1273777 九、發明說明： 【發明所屬之技術領域】 本發明係關於一種搜尋具有低解碼複雜度及高錯誤修 正能力捲積碼的方法。 5 【先前技術】 在通訊系統中，發射端發射通信訊號至遠端之接收端， 當通信訊號經過無線通道而造成訊號衰落（fading )並導致 訊號錯誤等現象。因此，通信訊號需進行捲積編碼處理 (convolutional encoding)後方發射至遠端，再由遠端之接 10 收器對捲積編碼處理後之通信訊號進行捲積解碼處理 (convolutional decoding )以取得通信訊號，如此一來即可 避免上述缺失。而上述捲積編碼處理又稱為通道編碼 (channel encoding )，乃由通道編碼器所執行。一般而言， 捲積碼包含三個參數，輸入位元參數k以及輸出位元參數η 15 所決定，並以碼率（code rate ) =k/n表示之，k以及η皆為正 整數。另一重要參數為限制長度（constraint length) ν，用以 表示該碼的記憶量。利用維特比演算法（Viterbi algorithm) 以進行捲積解碼處理可提供較佳之編碼增益（coding gain)，因此目前通訊系統中多組設維特比解碼器以執行捲 20 積解碼處理。維特比解碼處理為一種最大似然（ maximum likelihood)之解碼技術，其依序接收通信訊號之字組並與已 建立之籬狀圖（trellis diagram )對應之分支輸出比較，算出 其分支距#值（branch metric )，進而累積各分支距離值而 取得籬狀圖中各路徑之路徑距離值（path metric)，最後選 1273777 取具有最小路徑距離值之路徑作為解碼處理所需之存活路 徑（surviving path)。對碼率2/n的捲積碼而言，每一級的 籬狀圖總共有2V+2條分支，且因為每一分支總共有讀位元， 所以每一分支總共有2n種可能的輸出。一般而言，2v+2會遠 5大於2n ’也就是說分支間必存在某種的對㈣係。在台灣專 利申睛93131423號之技術内容中，提出—種蝴蝶結構，利用 这樣的蝴蝶結構可輕易的找出存在分支間的對稱關係並用 它來降低分支距離值的計算。以目前常見的2/3捲積碼為 ^利料樣的蝴蝶結構，大部份的碼可將分支距離值的計 1〇 2里減少為原來的1/2或1/4，如此就可簡化維特比解碼器的 貝現。本發明提出—搜尋方法，用於搜尋具有更高對稱關係 j捲積馬以目如找到的新型碼為例，它們的分支距離值計 算量可以進一步被簡化為而來的1/4或1/8,且具有與熟知2/3 捲積碼相近的錯誤修正能力。這樣的碼更能滿足使用者對高 15錯誤修正能力及低解碼複雜度通道編碼的需求。 【發明内容】 f發明之目的係在提供一種用於搜尋具有低解碼複雜 度及鬲錯誤修正能力的捲積碼之方法。 2〇 、 為達成上述目的，本發明提供一種用於搜尋同時具有高 刀支對稱關係（hiSh branch symmetry)及好的距離特性捲積 馬的方法，該方法包含：（A)初始化碼的資訊，其係設定碼 率、限制長度參數及自由距離上限值（b〇und 〇n the ee ) db ’（B)遥擇一具有對稱條件的碼；（c)計算該碼的 6 1273777 Z離頻4，（D)判斷_的自由距離是否等於已知之自由距 離上限值db;⑻若步驟⑼中判㈣碼的自由距離不等於已 择谈自由距離上限Μ，再判斷是否完成所有符合該對稱關 係捲積碼的搜尋；f"p) # j 驟⑻中判定完成所有符合該對稱 關係捲積碼的搜尋，再判磨 ⑺中判定有被紀錄 、， 、 ”、、&取具有較小距離頻譜的捲積 …、，亚輸出八生成序列及距離頻譜。 、 【實施方式】 10 15 在本發明中’高分支對稱關係是由限定生成 Γ㈣⑽)來達成，並藉由比較各個碼的自由長度 誤修正能力的碼。此外高錯 (~。—)，以確保該碼之可-二 "冉關係細即睛參考台灣專利申請叫助 術内谷。由該文件我們知 〜支 到該碼存在蝴蝶結構中的對：二用：積碼的生成序列來得 來間化維特比解碼器的實現 _對稱關係 每-位元的對稱關係交隹，^刀、冉關係是由分支中 性便、>定7八’、木侍，因此位元間對稱關係的相似 同對稱關係時，該碼則擁有最好斤:位-擁有相 限定生成序列來盡可能使位元對稱關传二關係。因為藉由 奇係不過’這樣的限制卻也可能會造成修正能力 20 12737771273777 IX. Description of the Invention: [Technical Field of the Invention] The present invention relates to a method of searching for a convolutional code having low decoding complexity and high error correction capability. 5 [Prior Art] In the communication system, the transmitting end transmits the communication signal to the receiving end of the remote end. When the communication signal passes through the wireless channel, the signal fading and causing the signal error. Therefore, the communication signal is transmitted to the remote end after convolutional encoding, and then the convergent decoding is performed on the convolutional coded communication signal by the remote receiver 10 to obtain communication. Signal, so you can avoid the above missing. The above convolutional coding process, also known as channel encoding, is performed by the channel encoder. In general, the convolutional code contains three parameters, the input bit parameter k and the output bit parameter η 15 , and is represented by a code rate = k/n, where k and η are both positive integers. Another important parameter is the constraint length ν, which is used to represent the amount of memory of the code. The use of a Viterbi algorithm for convolutional decoding processing provides better coding gain, so that a plurality of Viterbi decoders are currently set in the communication system to perform volume 20 decoding processing. The Viterbi decoding process is a maximum likelihood decoding technique that sequentially receives the block of communication signals and compares it with the branch output corresponding to the established trellis diagram to calculate the branch distance # value. (branch metric), and then accumulate the branch distance values to obtain the path metric of each path in the hedge diagram, and finally select 1273777 to take the path with the minimum path distance value as the survival path required for decoding processing (surviving path) ). For a convolutional code with a rate of 2/n, the hedge graph for each level has a total of 2V + 2 branches, and since there are a total of read bits per branch, there are a total of 2n possible outputs per branch. In general, 2v+2 will be farther than 5n', which means that there must be some kind of pair (four) between branches. In the technical content of Taiwan Patent Application No. 93314423, a butterfly structure is proposed, and the butterfly structure can be used to easily find the symmetrical relationship between the branches and use it to reduce the calculation of the branch distance value. With the current common 2/3 convolutional code as the butterfly structure, most of the codes can reduce the branch distance value from 1 to 2 to 1/2 or 1/4 of the original value. Simplify the appearance of the Viterbi decoder. The present invention proposes a search method for searching for a new type of code with a higher symmetric relationship j convolutional horse. The calculation of the branch distance value can be further simplified to 1/4 or 1/ 8, and has the error correction capability similar to the well-known 2/3 convolutional code. Such a code can better satisfy the user's need for high error correction capability and low decoding complexity channel coding. SUMMARY OF THE INVENTION The object of the invention is to provide a method for searching for a convolutional code having low decoding complexity and error correction capability. In order to achieve the above object, the present invention provides a method for searching for a hiSh branch symmetry and a good distance characteristic convolution horse, the method comprising: (A) information of an initialization code, It sets the code rate, the limit length parameter and the free distance upper limit value (b〇und 〇n the ee ) db '(B) to select a code with a symmetric condition; (c) calculate the code of the 6 1273777 Z off-frequency 4, (D) determine whether the free distance of _ is equal to the known free distance upper limit value db; (8) if the free distance of the (four) code in step (9) is not equal to the upper limit of the selected free distance, then determine whether all of the symmetry is met Search for the relational convolutional code; f"p) # j (8) determines that all the search for the convolutional code that satisfies the symmetric relationship is completed, and then judges that there is a record in the (7), and that ",", & The convolution of the distance spectrum..., the sub-output eight generation sequence and the distance spectrum. [Embodiment] 10 15 In the present invention, the 'high-branch symmetry relationship is achieved by the limit generation Γ(4)(10)), and by comparing the freedom of each code Length Miscorrected ability code. In addition to high error (~.-), to ensure that the code can be - two " 冉 细 参考 参考 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾 台湾There is a pair in the butterfly structure: two uses: the generation sequence of the product code to obtain the realization of the Viterbi decoder _ symmetry relationship per-bit symmetry relationship, ^ knife, 冉 relationship is branched neutral, > 定7八', 木客, so the similarity and symmetry relationship between the symmetry relations between the bits, the code has the best jin: bit-has a phase-limited generation sequence to make the bit symmetry as far as possible. Because it is possible to cause corrections by the limitations of the odds, however, 20 1273777
的下降。因此本搜尋方法則希望在限制生成序列下，亦能找 到具有尚錯誤修正能力的碼。 如圖1所示，2/n捲積編碼器包括2個位移暫存器且其限 制長度分別為vl以及v2，所以總限制長度v=vl+v2, v卜v2、 5 及v之值皆為正整數。在一個單位時間中，通道編碼器可輸 入二個位元，分別為位元W以及V2,且可輸出n個位元，而輸 出之位元yi可表示如下： 乃=‘ % ㊉…㊉‘ χ 'νΐ φ ‘ x % ㊉…㊉ x 'v2 ( 1) 其中，i為不大於n之正整數，，㊉表示模數2的加法器 10 (modulo_2 adder)。當以籬狀圖表示捲積碼時，則籬狀圖 之狀悲共計有2V個可能狀態。如圖2所示，假設狀態j表示目 丽狀態，狀態j’為狀態j之下一級狀態，狀態〗與狀態〗，各具有 N個可此值。為了找到分支間的對稱關係，必需先將籬狀圖 進行弟一步分解以成數個基數為4 ( radix_4 )之蝴蝶單元， 15分解之準則為選定狀態Γ中新輸入之位元111及112以及狀態j中 即將被剔除之位元Slvl及位元hv2為變數，其他位元為非變 數，在往後圖示中並以XX表示之，如此一來，基數為4之蝴 蝶單元將如圖3所示，此時在蝴蝶單元中位元％可改寫並表 示如下： 20 兄· = ‘ x ㊉ ‘ x ㊉ ‘ X % ㊉ g，v2 w2v2 ㊉尤 (2) 其中，Xi表示共同項，由於Xi為分支間的共同項，故不 會影響分支間的關係，所以由式（2)可看出分支間的關係只 文生成序列客;。、、‘及g(v2影響。之後，再藉由固定狀態 r中新輸入之位元A以及狀態j中即將被剔除之位元值而 1273777 將每一個基數為4之蝴蝶單元分解以成4個基數為2 (radix-2) 之蝴蝶單元Β〗、B2、B3及B4。如圖4所示，每一個基數為2之 蝴蝶單元之分支輸出bl、b2、卜及匕的對稱關係將由‘及 所決定。基數為2之蝴蝶單元彼此之間之對稱關係將由及Decline. Therefore, this search method hopes to find a code with error correction capability under the restriction generation sequence. As shown in Figure 1, the 2/n convolutional encoder includes two displacement registers and their limit lengths are vl and v2, respectively, so the total limit length is v=vl+v2, and the values of v, v2, 5 and v are Is a positive integer. In one unit time, the channel encoder can input two bits, which are bit W and V2, respectively, and can output n bits, and the output bit yi can be expressed as follows: yes = '% ten... ten' χ 'νΐ φ ' x % ten... ten x 'v2 ( 1) where i is a positive integer not greater than n, and ten represents a modulo 2 adder 10 (modulo_2 adder). When the convolutional code is represented by a hedge diagram, there is a total of 2V possible states for the shape of the hedge. As shown in Fig. 2, it is assumed that the state j represents the state of the state, the state j' is the state of the state below the state j, the state and the state, each having N values. In order to find the symmetry relationship between the branches, the hedge diagram must be first decomposed into a number of butterfly units with a base of 4 (radix_4). The criterion of 15 decomposition is the newly input bits 111 and 112 and the state in the selected state. The bit Slvl and the bit hv2 which are about to be removed in j are variables, and the other bits are non-variables, which are represented by XX in the following figure, so that the butterfly unit with base 4 will be as shown in FIG. In this case, the bit % in the butterfly unit can be rewritten and expressed as follows: 20 brother · = ' x ten ' x ten ' X % ten g, v2 w2v2 ten (2) where Xi represents a common term, since Xi is The common items between the branches do not affect the relationship between the branches. Therefore, it can be seen from equation (2) that the relationship between the branches only generates sequence users. , , and g (v2 influence. After that, by the newly input bit A in the fixed state r and the bit value to be culled in the state j, 1273777 decomposes each butterfly unit with a base of 4 into 4 The butterfly unit 基, B2, B3, and B4 with a base of 2 (radix-2). As shown in Figure 4, the symmetrical relationship of the branch outputs bl, b2, and 匕 of each butterfly unit with a base of 2 will be determined by ' And the decision is made. The symmetrical relationship between the butterfly units with base 2 will be
Ww所決定。生成序列與基數為2之蝴蝶單元内分支之對稱關 係如表一所示，生成序列與基數為2之蝴蝶單元彼此之間之 對稱關係及表二所示： 《1,0 ?2,v2 基數為2之蝴蝶單元内分支之對稱關係 0 0 bi= b2:=: b3= b4 1 r\ 0 b广b〗’=b3= ’ 0 bf ΐ>2= b3’= b/ 1 1 b!= b2，= b3，= b4 * 表一Ww decided. The symmetric relationship between the generated sequence and the branch within the butterfly unit with base 2 is as shown in Table 1. The symmetric relationship between the generated sequence and the butterfly unit with base 2 is shown in Table 2: "1,0 ?2, v2 base The symmetry relationship of the branches in the butterfly unit of 2 0 0 bi= b2:=: b3= b4 1 r\ 0 b wide b〗 '=b3= ' 0 bf ΐ>2= b3'= b/ 1 1 b!= B2,= b3,= b4 * Table 1
=b2=b3=b4=b2=b3=b4
表 一 j利將關係/、存在於分支的某一七 二分，稱關係必須由分支上所有位元的對稱關係交, 及表二所整 隼二=核尋方法藉由限制生成序列，使該碼各位元; =出來具有面分支對稱關係。如圖5所示，本 2/·積碼之方法包括下列步驟： 月技寸則 10 1273777' 步驟S12:初始化已知捲積碼之資訊。已知捲積碼之資 訊包括碼率、長度限制參數¥1，¥2、及自由距離上限值以的“ on the free distance) db。 步驟S14 ·糟由限制生成序列來選取具有高對稱關係捲 5積碼。在本文中，我們定義1/χ對稱關係意指於在_ μ 中，只需要計算其中一支，其它X-1個分支可由該對稱關係 取得。如圖6所示，以長度限制參數ν=7為例，當2/η生成序 列為16，13,3以及11，23,32時，則該碼具有1/4的對稱關係。 步驟S16 :纟所選取碼的生成序列來計算其距離頻譜。 > 步驟S18 ·判斷該碼的自由距離^是否等於已知之自 由距離上限值db，如果成立則執行步驟S2()，否則執行步驟 步驟S20 :判斷該碼是否為惡性碼（catastrophic code )， 如果成立則執行步驟S24。由於惡性碼具有有限輸入錯誤造 成…、限解碼輸出錯誤的問題，因此無法用於實際應用。 步驟S22 :紀錄該碼的生成序列及其距離頻譜。 步驟S24:判斷是否完成所有符合該對稱關係捲積碼的 尋動作，如果不成立則執行步驟S14。 2〇步驟S26 ·判斷是否有被紀錄的碼，如果不成立則執行 步驟S28 ·選取具有較小距離頻譜的捲積碼，並輸出盆 生成序列及距離頻譜。 八 =步驟S30 · db=db-l，並執行步驟S14。當長度限制參數 v—6，越高對稱關係的碼符合u。目此，本發明搜尋 10 1273777 方法將自動搜尋是否有滿足自由距離4^=6之具高對稱關係 碼存在。 圖6為針對碼率2/3使用本搜尋方法所得到的新碼，跟一 些常見的碼（best known codes)相比，我們所搜尋的碼與這些 5常見的碼具有相近的錯誤的修正能力，而這些新碼的分支計 $值的計算量可以進一步被簡化為原來的1/4或1/8。亦即利 用本發明可搜尋到同時具有低解碼複雜度及高錯誤修正能 力的碼。 上述實施例僅係為了方便說明而舉例而已，本發明所主 10張=權利範圍自應以中請專利範圍所述為準，而非僅限於上 【圖式簡單說明】 圖1係2/n捲積編碼器的示意圖。 圖2係碼率2/n之捲積碼所對應之籬狀圖。 15 20 圖3係本發明之基數為4 ( radix_4 )的蝴蝶單元 稱 圖4係本發明之基數為2之蝴蝶單八 關係之示意圖。 之刀支輪出的對 圖5係本發明搜尋碼率2/n捲積碼之方法的节。 圖6係使用本發明搜尋碼率2/n捲積 i圖。 新碼。 馬之方法所得到的 【主要元件符號說明】 無 11 25Table 1 j will be the relationship /, exist in the branch of a certain seven or two points, said the relationship must be the symmetry relationship of all the bits on the branch, and the second table of the two = nuclear search method by limiting the generation sequence, so that The code each element; = out has a surface branch symmetry relationship. As shown in FIG. 5, the method of the 2/. product code includes the following steps: The monthly skill level is 10 1273777'. Step S12: Initialize the information of the known convolutional code. The information of the known convolutional code includes the code rate, the length limit parameter of ¥1, ¥2, and the free-range upper limit value of "on the free distance" db. Step S14 · The difference is generated by the sequence to select a high symmetric relationship Volume 5 product code. In this paper, we define the 1 / χ symmetry relationship means that in _ μ, only one of them needs to be calculated, and the other X-1 branches can be obtained from the symmetry relationship. As shown in Figure 6, The length limit parameter ν=7 is taken as an example. When the 2/η generation sequence is 16, 13, 3, and 11, 23, 32, the code has a 1/4 symmetric relationship. Step S16: 生成 The generated sequence of the selected code To calculate the distance spectrum. > Step S18 · Determine whether the free distance ^ of the code is equal to the known free distance upper limit value db, if yes, execute step S2(), otherwise perform step S20: determine whether the code is malignant The catastrophic code, if it is established, performs step S24. Since the malicious code has a finite input error, and the decoding output error is limited, it cannot be used for practical applications. Step S22: Record the generation sequence of the code and its distance spectrum Step S2 4: judging whether all the seek operations conforming to the symmetric relationship convolutional code are completed, and if not, performing step S14. 2. Step S26 · determining whether there is a recorded code, if not, performing step S28 · selecting a spectrum having a smaller distance The convolutional code, and output the basin generation sequence and the distance spectrum. Eight = step S30 · db = db-l, and step S14 is performed. When the length limit parameter v-6, the higher the symmetric relationship of the code conforms to u. The search method of the present invention 10 1273777 will automatically search for the existence of a high symmetric relation code satisfying the free distance 4^=6. Fig. 6 is a new code obtained by using the search method for the code rate 2/3, with some common codes. Compared to the best known codes, the code we searched has similar erroneous correction capabilities to these 5 common codes, and the calculation of the branch value of these new codes can be further reduced to the original 1/4 or 1/8. That is to say, the code with low decoding complexity and high error correction capability can be searched by using the present invention. The above embodiments are only examples for convenience of description, and the main 10 sheets of the present invention = right scope It should be based on the scope of the patent application, but not limited to the above [Simplified Schematic] Figure 1 is a schematic diagram of a 2/n convolutional encoder. Figure 2 is a convolutional code with a code rate of 2/n. Fig. 3 is a schematic diagram of a butterfly unit having a base of 4 (radix_4) according to the present invention. Fig. 4 is a schematic diagram showing the relationship of a butterfly with a cardinality of 2 in the present invention. A section of the method of searching for a code rate 2/n convolutional code is shown in Fig. 6. Fig. 6 is a diagram of a search rate 2/n convolution i map using the present invention. New code. [Major component symbol description] obtained by Ma method No 11 25