523996 五、發明說明（1) 發明領域： 本發明係有關一種計算徵兆多項式（syndr〇me = i之方法’特別是關於一種用以在解碼經過錯 ^ 二广理或疋錯誤和抹除訂正編碼處理之接收字碼 (codeword )中計算徵兆多項式的方法。 子馬 發明背景： 於，宙ί枋在5供數位化資訊與通訊的技術中’錯誤訂正碼 位影音光碟（DVD)，未來的數位式廣播（dvb)、以 視：J的數位式衛星直播，電腦各式記憶體及 如k機存取記憶體（RAM)、唯讀記憶體（r〇m) :置 ，、光碟機、甚至運算處理單元，網際網路資料編碼格 專^採用里德-所羅門碼（Reed_s〇1〇m〇n c〇des)，式 RS碼’作為錯誤更正碼來提升訊息的可靠性與整體性0。冉 習知RS碼的解碼過程示意圖係如第—圖所示，— 計算器（syndrome calculator ) 10在接收到的字碼 、 式R(x)後產生有2t個徵兆值，其中t為最大可更正錯—吳喝 數；由這些徵兆值（\〜、）中，關鍵方程式解答’$器块 (key equation solver ) 12可以產生錯誤定位器多°°項 σ(χ) (error locator polynomial)及錯誤求值 ^ 夕式 式 Ω(χ) (error evaluator polynomial )，接著再 ^ 項 錢氏搜尋器（Ch i en search ) 1 4與錯誤值求值器1 6來#\用 計算出錯誤位置與錯誤值。 A > Μ523996 V. Description of the invention (1) Field of the invention: The present invention relates to a method for calculating a symptom polynomial (syndrom = i), and in particular, to a method for decoding errors and erasing correction codes during decoding. Method for calculating the symptom polynomial in the received codeword of processing. Zima's background of the invention: Yu, Zhou 错误 in the 5 digital information and communication technology 'error correction code bit video disc (DVD), future digital Broadcast (dvb), video: digital satellite live broadcast of J, all kinds of computer memory, such as k machine access memory (RAM), read-only memory (r0m): set, optical drive, and even computing Processing unit, Internet data encoding grid specifically adopts Reed-Solomon code (Reed_s〇１〇m〇nc〇des), the type RS code 'as an error correction code to improve the reliability and integrity of the message. 0 Ran Xizhi RS The schematic diagram of the decoding process of the code is shown in the first figure. — The calculator 10 generates 2t symptom values after the received word code and formula R (x), where t is the maximum correctable error—Wu Drink Number; from these signs In (\ ~,), the key equation solver '$ equation block (key equation solver) 12 can generate error locator with multiple °° terms σ (χ) (error locator polynomial) and error evaluation ^ Xi formula Ω (χ) (error evaluator polynomial), followed by ^ terms Chi En search 1 4 and error value evaluator 16 to # \ use the calculated error position and error value. A > Μ
第4頁 5239% 五、發明說明（3) __ 碼’什鼻出如t個徵兆值，其中t為曰 接著，再判斷該前t個徵兆值是否 '為烫:大可更正錯誤數目，· 為零，則停止計算，否則繼續計曾:令，若該前ί個徵跑 底下藉由具體實施例配合所徵兆值。 值 容易瞭解本發明之目的、技術内宏二式坪加說明，當旻 效。 特點及其所達成之： 圖號說明： 10 徵兆計算器 12 關鍵方程式解答器 14 錢氏搜尋器 16 錯誤值求值器 詳細說明： RS碼是數位通訊與資料儲存系統 錯誤更正碼，它對於多重的 :用，的一種 能力。習知之設計不論接收到的字：t ::的谓測及更正 出2t個徵兆值；然而，由扭錯块，都必須算 之關係式可以推論出當j /、、"决疋位器多項式係數 亦為零，由此可知，： = 為零時，表示、〜、 t個徵兆值就可以判斷所你接子碼錯誤與否日夺，僅需要 -種用以在解到，Λ碼Λ… 算徵兆多項式之方C丁正碼處理之接收字碼中計 步驟：首先，將所有妹；二-圖所不’該方法係包括下列 用-徵兆計算器，：誤訂正碼處理之接收字碼’利 叶外出前t個徵兆值（Sl〜St )，如步驟 第6頁 523996 五、發明說明（4) =0所不，其中t值係為可更正錯誤數目。接著， 夺 S 2 0所示，判斷該前t個科 θ 乂驟 值f ς e 刚1個徵兆值疋否為零，若該前t個徵兆 灾，則11零，即表示後七個徵兆值（s⑴〜S2t )亦為 為焚日,士 丁丈迷介阳、、口果，右该刖ΐ個徵兆值並非 々a則繼續進行步驟S4〇，計算後t個徵兆值。 為灾當::Ϊ出的徵兆值Sl〜St為零可推論出徵死值s…〜、 接收到=的當計算出的徵兆值S1不等於零，即表示 則必項^予碼有錯誤存在；發現接收字碼有錯誤存在時， 值來=:找出錯誤位置與錯誤值，此時即可利用該等徵兆 出之^ =出該錯誤值與位置。請參閱第一圖所示，在計算 計曾二31值（Sl〜、）中’利用關鍵方程式解答器1 2可以 (χΓ，4錯誤定位器多項式σ(χ)及錯誤求值器多項式Ω 中計算再利用錢氏搜尋器14於錯誤定位器多項式σ (χ) 器多=4錯誤位置，以及利用錯誤值求值器1 6由錯誤求值 、式Ώ ( X )計算出錯誤值。 另休 ’其你 口- 口丨t決日口八丨儿且丨in' PJ π上迷X抱1夕丨j I 、之計算方式皆與上述内容相同，故於此不再贅5239% on page 5 5. Description of the invention (3) The __ code is like a t-symptom value, where t is the next, then judge whether the first t-symptom value is hot: you can correct the number of errors, · If it is zero, the calculation will be stopped, otherwise the calculation will be continued: if the previous one runs, the specific indication value will be matched with the specific embodiment. Value It is easy to understand the purpose of the present invention, and the macro-type two-type pedestal description in the technology is effective. Features and what they achieve: Description of drawing number: 10 Symptom calculator 12 Key equation solver 14 Qian's searcher 16 Error value evaluator Detailed description: RS code is a digital communication and data storage system error correction code. : A kind of ability. Regardless of the received design: the predicate of t :: is corrected and 2t symptom values are corrected; however, by twisting the wrong block, the relationship must be calculated to infer that when j / ,, " The polynomial coefficient is also zero. From this, we can know that: when it is zero, you can determine that the number of symptom values is ~, t, and you can determine whether your pick code is wrong or not. You only need one kind to solve the problem, Λ code. Λ ... Calculate the sign of the polynomial of the sign C. The processing steps of the received code are: first, all the sisters; the second figure is not used. This method includes the following use-the sign of the calculator, the wrong code of the received code processing 'The first t symptom values (Sl ~ St) when Liye goes out, as shown in step 6 on page 523996. 5. Description of the invention (4) = 0, where t is the number of correctable errors. Then, as shown in S 2 0, determine whether the first t families θ 乂 乂 f ς e has just 1 symptom value 疋 is zero. If the first t symptoms are disasters, then 11 is zero, which means the last seven symptoms. The values (s⑴ ~ S2t) are also for burning the sun, Shidingzhang Mijieyang, and Guoguo. If the value of the sign is not 々a, continue to step S4O, and calculate the value of t signs. For the disaster :: the indication value Sl ~ St of zero is inferred, and the death value s ... ~ can be deduced. When the received indication value S1 is not equal to zero, it means that there must be an error in the prerequisite code; When it is found that there is an error in the received code, the value comes to =: find the error location and error value, and at this time, you can use the signs ^ = to indicate the error value and location. Please refer to the first figure, in the calculation of the two 31 values (Sl ~,) 'Using the key equation solver 12 2 (χΓ, 4 error locator polynomial σ (χ) and error evaluator polynomial Ω The calculation uses the Chan's searcher 14 at the error locator polynomial σ (χ) and the error position is 4 =, and the error value evaluator 16 calculates the error value from the error evaluation and expression Ώ (X). '其 你 口-口 丨 t 定日 口 八 丨 儿 和 丨 in' PJ π 上 上 迷 X 抱 1 夕 丨 j I, the calculation method is the same as the above content, so I will not repeat it here
字螞進彳-」ί發明除了對該些經過錯誤訂正碼處理之接收 與辣除/冲异以得到徵兆值之外，本發明亦可對經過錯誤 錯鴿與Ζ正碼處理之接收字碼進行計算；並可由徵兆值及 〜St為雯日ί定位器多項式係數之關係式推論出當徵兆值S1 就可以lit，表示St + 1〜S2t亦為零’所以僅需要t個徵兆值 誤與抹p；!斷所收到的字碼是否發生錯誤。由於此種經過錯 誤與括t叮正碼處理之接收字碼的計算方式，除了使用錯 外，# 、义位器來計算錯誤位置而不同於上述實施例之The word "Mao Jin"-"In addition to the receiving and processing of the error correction code processing and differentiating / differentiation to get the indication value, the present invention can also It can be deduced from the relationship between the symptom value and ~ St is the polynomial coefficient of the locator polynomial. It can be deduced that the symptom value S1 can be lit, indicating that St + 1 ~ S2t is also zero. p ;! Check whether the received code is wrong. Due to the calculation method of the received word code processed by error and bracketing code, in addition to using the error, # and the positioner are used to calculate the error position, which is different from that in the above embodiment.
Ob. ' 523996 五、發明說明（5) 述。 其中，該前t個徵兆值為零而表示後t個徵兆值亦為零 之結果係由該徵兆值（Si〜s2t )與錯誤定位器多項式係數 (〜)之關係所推導得知者，該徵兆值與錯誤定位器 多項式係數之關係式係如下列所示： q 一 - S+l VS H β Λ H 奉·· · • · · · σί-2 = j u2 …v _-\一 特別要注意的是，此等式僅成立於當實際發生錯誤數目e 小於或等於最大可更正錯誤數目t之際（e^t)。而在里 德-所羅門解碼器（R e e d - S ο 1 〇 m ο n d e c 〇 d e r )的應用中， 本發明所關心的也是當e S t，也就是說發生錯誤數目小於 最大可更正錯誤數目的情況下所進行之錯誤更正動作，換 言之，根據上列等式，本發明可先計算一半的徵兆值；當 徵兆值Si〜St為零時，不論e值是否大於t值，都不再進行 後續之計算，直接設定錯誤值為零。此乃因e = 0時，此時 可以認定Si〜St為零將使得徵兆值St+1 〜S2t必定為零，此種 情況下不需要作任何錯誤更正動作；若e > t時，此時作任Ob. '523996 V. Description of Invention (5). Among them, the result of the first t symptom values being zero and indicating that the next t symptom values are also zero is derived from the relationship between the symptom value (Si ~ s2t) and the error locator polynomial coefficient (~), which The relationship between the symptom value and the polynomial coefficient of the error locator is as follows: q a-S + l VS H β Λ H Bong ·· · · · · · σί-2 = j u2… v _- \ 一 要 要Note that this equation holds only when the actual number of errors e is less than or equal to the maximum number of correctable errors t (e ^ t). In the application of the Reed-Solomon decoder (R eed-S ο 1 〇m ο ndec 〇der), the present invention is also concerned with when e S t, that is, the number of errors that occur is less than the maximum number of correctable errors. In the case of error correction actions, in other words, according to the above equation, the present invention can first calculate half of the symptom value; when the symptom value Si ~ St is zero, no matter whether the e value is greater than the t value, no further follow-up is performed. For calculation, directly set the error value to zero. This is because when e = 0, it can be determined that Si ~ St is zero at this time, and the symptom value St + 1 ~ S2t must be zero. In this case, no error correction action is required; if e > t, this Current job
523996 五、發明說明（6) ί錯誤更正動作都可能將原本對的資料改掉斯 要作任何錯誤更正的動作。 +改掉，所以也不需 由徵兆值與錯誤定位器多項式係 當Sl〜st為零時表示徵兆值s⑴〜、亦為^ : '推論出 要t個徵死值就可以判斷所接收到之字、'、v /、味，僅需 生錯誤。且由於在實際電路運作上，益(8馬）疋否發 率遠遠大於錯誤情況1此所提機夂 J電路在實際運作上的運算量，•而達; = = :降 再者，在大多數的應用當中，平均功 無錯誤狀…在沒有錯誤的情況下，以：，決於 m //u r ，、有徵兆計算哭雲 ®此’本發明所提出之減少一半運算量就可：判 π D吳有無發生之方法，可以有效減低整體如B c η解碼器 (Base-Chaudhuri-Hocquenghem decoder)或里择—所^ 門解碼器之功率消耗。因此，本發明在降低功率^耗之 際’同時兼具有相當高的錯誤偵測與更正能力，以轉保次 料之正確度。 μ貝 以上所述之貝^例僅係為說明本發明之技術思想及特 點’其目的在使熟習此項技藝之人士能夠瞭解本發明之内 容並據以實施，當不能以之限定本發明之專利範圍，即大 凡依本發明所揭示之精神所作之均等變化或修飾，仍應涵 蓋在本發明之專利範圍内。 u523996 V. Description of the Invention (6) The error correction action may change the original pair of data. Any error correction action is required. + Changed, so there is no need to use the symptom value and the error locator polynomial system when Sl ~ st is zero to indicate the symptom value s⑴ ~, which is also ^: 'It can be judged that t sign death values can be received. Words, ', v /, taste, just make mistakes. And because in the actual circuit operation, the benefit rate (8 horses) is much larger than the error case 1. The circuit of J circuit mentioned in the actual operation, the amount of operation, and =; In most applications, there is no error in the average power ... In the case of no error, it is determined by: m // ur, and there are signs to calculate Cry Cloud ® This' half the amount of calculation proposed by the present invention can be: The method of judging the occurrence of π D Wu can effectively reduce the overall power consumption of a decoder such as a B c η decoder (Base-Chaudhuri-Hocquenghem decoder). Therefore, the present invention has a relatively high error detection and correction capability while reducing power consumption, so as to guarantee the accuracy of the secondary material. The above-mentioned examples are merely to explain the technical ideas and characteristics of the present invention. The purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. It should not be used to limit the scope of the present invention. The scope of patents, that is, all equal changes or modifications made in accordance with the spirit disclosed by the present invention, should still be covered by the patent scope of the present invention. u
523996 圖式簡單說明 圖式說明： 第一圖為習知RS碼的解碼過程示意圖。 第二圖為本發明之流程示意圖。 11111 第10頁523996 Brief description of the drawings Description of the drawings: The first picture is a schematic diagram of the decoding process of a conventional RS code. The second figure is a schematic flow chart of the present invention. 11111 Page 10