CN104779962A - Efficient generation method of segmentation vector with lowest computation complexity in Max-Log-MAP decoding algorithm - Google Patents

Abstract

The invention discloses an efficient generation method of a segmentation vector with lowest computation complexity in a Max-Log-MAP decoding algorithm. The method comprises steps as follows: (1) obtaining state vectors and information bit vectors corresponding to all depths in a minimal trellis Mmin according to the minimal trellis Mmin of the Max-Log-MAP decoding algorithm; (2), obtaining segmentation vectors of sections in the minimal trellis Mmin according to the state vectors and the information bit vectors corresponding to all the depths in the minimal trellis Mmin in the step (1); (3) combining the segmentation vectors, obtained in the step (2), of all the sections in the minimal trellis Mmin to obtain the segmentation vector Vetsec with the lowest computation complexity for the Max-Log-MAP decoding algorithm. The segmentation vector Vetsec with the lowest computation complexity in the Max-Log-MAP decoding algorithm can be generated efficiently with the efficient generation method.

Description

The efficient generation method of the segment vectors that Max-Log-MAP decoding algorithm complexity is minimum

Technical field

The invention belongs to communication technical field, relate to a kind of generation method of segment vectors Vetsec, be specifically related to the efficient generation method of the minimum segment vectors of a kind of Max-Log-MAP decoding algorithm complexity.

Background technology

In baseband transmission, chnnel coding (error correcting code) often consumes a big chunk energy of communication equipment, as at B.Bougard et al., " Energy-scalability enhancementof wireless local area network transceivers; " in Proc.2004IEEEWorkshop on Signal Processing Advances in Wireless Communications, in pp.449 – 453, Viterbi decoding, in typical 802.11 receivers, occupies 35% of its total power consumption.The problem of energy ezpenditure governs communication equipment miniaturization and mobility, how to improve the code check of coding, makes the generated codeword of unit length to transmit more information bit, have very large using value.For Turbo code decoding, improve total bitrate, generally take to delete remaining mode, as M.A.Kousa and A.H.Mugaibel, " Puncturingeffects on turbo codes, " IEEE Proc.Commun., vol.149, the method introduced in no.3, pp.132-138, June 2002.Another method improving total bitrate is the member's code using high code check, for convolution code C (n, k, v), this method has the percent of pass improved in the unit interval, reduces the effects such as time delay, but along with the increase of k, the complexity of decoding exponentially doubly can increase along with the increase of k.

Convolution code C (n, k, v) can represent with a semi-infinite grid chart, and this grid chart is the cycle, and its most short period is called mesh module.Be the mesh module of k/n for a code check, it contains individual segmentation, has at degree of depth i individual state, each state is launched bar limit, a _i(0≤i≤n-1) represents the bit number of the output codons representated by limit connecting a certain state of degree of depth i and a certain state of degree of depth i+1, and total constraint length is v, v _iand b _ibe called as the state complexity of this mesh module on degree of depth i and branching complexity respectively, for Viterbi algorithm, the complexity of grid chart module is defined as:

$\mathrm{TC}\left(M\right)=\frac{1}{k}\underset{i=1}{\overset{\hat{n}-1}{\mathrm{\Σ}}}{a}_i\·2^{v_i+b_i}---\left(1\right)$

Conventional mesh figure (Conventional trellis) is a kind of form of expression of the most frequently used convolution code mesh module, and it contains individual segmentation, has 2 ^vindividual initial condition and 2 ^vindividual state of termination, each initial condition exhales 2 ^kbar limit is connected with state of termination, and every bar limit represents n-bit (see Fig. 1).

Another kind of important convolution code mesh module takes the form of minimal trellises (Minimaltrellis), and it contains individual segmentation is information (b for the segmentation of k wherein _i, and an other n-k segmentation is asemantic (b=1) _i=0), minimal trellises contains 2 ^vindividual initial condition and 2 ^vindividual state of termination, every bar limit represents the generated codeword (see Fig. 2) of 1 bit.Minimal trellises can carry out decoding with the method that complexity is minimum in Viterbi decoding, therefore application minimal trellises, corresponding energy ezpenditure can be reduced and improve the utilance of hardware.But for other decoded mode, as Max-Log-MAP decoding, minimal trellises can not ensure that its complexity is necessarily minimum.

State on a certain for minimal trellises degree of depth i is all removed, and the state on degree of depth i-1 is directly connected with the state on degree of depth i+1, so just obtain a new segmentation, it is merged by the segmentation of two on original minimal trellises to form, and the grid chart after merging only is left individual segmentation.Popularization is come, and this operation multiple segmentation being merged into a segmentation is called staged operation, and the grid chart obtained after segmentation is called segmentation grid chart (Sectionalizedtrellis).Staged operation is a kind of being applied on minimal trellises to obtain the operation of new grid chart topological structure, it is by deleting the state on a certain degree of depth i of minimal trellises, and the state on degree of depth i-1 and the state on degree of depth i+1 are re-started be connected, obtain a compact structure more.Along with the number of times of segmentation gets more and more, grid chart structure will be further compact, finally, after intermediateness all being deleted, obtains conventional mesh figure.For convolution code C (n, k, v), its possible segmented mode has 2 ^n-1kind, in order to express the various different segmented mode for minimal trellises, we define a binary segment vectors vetsec={vetsec _i, i=1 ..., n-1, when minimal trellises is deleted and after the state on degree of depth i-1 being directly connected with the state on degree of depth i+1 in the state of degree of depth i, then vetsec _i=1, otherwise, vetsec _i=0 (see Fig. 3).We use respectively represent the complexity of state on the bit number of the generated codeword representated by the limit of segmentation grid chart on degree of depth i to degree of depth i+1 and degree of depth i and branch, such as, Fig. 3 is the C (5 shown in Fig. 2,3,5) the segmentation grid chart of minimal trellises under the condition of segment vectors vetsec=(0010), the degree of depth 3 of the minimal trellises shown in Fig. 2 carries out staged operation, delete by the state in the degree of depth 3, and the degree of depth 2 is directly connected with the state in the degree of depth 4.Carry out the grid chart after staged operation to have individual segmentation, its limit complexity vector and the trellis complexity defined by (1) formula, the complexity TC (M of conventional mesh figure can be drawn _conv)=427.5, the complexity TC (M of minimal trellises _min)=74.7, and under the condition of segment vectors vetsec=(0010), the complexity TC (M of segmentation grid chart _sec)=96.

At R.J.McEliece and W.Lin, " The trellis complexity ofconvolutional codes; " IEEE Trans.Inf.Theory, vol.42, no.6, pp.1855-1864, in the theoretical complexity of the grid chart defined in Nov.1996, for Viterbi decoding, the complexity of minimal trellises is less than the complexity of conventional mesh figure, and uses minimal trellises can't bring any performance loss.But for Max-Log-MAP decoding algorithm, use minimal trellises to carry out decoding and not necessarily will can obtain minimum decoding complexity.

The computation complexity of the Max-Log-MAP decoding algorithm of segmentation grid chart can represent with each section of addition, multiplication and the cumulative of the number of times compared, and we represent addition, multiplication and comparison operation with M, S, C respectively here.At Moritz G, Souza R, Max-Log-MAP decoding algorithm is given for γ in i-th segmentation of segmentation grid chart in Pimentel C, et al. " Turbo Decoding Using the Sectionalized Minimal Trellis of the ConstituentCode:Performance-Complexity Trade-Off " .2013. _i, α _i, β _i, Λ _ithe computing formula of computation complexity and total computation complexity.With C (5,3,5) be example, suitable packet mode is selected in Max-Log-MAP decoding, under the condition of the certain performance of loss, the addition of the segmented mode that its computation complexity is minimum reduces 63.8% and 59.4% with the number of times of comparison operation respectively compared with conventional mesh figure, and complexity greatly reduces.Existing technical scheme for the method how finding segment vectors that the Max-Log-MAP decoding algorithm complexity of C (n, k, v) code is minimum special, can only to its 2 ^n-1compare after kind segmented mode carries out traversal computing and draw.

Summary of the invention

Effect of the present invention is to overcome the shortcoming that above-mentioned existing method need carry out traveling through computing, provide the efficient generation method of the minimum segment vectors of a kind of Max-Log-MAP decoding algorithm complexity, the method can generate the minimum segment vectors Vetsec of Max-Log-MAP decoding algorithm computation complexity efficiently.

For achieving the above object, the generation method of the segment vectors Vetsec that Max-Log-MAP decoding algorithm computation complexity of the present invention is minimum comprises the following steps:

1) according to the minimal trellises M of Max-Log-MAP decoding algorithm _min, obtain described minimal trellises M _minthe state vector that upper each degree of depth is corresponding and information bit vector;

2) according to step 1) minimal trellises M _minthe state vector that upper each degree of depth is corresponding and information bit vector obtain minimal trellises M _minin the segment vectors of each section;

3) combination step 2) the minimal trellises M that obtains _minin the segment vectors of each section, obtain for the minimum segment vectors Vetsec of Max-Log-MAP decoding algorithm computation complexity.

Step 2) detailed process be:

Judge minimal trellises M _minstate vector v corresponding on upper degree of depth i _iand information bit vector b _ithe state vector v corresponding with on degree of depth i+1 _i+1size, wherein, i=0,1 ..., n-2, n are minimal trellises M _minthe sum of the upper degree of depth;

Work as v _i=v _i+1when-1, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=1;

Work as v _i=v _i+1when+1, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=0;

Work as v _i=v _i+1, and minimal trellises M _mininformation bit vector b corresponding on upper degree of depth i _iwhen=1, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=0;

Work as v _i=v _i+1, and minimal trellises M _mininformation bit vector b corresponding on upper degree of depth i _iwhen=0, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=1.

The present invention has following beneficial effect:

The efficient generation method of the segment vectors that Max-Log-MAP decoding algorithm complexity of the present invention is minimum, only need according to its minimal trellises M when operating _minthe state vector v that upper each degree of depth is corresponding _iand information bit vector b _icompare to determine obtain minimal trellises M _minin the segment vectors vetsec of each section _i, then combined by the segment vectors of each section, generating the minimum segment vectors Vetsec of complexity with tradition needs to carry out compared with traversal computing, to invention increases the efficiency finding Max-Log-MAP decoding algorithm computation complexity lowest segment mode.In addition, from theory, for the application scenario sometimes becoming generator matrix, under the condition knowing its minimal trellises, the method can online in real time quick-pick complexity minimum one set of segmentation vector.

Accompanying drawing explanation

Fig. 1 is the conventional mesh figure of C (5,3,5) code;

Fig. 2 is the minimal trellises of C (5,3,5) code;

Fig. 3 is the segmentation grid chart of C (5,3,5) code under the condition of segment vectors vetsec=(0010);

Fig. 4 is the minimal trellises of C (7,4,4);

Fig. 5 is the complicated dynamic behaviour result figure under C (7,4,4) the various segmented mode using traversal to calculate.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail:

The efficient generation method of the segment vectors that Max-Log-MAP decoding algorithm complexity of the present invention is minimum comprises the following steps:

1) according to the minimal trellises M of Max-Log-MAP decoding algorithm _min, obtain described minimal trellises M _minthe state vector that upper each degree of depth is corresponding and information bit vector;

2) according to step 1) minimal trellises M _minthe state vector that upper each degree of depth is corresponding and information bit vector obtain minimal trellises M _minin the segment vectors of each section;

3) combination step 2) the minimal trellises M that obtains _minin the segment vectors of each section, obtain for the minimum segment vectors Vetsec of Max-Log-MAP decoding algorithm computation complexity.

Step 2) detailed process be:

Judge minimal trellises M _minstate vector v corresponding on upper degree of depth i _iand information bit vector b _ithe state vector v corresponding with on degree of depth i+1 _i+1size, wherein i=0,1 ..., n-2, n are minimal trellises M _minthe sum of the upper degree of depth;

Work as v _i=v _i+1when-1, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=1;

Work as v _i=v _i+1when+1, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=0;

Work as v _i=v _i+1, and minimal trellises M _minthe information bit vector b that upper degree of depth i is corresponding _iwhen=1, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=0;

Work as v _i=v _i+1, and minimal trellises M _minthe information bit vector b that upper degree of depth i is corresponding _iwhen=0, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=1.

To C (n, k, v), with Max-Log-MAP algorithm, segmented decodings is carried out to it, if need to choose the minimum segmented mode of complexity, need to its 2 ^n-1plant segmented mode to travel through, addition, multiplication and the number compared required under calculating often kind of segmented mode respectively.And the method that the present invention is used, only need knowing the state vector V={v of its minimal trellises _iand information bit vector B={b _iwhen, just can draw by simple judgement computing a kind of segmented mode that its complexity is minimum, it is secondary that the total degree of judgement computing is not more than 2* (n-1), and use traditional traversal computing needs $\underset{j=1}{\overset{2^{n-1}}{\mathrm{\Σ}}}\underset{i=0}{\overset{{\hat{n}}_j-1}{\mathrm{\Σ}}}(T_{{\mathrm{\γ}}_{j,i}}^{\sec }+T_{{\mathrm{\α}}_{j,i}}^{\sec }+T_{{\mathrm{\β}}_{j,i}}^{\sec }+T_{{\mathrm{\Λ}}_{j,i}}^{\sec })$ Secondary computing, wherein with be illustrated respectively in the γ of the i-th+1 section in segmentation grid chart under jth kind segmented mode, α, β, the computation complexity of Λ and total segments, this is significant for finding out rapidly the amount of calculation that the minimum Max-Log-MAP decoding algorithm of computation complexity saves, and along with the increase of n, k, the advantage of this method can be further obvious.In addition, for the application scenario sometimes becoming generator matrix, under the condition knowing its minimal trellises, the method can quick-pick complexity is minimum in real time online a set of segmentation vector, drastically increases the speed finding Max-Log-MAP decoding algorithm computation complexity lowest segment mode.The determination of this computation complexity lowest segment mode is applicable to the application scenario to computational complexity sensitivity, and reducing the energy consumption of communication equipment, it is considerable for improving operation efficiency aspect, with the C (7 shown in Fig. 4,4,4) code is example, uses above-mentioned generation method:

V ₀=v ₁-1, so minimal trellises M _minin the segment vectors vetsec of the 1st section ₁=1;

V ₁=v ₂-1, so minimal trellises M _minin the segment vectors vetsec of the 2nd section ₂=1;

V ₂=v ₃+ 1, so minimal trellises M _minin the segment vectors vetsec of the 3rd section ₃=0;

V ₃=v ₄, and minimal trellises M _minthe information bit vector b of the upper degree of depth 3 correspondence ₃when=1, so minimal trellises M _minin the segment vectors vetsec of the 4th section ₄=0;

V ₄=v ₅+ 1, so minimal trellises M _minin the segment vectors vetsec of the 5th section ₅=0.

V ₅=v ₆-1, so minimal trellises M _minin the segment vectors vetsec of the 6th section ₆=1;

The segmented mode vetsec=[110001] that the computation complexity obtained according to above-mentioned generation method is minimum, with be the same by the segmented mode vetsec=[110001] that travels through computation complexity that computing obtains minimum shown in Fig. 5, its operation times saving rate is $1-\{(6+1)/[\underset{j=1}{\overset{2^{n-1}}{\mathrm{\Σ}}}\underset{i=0}{\overset{{\hat{n}}_j-1}{\mathrm{\Σ}}}(T_{{\mathrm{\γ}}_{j,i}}^{\sec }+T_{{\mathrm{\α}}_{j,i}}^{\sec }+T_{{\mathrm{\β}}_{j,i}}^{\sec }+T_{{\mathrm{\Λ}}_{j,i}}^{\sec })\},$ Be about 99.99%.

In Fig. 5, S, M, C represent addition respectively, multiplication and comparison operation number of times, and Tr, Ta, Tb, Tv represent respectively and under the segmented mode of correspondence, calculate α in Max-Log-MAP decoding algorithm, beta, gamma, the operand needed for Λ.

Note: Fig. 1 to Fig. 3 selects from Moritz G L, Demo Souza R, Pimentel C, etal.Turbo decoding using the sectionalized minimal trellis of theconstituent code:performance-complexity trade-off [J] .Communications, IEEE Transactions on, 2013, 61 (9): 3600-3610. Fig. 4 select from Benchimol I, Pimentel C, Demo Souza R.Sectionalizationof the minimal trellis module for convolutionalcodes [C] //Telecommunications and Signal Processing (TSP), 201235th International Conference on.IEEE, 2012:227-232.

Claims (2)

1. an efficient generation method for the segment vectors that Max-Log-MAP decoding algorithm complexity is minimum, is characterized in that, comprise the following steps:

1) according to the minimal trellises M of Max-Log-MAP decoding algorithm _min, obtain described minimal trellises M _minthe state vector that upper each degree of depth is corresponding and information bit vector;

2) according to step 1) minimal trellises M _minthe state vector that upper each degree of depth is corresponding and information bit vector obtain minimal trellises M _minin the segment vectors of each section;

3) combination step 2) the minimal trellises M that obtains _minin the segment vectors of each section, obtain for the minimum segment vectors Vetsec of Max-Log-MAP decoding algorithm computation complexity.

2. the efficient generation method of the segment vectors that Max-Log-MAP decoding algorithm complexity according to claim 1 is minimum, is characterized in that, step 2) detailed process be:

Judge minimal trellises M _minstate vector v corresponding on upper degree of depth i _iand information bit vector b _ithe state vector v corresponding with on degree of depth i+1 _i+1size, wherein, i=0,1 ..., n-2, n are minimal trellises M _minthe sum of the upper degree of depth;

Work as v _i=v _i+1when-1, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=1;

Work as v _i=v _i+1when+1, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=0;

Work as v _i=v _i+1, and minimal trellises M _mininformation bit vector b corresponding on upper degree of depth i _iwhen=1, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=0;

Work as v _i=v _i+1, and minimal trellises M _mininformation bit vector b corresponding on upper degree of depth i _iwhen=0, then minimal trellises M _minin the segment vectors vetsec of the i-th+1 section _i+1=1.