polynomial is an affine permutation polynomial.

5. The ordered statistical decoding method according to claim 4, characterized in that: Taking the position coordinates of the reliable bits in the target sequence as independent variables and the position coordinates of the information bits in the target sequence as dependent variables, constructing a permutation function polynomial, including: The position coordinates of different partial reliable bits in the target sequence are respectively used as independent variables, and the position coordinates of the information bits in the target sequence are used as dependent variables to construct a permutation function polynomial, thereby obtaining a plurality of permutation function polynomials.

6. The ordered statistical decoding method according to claim 5, characterized in that: The method comprises: performing permutation adjustment on the coordinate position of each bit in the target sequence based on the permutation function polynomial, comprising: Performing substitution and adjustment on the coordinate position of each bit in the target sequence based on each substitution function polynomial to obtain multiple substitution sequences; The target permutation sequence is selected from the permutation sequences based on the confidence of each permutation sequence information bit.

7. The ordered statistical decoding method according to any one of claims 1 to 6, characterized in that: Before determining the reliable bits in the target sequence, it also includes: Derivative the local attenuation sequence in multiple directions to obtain a derivative sequence of the local attenuation sequence in each direction; Taking each of the derivative sequences as a target sequence, jumping to the step of determining reliable bits in the target sequence, and obtaining a decoding result corresponding to each of the derivative sequences; A decoding sequence is reconstructed based on the decoding result corresponding to each of the derivative sequences.

8. The ordered statistical decoding method according to claim 7, characterized in that: After reconstructing the decoding sequence based on the decoding results corresponding to each of the derivative sequences, the method further includes: Using a check matrix to check the decoding sequence; If the verification is passed, a decoding result is output based on the decoding sequence; If the verification fails, the process jumps to the multi-directional derivation step to perform multi-directional derivation on the decoding sequence.

9. The ordered statistical decoding method according to claim 8, characterized in that: When the check fails and the decoder converges in an incorrect direction, the local bits of the received sequence with attenuated confidence are adjusted to update the local attenuated sequence.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the program, the ordered statistical decoding method according to any one of claims 1 to 9 is implemented.

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