CN117040547A - SCF decoding method and system based on double threshold values - Google Patents

Abstract

The invention discloses a SCF decoding method and system based on double threshold values, which relate to the technical field of communication, and the method comprises the following steps: SC decoding is carried out on the data to be decoded to obtain an initial decoding bit sequence; if the cyclic redundancy check is not passed, calculating a first probability threshold value of errors after channel transmission bits based on conditional probability distribution of errors after transmission bits of the polarized sub-channels under a limited code length; forming a turnover bit position searching range by bit positions corresponding to channels with probability values of errors larger than a first probability threshold after bit transmission; determining a final flip bit position set according to the flip bit position searching range, the probability threshold value of the bit being wrongly decoded and the channel position critical value of the error probability tending to 0; and sequentially turning over the corresponding bit values in the set until the set is traversed or the currently obtained decoding bit sequence passes the cyclic redundancy check, and outputting the currently decoding bit sequence. The invention reduces the complexity of SCF decoding.

Description

SCF decoding method and system based on double threshold values

Technical Field

The invention relates to the technical field of communication, in particular to a SCF decoding method and system based on double threshold values.

Background

In order to promote the next generation mobile communication system to realize the improvement of higher communication rate, research is required from the perspective of key technology of a transmission layer, and a high-efficiency information processing and high-reliability transmission technology capable of meeting the requirement of diversity is provided. The existing polarization code is the only constructability coding method which proves that the channel capacity can be achieved in the mathematical theory at present, after polarization phenomena occur on a plurality of channels which are independent of each other and have the same channel capacity, the channel relevance and the channel capacity difference are introduced, so that the polarization code based on the differential construction principle is very suitable for serving various diversified scene requirements.

The Arikan professor strictly demonstrates mathematically that polar codes can achieve shannon capacity well with infinite code length using serial cancellation or successive cancellation (Successive Cancellation, SC) decoding algorithms. However, when the code length is limited and long, the corresponding channel cannot be polarized sufficiently, the reliability of the sub-channel transmitting the non-frozen bit is reduced, and the possibility of error propagation is improved, so that the performance of the polarized code in the SC decoding algorithm is not ideal. To improve the performance of the polar SC decoding algorithm under limited code length, scholars propose serial cancellation list (Successive Cancellation List, SCL) decoding algorithm, cyclic redundancy check (CRC-aided Successive Cancellation List, CA-SCL) decoding algorithm, adaptive serial cancellation list (Adaptive Successive Cancellation List, AD-SCL) decoding algorithm, serial cancellation stack (Successive Cancellation Stack, SCs) decoding algorithm, etc. from different angles. By adding a plurality of candidate paths which are allowed to be reserved when decoding the bits, the probability of containing the correct bit sequence in the final candidate path is improved, and the performance of a decoding algorithm is effectively improved. However, as the code length and number of reserved candidate paths increases, the corresponding coding complexity increases significantly.

In order to ensure lower decoding complexity and space storage complexity of the SC decoding algorithm and improve error correction performance of the decoding algorithm, orion et al propose an SC Flip (SCF) decoding algorithm. Different from SCL decoding algorithm, SCF decoding algorithm judges bit position easy to generate first bit judgment error in decoding process to form turnover bit set based on channel polarization phenomenon, then after failure of first executing SC decoding algorithm, successively turnover bit value corresponding to element in position set, until decoding is correct or maximum number of times of trial turnover is reached, stopping decoding. The SCF decoding algorithm improves the performance of the decoding algorithm while maintaining low decoding complexity and spatial storage complexity in the high signal-to-noise ratio region. However, the decoding complexity in the low signal-to-noise region is much higher than that of the SC decoding algorithm.

In order to reduce the search range for the flip bits of the SCF decoding algorithm, the learner has demonstrated that the first bit to make an erroneous decision is almost entirely contained in the critical set S if the SC decoding algorithm fails to decode. Meanwhile, a progressive multi-stage bit-flipping decoding algorithm based on an iterative modification critical set is also provided, and compared with the traditional SC decoding algorithm, the algorithm has stronger error correction capability. To further improve the performance of the decoding algorithm, a new metric is proposed by a learner to determine the position of the flipped bit in the decoding process, and the metric method improves the error correction performance of the decoding algorithm and reduces the decoding complexity. Still further, scholars have proposed Dynamic SCF (D-SCF) decoding algorithms that are comparable to CA-SCL (l=16) decoding algorithms in performance, while having an average complexity in the high signal-to-noise ratio region that is close to that of SC decoding algorithms.

In order to enable the D-SCF decoding algorithm to be realized on hardware at low cost, a learner proposes a Fast-DSCF decoding algorithm suitable for hardware realization by replacing logarithmic and exponential calculations with simple constant approximation and combining a decoding technology of a special node and a metric normalization and sequencing length reduction method. The learner introduces the bit flipping method into the SCL decoding algorithm, proposes the SCLF decoding algorithm, and avoids the exponential complexity caused by multi-bit flipping. The learner proposed a segment SCF (Partitioned Successive CancellationFlip, PSCF) decoding algorithm, which can correct a plurality of decoded bit errors during decoding, and compared with the conventional SCF decoding algorithm, when p=2 and p=4, the error correction performance of 0.26dB and 0.2dB can be respectively improved, and the average number of iterations is effectively reduced. Based on the concept of segmentation, a generalized bit-flipping decoding algorithm is then proposed, which takes the positions of the CRC bits and the error probability of each bit into account. Currently, the complexity of SCF decoding algorithms in the low signal-to-noise ratio region is much higher than that of SC decoding algorithms, and further reduction of the complexity is needed.

Disclosure of Invention

The invention aims to provide a SCF decoding method and system based on double threshold values, which reduce the complexity of SCF decoding.

In order to achieve the above object, the present invention provides the following solutions:

the invention discloses an SCF decoding method based on double threshold values, which comprises the following steps:

a dual threshold based SCF decoding method, comprising:

SC decoding is carried out on the data to be decoded to obtain an initial decoding bit sequence;

judging whether the current decoding bit sequence passes the cyclic redundancy check or not;

if the cyclic redundancy check is passed, outputting a current decoding bit sequence, and ending decoding;

if the cyclic redundancy check is not passed, calculating a probability threshold value of errors after channel transmission bits based on conditional probability distribution of errors after transmission bits of the polarized sub-channels under a limited code length, and marking the probability threshold value as a first probability threshold value;

forming a turnover bit position searching range by using bit positions corresponding to channels with probability values larger than the first probability threshold in the probability distribution;

determining a final flip bit position set according to the flip bit position searching range, a second probability threshold value and a channel position critical value with probability value tending to 0 in the probability distribution; the second probability threshold is a probability threshold that a bit is wrongly decoded;

sequentially extracting turning bit positions from the final turning bit position set, turning over the corresponding bit values on the current turning bit positions of the current decoding bit sequence if the current turning bit positions are smaller than or equal to the number of elements in the final turning bit position set, judging whether the turned over current decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence if the turned over current decoding bit sequence passes the cyclic redundancy check; if not, continuing to extract the turning bit position from the final turning bit position set until the final turning bit position set is traversed or the current obtained decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence.

Optionally, determining the final flipped bit position set according to the flipped bit position search range, the second probability threshold and the channel position critical value with probability value tending to 0 in the probability distribution specifically includes:

determining a first flipped bit position set according to the flipped bit position search range;

determining a log-likelihood ratio threshold range of the bit attempting to flip according to the second probability threshold;

screening bit positions conforming to the log likelihood ratio threshold range from the first flip bit position set to obtain a second flip bit position set;

and forming the final flipped bit position set by bit positions smaller than the channel position critical value in the second flipped bit position set.

Optionally, determining the first flipped bit position set according to the flipped bit position search range specifically includes:

if the number of bits in the turnover bit position searching range is greater than or equal to a preset maximum turnover number, sorting the absolute values of log likelihood ratios of all bits in the turnover bit position searching range from small to large, selecting the ordered bits with the preset maximum turnover number, and forming the positions corresponding to the selected bits into the first turnover bit position set;

and if the number of bits in the flip bit position searching range is smaller than the preset maximum flip times, forming the first flip bit position set according to the order of the absolute values of the log likelihood ratios of the bits from small to large.

Optionally, the first probability threshold is expressed as:

wherein,representing the first probability threshold, P _i ^e For channel->Transmission bit u _i The probability of an error occurring after that,k is the number of non-frozen bits, ">Representing the set of positions taking non-frozen bits +.>Middle and late->And the set of positions corresponding to the individual polarized sub-channels.

Optionally, the second probability threshold is expressed as:

wherein,representing said second probability threshold, ++>Parameter representing the number of polarized sub-channels, +.>K is the number of non-frozen bits, ">To get the collection->Front middle>A set of position indexes corresponding to the polarized sub-channels, P _i ^e Representation bit u _i Probability of erroneous decoding occurring, +.>A set of positions that are non-frozen bits;

the log likelihood ratio threshold range is expressed as:

wherein,representation bit u _i Corresponding log likelihood ratio, ++>Representing data received from a channel,/->For decoding the value sequence,/-> Representation bit u ₁ Decoding value of->Representation bit u ₂ Decoding value of->Representation bit u _i-1 Is decoded and valued.

The invention also discloses an SCF decoding system based on the double threshold values, which comprises:

the SC decoding module is used for carrying out SC decoding on the data to be decoded to obtain an initial decoding bit sequence;

the cyclic redundancy check module is used for judging whether the current decoding bit sequence passes cyclic redundancy check or not;

the decoding bit sequence output module is used for outputting the current decoding bit sequence if the cyclic redundancy check is passed;

the probability threshold determining module is used for calculating a probability threshold of error after channel transmission bits based on conditional probability distribution of error after polarization sub-channel transmission bits under a limited code length if the cyclic redundancy check is not passed, and marking the probability threshold as a first probability threshold;

the turnover bit position searching range determining module is used for forming a turnover bit position searching range from bit positions corresponding to channels with probability values larger than the first probability threshold in the probability distribution;

the final flip bit position set determining module is used for determining a final flip bit position set according to the flip bit position searching range, the second probability threshold and a channel position critical value with probability value tending to 0 in the probability distribution; the second probability threshold is a probability threshold that a bit is wrongly decoded;

the overturn processing module is used for sequentially extracting overturn bit positions from the final overturn bit position set, overturning the corresponding bit value on the current overturn bit position of the current decoding bit sequence if the current overturn bit position is smaller than or equal to the number of elements in the final overturn bit position set, judging whether the overturned current decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence if the overturned current decoding bit sequence passes the cyclic redundancy check; if not, continuing to extract the turning bit position from the final turning bit position set until the final turning bit position set is traversed or the current obtained decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence.

According to the specific embodiment provided by the invention, the invention discloses the following technical effects:

according to the invention, according to the conditional probability distribution of errors after the transmission of the bit sequence of the polarized sub-channel under the limited code length, the searching range of the turning bit position is determined according to the probability threshold of errors after the transmission of the bit of the channel, the final turning bit position set is determined according to the searching range of the turning bit position, the probability threshold of error decoding of the bit and the channel position critical value of the error probability approaching 0, and based on the final turning bit position set, the bit turning and cyclic redundancy check are carried out on the current decoding bit sequence, so that the searching range of the turning bit is reduced, some redundant bit positions are deleted, the number of elements in the turning position set is reduced, and the storage complexity and the average complexity of a decoding algorithm are reduced.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

Fig. 1 is a schematic flow chart of an SCF decoding method based on dual threshold according to an embodiment of the present invention;

FIG. 2 shows code lengths 2048 and E according to an embodiment of the present invention _b /N ₀ A conditional probability distribution map of 0.5dB for errors after channel transmission bits;

FIG. 3 shows code lengths 2048 and E according to an embodiment of the present invention _b /N ₀ A conditional probability distribution map of 2.5dB for errors after channel transmission bits;

FIG. 4 shows code lengths 1024 and E according to an embodiment of the present invention _b /N ₀ A probability division diagram of 0.5dB that errors occur after the channel transmits bits;

FIG. 5 shows code lengths 1024 and E according to an embodiment of the present invention _b /N ₀ 2.5dB, and dividing a graph of probability of error after the channel transmits bits;

FIG. 6 shows code lengths 512 and E according to an embodiment of the present invention _b /N ₀ A conditional probability division diagram of 0.5dB that errors occur after the channel transmits bits;

FIG. 7 shows code lengths 512 and E according to an embodiment of the present invention _b /N ₀ A conditional probability division diagram of 2.5dB that an error occurs after a channel transmits a bit;

FIG. 8 shows a code length of 512 for a LC-SCF decoding algorithm according to an embodiment of the present inventionAnd E is _b /N ₀ Searching a range number comparison graph under the value;

FIG. 9 shows a code length of 1024, and different LC-SCF decoding algorithms according to the embodiment of the present inventionAnd E is _b /N ₀ Searching a range number comparison graph under the value;

FIG. 10 shows a code length 2048 for a LC-SCF decoding algorithm according to an embodiment of the present inventionAnd E is _b /N ₀ Searching a range number comparison graph under the value;

FIG. 11 shows a code length of 1024, and different LC-SCF algorithms according to the embodiment of the present inventionValue sum E _b /N ₀ Turning over the number comparison graph of the collection under the value;

FIG. 12 is a chart showing the comparison of the number of flipped bit positions of the LC-SCF decoding algorithm under different parameter values according to the embodiment of the present invention;

FIG. 13 shows a LC-SCF decoding algorithm according to an embodiment of the present invention in different casesBLER performance versus values;

FIG. 14 is a diagram illustrating a different embodiment of the present inventionAverage complexity contrast diagram of LC-SCF decoding algorithm corresponding to the value;

fig. 15 is a graph showing comparison between BLER performance of an LC-SCF decoding algorithm and different decoding algorithms according to an embodiment of the present invention;

fig. 16 is a graph showing average complexity of LC-SCF decoding algorithm and different decoding algorithms according to an embodiment of the present invention.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

The invention aims to provide a SCF decoding method and system based on double threshold values, which reduce the complexity of SCF decoding.

In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.

The invention discloses an SCF decoding method based on a dual threshold, in particular to a Low Complexity SCF (LC-SCF) decoding algorithm based on a dual dynamic threshold. Firstly, setting a probability threshold value of errors after transmitting bits of a polarized sub-channel according to conditional probability distribution of errors after transmitting bits of the polarized sub-channel under a limited code length, and forming a new flip bit position searching range by bit positions corresponding to channels with the probability of errors after transmitting bits larger than the probability threshold value. And then, according to the conditional probability of error after transmitting the bits of the polarized sub-channel under the limited code length, calculating a probability threshold value of error decoding of the bits and a channel position critical value of which the probability of error after transmitting the bits of the polarized sub-channel is close to 0, and selecting information bit indexes meeting the conditions of the threshold value and the critical value from the initial flip position set to form a new flip bit position set. Finally, based on the setting of multiple probability threshold values, the LC-SCF decoding algorithm reduces the search range of the inversion bit, deletes some redundant bit positions, reduces the number of elements in the inversion position set, and reduces the storage complexity and average complexity of the decoding algorithm.

Example 1

As shown in fig. 1, the SCF decoding method based on the dual threshold provided in this embodiment includes the following steps.

Step 101: and carrying out SC decoding on the data to be decoded to obtain an initial decoding bit sequence.

The step 101 specifically includes: the data received from the channel isThe bit sequence to be decoded is denoted +.>The initial maximum number of inversions T.

Judging ith bit u by SC decoding algorithm _i The specific formula of the value is as follows:

wherein,representing the ith bit u _i Decoding and taking value of L ₁ Representing a set of information bits>Representing frozen bit set, ">Representation-> The definition is as follows.

Wherein,representing the polarized sub-channels, N representing the code length, and i in equation (2) representing the polarized sub-channel index.

The log likelihood ratio (Log Likelihood Ratio, LLR) recursive formula in the above equation is:

wherein,represents the 2i-1 thBit u _2i-1 Decoding and taking value of tau ₁ And τ ₂ As an input parameter to the function f (),

step 102: it is determined whether the currently decoded bit sequence passes a cyclic redundancy check (CRC check).

In step 102, the current decoding bit sequence is the initial decoding bit sequence.

Step 103: and if the cyclic redundancy check is passed, outputting the current decoding bit sequence. I.e. the decoding is ended.

Step 104: if the cyclic redundancy check is not passed, calculating a probability threshold of error after channel transmission bit based on a conditional probability distribution of error after polarization sub-channel transmission bit under a limited code length, and marking the probability threshold as a first probability threshold.

Step 105: and forming a turnover bit position searching range by using bit positions corresponding to channels with probability values larger than the first probability threshold in the probability distribution.

The polarized channel error probability threshold calculating method in step 104 and step 105 is as follows:

given the translated bit sequence u _i Assuming that all bits were decoded correctly before, i.eThen polarized subchannel->Transmission bit u _i Event of later error->The method comprises the following steps:

event(s)Probability of->The method comprises the following steps:

wherein,x represents the input parameter of the function ζ (), t represents time, +.>Representation->Is not limited to the above-described embodiments.

Under the condition that the previous bits are decoded correctly, the sub-channels are polarizedTransmission bit u _i Probability of post-occurrence error P _i ^e The method comprises the following steps:

and setting a probability threshold value of error after transmitting bits by the polarized sub-channels, and determining a bit position searching range required to be turned over in the decoding process. The larger the probability threshold value is, the smaller the corresponding search range is, otherwise, the larger the corresponding search range is. The invention provides a method for selecting a corresponding polarized sub-channel when calculating a probability threshold of error after transmitting bits of the polarized sub-channel according to the channel polarization phenomenon under a limited code length because the block error performance and the decoding complexity of a decoding algorithm are closely related to the searching range of the inversion bits.

Firstly, setting the number parameter of the polarized sub-channels to be selected when calculating the probability threshold value of error after transmitting bits of the polarized sub-channels asThe set of positions of all non-frozen bits is +.>Then, based on the channel polarization phenomenon under the limited code length, the rule of selecting the polarized sub-channels is set as follows: get collection->Middle and late->Position composition set corresponding to each polarized sub-channelProbability threshold value of error after transmitting bits of polarized sub-channel based on mean value idea +.>The definition is as follows:

wherein P is _i ^e For channelsTransmission bit u _i Error probability of later occurrence, < >>K is the number of non-frozen bits.

Combining the channel polarization phenomena under a limited code length (fig. 2 to 7), as can be derived from fig. 2, the code length is 2048 and E _b /N ₀ When the channel index is 0.5dB or more, the conditional probability of error after transmission of bits of the polarized channel gradually tends to 0, and when the channel index is about 500 or less, the conditional probability value of error after transmission of bits of the corresponding polarized channel tends to 0.45. Meanwhile, as can be taken from fig. 2 and 3, at E _b /N ₀ When the number of the polarized channels is 2.5dB, the conditional probability value of error after the transmission of bits by the polarized channels tends to 0, and the number of the polarized channels with the channel index more than or equal to 1600 is higher than E _b /N ₀ At 0.5 dB. The simulation results of fig. 4 and 5 show that at a code length of 1024 and a code rate of 0.5, for different E' s _b /N ₀ And when the channel index is greater than or equal to 800, the conditional probability value of error after the corresponding polarized sub-channel transmits the bit gradually tends to 0. At the same time with E _b /N ₀ The more obvious the polarization phenomenon of the channel occurs due to the increase of the value, so that the number of the channels with the probability of 0 after the transmission of the bits of the polarized sub-channels is gradually increased. For a code length 512 and a code rate of 0.5, as can be seen from fig. 6 and 7, at E _b /N ₀ When the value is 0.5dB or 2.5dB, the channel index of which the probability value of error after transmission of bits by the polarized sub-channels is approximately equal to or greater than 400 is approximately equal to or greater than 0.

From the above analysis, it can be found that for different code lengths and E _b /N ₀ When the channel index is larger than or equal to 0.75N (N is the code length), the probability value of error after transmitting bits of the polarized sub-channels is approximately 0, so that the number parameter of the polarized sub-channels to be selected is needed when the probability threshold value is calculatedThe minimum value is 0.25. Next, the difference +.>The impact of the value on the flip bit position search range of the proposed LC-SCF decoding algorithm.

FIGS. 8-10 show the number of elements in the search range of flipped bit positions in the LC-SCF decoding algorithm with E for different code lengths _b /N ₀ Value and threshold parameterA variant wherein LC-SCF (1/4) represents +.>LC-SCF decoding algorithm 1/4. As shown in FIG. 8, when the code length is 512, # is given>LC-SCF decoding algorithm for 1/2 at E _b /N ₀ The number of elements in the search range is reduced by 71.09% compared with the SCF decoding algorithm when the number is 0.5dB, and the number is reduced in E _b /N ₀ The number of elements in the search range is reduced by 81.25% compared with the SCF decoding algorithm when the value is 2.5 dB. With E _b /N ₀ The LC-SCF decoding algorithm reduces the proportion of the SCF decoding algorithm flip bit search range and increases gradually. At the same time at the same E _b /N ₀ Under the values, the LC-SCF decoding algorithm reduces the ratio of the number of elements of the search range with +.>Gradually increasing and when +.>Search range element number and +.f for LC-SCF decoding algorithm at 9/16>Is 1/2 of the time.

In connection with the simulation results of fig. 9, when the code length is 1024, compared with the SCF decoding algorithm,LC-SCF decoding algorithm for 1/4 at E _b /N ₀ The number of elements in the bit search range is reduced by 67.19% when the number of elements is 0.5dB, and the number of elements in the bit search range is reduced by E _b /N ₀ At 2.5dB, the reduction is 80.66%. As can be seen from fig. 10, at E _b /N ₀ At 0.5dB>The number of elements in the bit search range of the LC-SCF decoding algorithm of 1/4 is reduced by 74.41 percent compared with that of the SCF decoding algorithm, and the bit search range is reduced by E _b /N ₀ At 1.3dB, 80.96% and E are reduced _b /N ₀ At 2.5dB, 86.72% is reduced. At the same time (I)>LC-SCF decoding algorithm for 1/2 at E _b /N ₀ The number of elements in the bit search range of 1.7dB is reduced by 84.96% compared with the SCF decoding algorithm, and the bit search range is E _b /N ₀ 2.5dB, +.>The number of elements in the search range of the LC-SCF decoding algorithm of 3/5 is reduced by 88.09 percent.

From the simulation results of FIGS. 8 to 10, it can be seen that at the same code length and threshold parametersThe LC-SCF decoding algorithm reduces the proportion of the flip bit search range with E compared to the SCF decoding algorithm _b /N ₀ The increase in (2) increases gradually. At the same time at the same E _b /N ₀ Under the value, the LC-SCF decoding algorithm reduces the proportion of the flip bit search range with the threshold +.>And increases with increasing size. In order to further discuss the degree to which the LC-SCF decoding algorithm can reduce the average complexity without reducing the performance of the block error rate of the SCF decoding algorithm, the threshold parameter selected when calculating the probability threshold of errors occurring after transmission bits of the polarized sub-channels in the LC-SCF decoding algorithm is selected>Set to 9/16.

The search range of the initial flipped bits is the set of the entire non-frozen bit index. The invention is thatBased on a probability threshold of error after channel transmission bits in an LC-SCF decoding algorithm of (a)Selecting bit positions corresponding to channels with probability of error larger than probability threshold after transmission bits are selected to form a new flip bit position search range F _s 。

Step 106: determining a final flip bit position set according to the flip bit position searching range, a second probability threshold value and a channel position critical value with probability value tending to 0 in the probability distribution; the second probability threshold is a probability threshold that a bit is miscoded.

Step 106 specifically includes:

determining a first flip bit position set according to the flip bit position search range, specifically including:

if the number of bits in the flip bit position search range is greater than or equal to the preset maximum flip times, i.e. |F _s The absolute value of Log Likelihood Ratio (LLR) of each bit in the searching range of the turning bit positions is sequenced from small to large, the preset maximum turning times of the bits are selected, the positions corresponding to the selected bits form the first turning bit position set, in short, the bit positions with the minimum absolute value of the T LLRs are selected to form the first turning bit position setWherein t is _q Representing the qth bit, 1.ltoreq.q.ltoreq.T, where the potential of the first set of flipped bit positions is T.

If the number of bits in the flip bit position search range is smaller than the preset maximum flip times, forming the first flip bit position set according to the order of the absolute values of the log likelihood ratios of the bits from small to largeWherein, gamma _p Represents the p-th bit, p is not less than 1 and not more than |F _s I, at this time, the first flipped bit position setThe potential of is |F _s |。

The first set of flipped bit positions is represented asOr->

Determining a log-likelihood ratio threshold range of the bit attempting to flip according to the second probability threshold; and screening bit positions conforming to the threshold range of the log likelihood ratio from the first turnover bit position set to obtain a second turnover bit position set, wherein the second turnover bit position set specifically comprises: deriving a range of bit LLR thresholds requiring attempted flipping from a first set of flipped bit positions based on probability thresholds for bit erroneous decodingOr->Selecting bits meeting the threshold range to form a second flip bit position set +.>The potential of the second set of flip bit positions is +.>

Theoretical analysis of flip bit position set threshold:

set in the decoding process, bit u _i The probability of error decoding isThe probability threshold for the non-frozen bit to be decoded in error is P _e Bit u _i Correctly decoded then requires the condition to be satisfied:

namely:

wherein,is at->And->Under the condition u _i Probability of j.

Due to

When the decoded bit u is defined by LLR values _i LLR values of (2)The formula (12) is simplified as:

and (3) the same principle:

then:

namely:

second, when the bit u is defined according to LLR values _i LLR values of (2) satisfyThe conversion of formula (12) to:

then:

namely:

the bit LLR value meeting relation requiring to be turned over in the decoding process is obtained

From equation (20), P in the LC-SCF decoding algorithm _e The value determines the turnover bit position set of the decoding algorithm, thereby affecting the block error rate performance and decoding complexity of the decoding algorithm. Thus, to analyze different P in detail _e Impact of values on LC-SCF decoding algorithm performance, P will be in the present invention _e Set as dynamic threshold, i.e.Wherein->Parameter indicating the number of selected polarized sub-channels, < ->Defining a probability threshold for a bit to be decoded in error>The method comprises the following steps:

wherein,is to take the collection->Front middle>Set of indexes corresponding to each polarized sub-channel, P _i ^e Representation bit u _i The probability of erroneous decoding can be calculated according to equation (13). And (3) injection: the mean concept is used for both equations (9) and (21), except that the selected polarization subchannels are different and the threshold parameter settings are different. The following will differ based on the phenomenon of channel polarization at limited code length +.>The values analyze the decoding performance impact of the LC-SCF decoding algorithm in detail.

FIG. 11 shows the difference between 1024 code lengths and 0.5 code rateThe number of elements in the flipped bit position set of the LC-SCF decoding algorithm of the value follows E _b /N ₀ A value change diagram, wherein "LC-SCF (1/64)" means +.>LC-SCF decoding algorithm of 1/64. (probability threshold parameter of error after transmission of bits by polarized subchannel in LC-SCF decoding algorithm after this section)Set to 9/16).

As shown in fig. 11, whenWhen the value is 1/8, the LC-SCF decoding algorithm is as follows _b /N ₀ The number of elements in the flipped bit position set at 0.5dB is reduced by 6.25% compared with the SCF decoding algorithm, at E _b /N ₀ 46.88% and 93.75% decrease at 1.3dB and 2.5dB, respectively. At the same time, when->At a value of 1/64, the LC-SCF decoding algorithm is compared with the SCF decoding algorithm in E _b /N ₀ The number of elements in the flip bit position set is reduced by 12.5% at 0.5dB, and E is as follows _b /N ₀ A53.13% reduction was achieved for 1.3 dB.

From the simulation results, it can be seen that inThe smaller the value, i.e. the larger the probability threshold value of the bit being wrongly decoded, the fewer the number of polarized subchannels satisfying the threshold value range of the bit LLR value as shown in formula (6) in the decoding process. The set +.1.21 pair>Or->Performing redundancy reduction to obtain a new flip bit position set (second flip bit position set)>

Forming the final flipped bit position set from bit positions smaller than the channel position critical value in the second flipped bit position set, specifically including:

in terms of channel position critical value (critical threshold) of 0.875N (N is code length) where the probability of error after transmission of bits by polarized sub-channel tends to 0The bit indexes less than 0.875N (N is the code length) are selected to form new turnoverA set of toggle bit positions (final set of toggle bit positions)/(final set of toggle bit positions)>Wherein (1)>

FIGS. 4 to 7 show the code length and E at different code lengths _b /N ₀ And under the value, polarizing a probability division diagram of errors after transmitting bits by the sub-channels. As can be derived from the simulation results of fig. 6 and 7, E _b /N ₀ When the value is 0.5dB or 2.5dB, for the polarized codes with the code length of 512 and the code rate of 0.5, the probability of error after the transmission of bits of the polarized sub-channels with the channel index of more than or equal to 450 is almost 0, and the error is detected in E _b /N ₀ When the value is large, the probability of error occurrence after bit transmission is almost 0, and the more channels with channel indexes larger than or equal to 450 are. In fig. 4 and 5, the probability of error after transmission of bits for the polarized sub-channel with a channel index of approximately 900 or more is at E _b /N ₀ The value is almost 0 when the value is 0.5dB or 2.5dB, and the reliability of the polarized sub-channel is high, so that the probability of the first decision error of the transmitted information bit in the decoding process is low.

The simulation results in connection with FIGS. 4-7 can be obtained for different code lengths and E _b /N ₀ The probability of error occurrence after transmission of bits by the polarized sub-channel with a channel index greater than or equal to 0.875N (N is the code length) is about equal to 0, i.e. the probability of error occurrence of the first decoding decision of the bits transmitted by the polarized sub-channel is very low in the decoding process, so that the set of bit positions to be flipped may not include such channel index.

Fig. 12 shows a comparison of sets of flipped bit positions corresponding to different parameter value LC-SCF decoding algorithms. In FIG. 12, LC-SCF (1/64, 7/8) representsLC-SCF decoding algorithm for 1/64 and channel index to code length N ratio less than 7/8. As can be taken from fig. 12, at E _b /N ₀ The value is 0.5dB, the number of elements in the inversion bit position set of the LC-SCF (1/64, 7/8) decoding algorithm is reduced by 3.57 percent compared with the LC-SCF (1/64) decoding algorithm, and the method is as follows _b /N ₀ At 1.9dB, the reduction is 12.5%. LC-SCF (1/8, 7/8) decoding algorithm at E _b /N ₀ At 0.5dB, the frequency is reduced by 6.67% compared with the LC-SCF (1/8) decoding algorithm.

Combining the simulation result analysis, and collectingBit positions smaller than 0.875N (N is the code length) constitute a new flipped bit position set +.>Wherein->

Step 107: sequentially extracting turning bit positions from the final turning bit position set, turning over the corresponding bit values on the current turning bit positions of the current decoding bit sequence if the current turning bit positions are smaller than or equal to the number of elements in the final turning bit position set, judging whether the turned over current decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence if the turned over current decoding bit sequence passes the cyclic redundancy check; if not, continuing to extract the turning bit position from the final turning bit position set until the final turning bit position set is traversed or the current obtained decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence.

Based on the channel polarization phenomenon under the limited code length, a probability threshold value of errors after transmitting bits of a polarized sub-channel is set, and the searching range of the position of the turning bit in the decoding process is reduced; redundant bit positions in the turnover bit position set are deleted by calculating an error probability threshold value of the bit error decoded and a channel position critical value of which the error probability value is towards 0, so that the bit turnover times in the decoding process are reduced, the storage space and the number of the turnover bit position sets in the decoding process are reduced, and the storage complexity and the average complexity of the decoding algorithm can be further reduced under the similar block error rate performance compared with the SC decoding algorithm.

The BLock error rate (BLock ErrorRatio, BLER) performance and the average complexity performance of the LC-SCF decoding algorithm proposed by the present invention are checked by a simulation experiment.

The channel of the simulation experiment is a binary input additive Gaussian white noise channel, the modulation mode is binary phase shift keying (Binary Phase Shift Keying, BPSK) modulation, and the code word is constructed by a Gaussian approximation (GaussianApproximation, GA) method. The code length is set to 1024, the code rate is 0.5, the adopted CRC check code is 16 bits, and the generating polynomial is g (x) =x ¹⁶ +x ¹⁵ +x ² +1. The initial maximum number of inversions was set to 32. The SCF decoding algorithm needs to perform multiple additional inversions in the decoding process, that is, the SC decoding algorithm is re-executed once, so that the complexity of the decoding algorithm is measured by adopting the average complexity, which refers to the average value of the number of times of actually attempting inversions in the decoding algorithm.

FIGS. 13 and 14 depict LC-SCF decoding algorithms at different points, respectivelyThe BLER performance and average complexity below are compared. From FIG. 13, it is possible to add->BLER curves of corresponding LC-SCF decoding algorithms with values of 1, 1/32 and 1/8 are basically coincident, and are not equal to +.>BLER performance of LC-SCF decoding algorithm at 1/64 and at E _b /N ₀ At a value of 2.6dB, there is a performance penalty of 0.1dB compared to the BLER performance of the SCF decoding algorithm. At the same time, compared to SCF decoding algorithm +.>The loss of BLER performance of the LC-SCF decoding algorithm with the value of 1/64 is within 0.05 dB.

As can be seen from FIG. 14, whenWhen LC-SCF decoding algorithm is in E _b /N ₀ The average complexity at 1dB is 12.38% lower than that of the SCF decoding algorithm, at E _b /N ₀ =1.4 dB and E _b /N ₀ The average complexity at=2 dB is reduced by 15.21% and 12.15%, respectively. Compared to SCF decoding algorithm->The average complexity of the LC-SCF decoding algorithm is E _b /N ₀ Reduced by 13.91% at =1 dB, at E _b /N ₀ The average complexity at=1.4 dB is reduced by 15.11%. When->When compared with the SCF decoding algorithm, the corresponding LC-SCF decoding algorithm is shown as E _b /N ₀ =1 dB and E _b /N ₀ The average complexity was reduced by 17.23% and 20.39% when=1.4 dB, respectively. In general, when->The smaller the value, the lower the average complexity of the corresponding LC-SCF decoding algorithm, and the greater the degree of decoding complexity reduction.

In order to analyze the LC-SCF decoding algorithm and reduce the degree of decoding complexity under the premise of BLER performance similar to SCF decoding performance, the simulation result analysis is combined to selectAnd the corresponding LC-SCF decoding algorithm is compared and analyzed with CA-SCL, SCF and SC decoding algorithms. In fig. 15, it can be seen that the BLER performance of the LC-SCF decoding algorithm is similar to that of the SCF decoding algorithm and approximates to that of the CA-SCL decoding algorithm under the condition of l=2, but is inferior to that of the CA-SCL decoding algorithm under the condition of l=4. The LC-SCF decoding algorithm improves BLER performance compared to the SC decoding algorithm. From the graph16, the LC-SCF decoding algorithm is available at E compared to the SCF decoding algorithm _b /N ₀ The average complexity is reduced by 17.23% at E when=1 dB _b /N ₀ The average complexity is reduced by 17.33% when=1.8db. The LC-SCF decoding algorithm reduces the average complexity in the high signal-to-noise ratio region compared to the CA-SCL decoding algorithm. Furthermore, LC-SCF decoding algorithms have similar average complexity to SC decoding algorithms in the high signal-to-noise ratio region.

The simulation results in connection with fig. 13-16 show that the LC-SCF decoding algorithm can significantly reduce the average complexity under similar BLER performance as the SCF decoding algorithm. In practical system applications, the parameters in the LC-SCF decoding algorithm may be set to different values according to the requirements of decoding performance.

Example 2

The embodiment discloses a SCF decoding system based on double threshold values, comprising:

and the SC decoding module is used for carrying out SC decoding on the data to be decoded to obtain an initial decoding bit sequence.

And the cyclic redundancy check module is used for judging whether the current decoding bit sequence passes the cyclic redundancy check.

And the decoding bit sequence output module is used for outputting the current decoding bit sequence if the cyclic redundancy check is passed.

And the probability threshold determining module is used for calculating the probability threshold of the error after the channel transmission bit based on the conditional probability distribution of the error after the sub-channel transmission bit is polarized under the limited code length if the cyclic redundancy check is not passed, and marking the probability threshold as a first probability threshold.

And the turnover bit position searching range determining module is used for forming a turnover bit position searching range from bit positions corresponding to channels with probability values larger than the first probability threshold in the probability distribution.

The final flip bit position set determining module is used for determining a final flip bit position set according to the flip bit position searching range, the second probability threshold and a channel position critical value with probability value tending to 0 in the probability distribution; the second probability threshold is a probability threshold that a bit is miscoded.

The overturn processing module is used for sequentially extracting overturn bit positions from the final overturn bit position set, overturning the corresponding bit value on the current overturn bit position of the current decoding bit sequence if the current overturn bit position is smaller than or equal to the number of elements in the final overturn bit position set, judging whether the overturned current decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence if the overturned current decoding bit sequence passes the cyclic redundancy check; if not, continuing to extract the turning bit position from the final turning bit position set until the final turning bit position set is traversed or the current obtained decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence.

In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.

The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.

Claims (6)

1. A dual threshold based SCF decoding method, comprising:

SC decoding is carried out on the data to be decoded to obtain an initial decoding bit sequence;

judging whether the current decoding bit sequence passes the cyclic redundancy check or not;

if the cyclic redundancy check is passed, outputting a current decoding bit sequence, and ending decoding;

if the cyclic redundancy check is not passed, calculating a probability threshold value of errors after channel transmission bits based on conditional probability distribution of errors after transmission bits of the polarized sub-channels under a limited code length, and marking the probability threshold value as a first probability threshold value;

forming a turnover bit position searching range by using bit positions corresponding to channels with probability values larger than the first probability threshold in the probability distribution;

determining a final flip bit position set according to the flip bit position searching range, a second probability threshold value and a channel position critical value with probability value tending to 0 in the probability distribution; the second probability threshold is a probability threshold that a bit is wrongly decoded;

sequentially extracting turning bit positions from the final turning bit position set, turning over the corresponding bit values on the current turning bit positions of the current decoding bit sequence if the current turning bit positions are smaller than or equal to the number of elements in the final turning bit position set, judging whether the turned over current decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence if the turned over current decoding bit sequence passes the cyclic redundancy check; if not, continuing to extract the turning bit position from the final turning bit position set until the final turning bit position set is traversed or the current obtained decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence.

2. The SCF decoding method based on dual thresholds of claim 1, wherein determining the final flipped bit position set according to the flipped bit position search range, the second probability threshold, and a channel position threshold in the probability distribution where the probability value tends to 0, specifically comprises:

determining a first flipped bit position set according to the flipped bit position search range;

determining a log-likelihood ratio threshold range of the bit attempting to flip according to the second probability threshold;

screening bit positions conforming to the log likelihood ratio threshold range from the first flip bit position set to obtain a second flip bit position set;

and forming the final flipped bit position set by bit positions smaller than the channel position critical value in the second flipped bit position set.

3. The dual threshold based SCF decoding method of claim 2, wherein determining the first set of flipped bit positions from the flipped bit position search range, in particular comprises:

if the number of bits in the turnover bit position searching range is greater than or equal to a preset maximum turnover number, sorting the absolute values of log likelihood ratios of all bits in the turnover bit position searching range from small to large, selecting the ordered bits with the preset maximum turnover number, and forming the positions corresponding to the selected bits into the first turnover bit position set;

and if the number of bits in the flip bit position searching range is smaller than the preset maximum flip times, forming the first flip bit position set according to the order of the absolute values of the log likelihood ratios of the bits from small to large.

4. The dual threshold based SCF decoding method of claim 1, wherein the first probability threshold is expressed as:

wherein,representing the first probability threshold, P _i ^e For channel->Transmission bit u _i The probability of an error occurring after that,k is the number of non-frozen bits, ">Representing the set of positions taking non-frozen bits +.>Middle and late->And the set of positions corresponding to the individual polarized sub-channels.

5. The dual threshold based SCF decoding method of claim 2, wherein the second probability threshold is expressed as:

wherein,representing said second probability threshold, ++>Parameter representing the number of polarized sub-channels, +.>K is the number of non-frozen bits, ">To get the collection->Front middle>A set of position indexes corresponding to the polarized sub-channels, P _i ^e For channel->Transmission bit u _i Error probability of later occurrence, < >>A set of positions that are non-frozen bits;

the log likelihood ratio threshold range is expressed as:

wherein,representation bit u _i Corresponding log likelihood ratio, ++>Representing the data received from the channel and,for decoding the value sequence,/-> Representation bit u ₁ Decoding value of->Representation bit u ₂ Decoding value of->Representation bit u _i-1 Is decoded and valued.

6. An SCF decoding system based on dual thresholds, comprising:

the SC decoding module is used for carrying out SC decoding on the data to be decoded to obtain an initial decoding bit sequence;

the cyclic redundancy check module is used for judging whether the current decoding bit sequence passes cyclic redundancy check or not;

the decoding bit sequence output module is used for outputting the current decoding bit sequence if the cyclic redundancy check is passed;

the probability threshold determining module is used for calculating a probability threshold of error after channel transmission bits based on conditional probability distribution of error after polarization sub-channel transmission bits under a limited code length if the cyclic redundancy check is not passed, and marking the probability threshold as a first probability threshold;

the turnover bit position searching range determining module is used for forming a turnover bit position searching range from bit positions corresponding to channels with probability values larger than the first probability threshold in the probability distribution;

the final flip bit position set determining module is used for determining a final flip bit position set according to the flip bit position searching range, the second probability threshold and a channel position critical value with probability value tending to 0 in the probability distribution; the second probability threshold is a probability threshold that a bit is wrongly decoded;

the overturn processing module is used for sequentially extracting overturn bit positions from the final overturn bit position set, overturning the corresponding bit value on the current overturn bit position of the current decoding bit sequence if the current overturn bit position is smaller than or equal to the number of elements in the final overturn bit position set, judging whether the overturned current decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence if the overturned current decoding bit sequence passes the cyclic redundancy check; if not, continuing to extract the turning bit position from the final turning bit position set until the final turning bit position set is traversed or the current obtained decoding bit sequence passes the cyclic redundancy check, and outputting the current decoding bit sequence.