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TWI334295B - Bit mapping scheme for an ldpc coded 32apsk system - Google Patents

Bit mapping scheme for an ldpc coded 32apsk system Download PDF

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TWI334295B
TWI334295B TW096107913A TW96107913A TWI334295B TW I334295 B TWI334295 B TW I334295B TW 096107913 A TW096107913 A TW 096107913A TW 96107913 A TW96107913 A TW 96107913A TW I334295 B TWI334295 B TW I334295B
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TW200816731A (en
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Juntan Zhang
Jilong Li
Fengwen Sun
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Availink Us Inc
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/25—Error detection or forward error correction by signal space coding, i.e. adding redundancy in the signal constellation, e.g. Trellis Coded Modulation [TCM]
    • H03M13/255—Error detection or forward error correction by signal space coding, i.e. adding redundancy in the signal constellation, e.g. Trellis Coded Modulation [TCM] with Low Density Parity Check [LDPC] codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/3405—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power
    • H04L27/3411—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power reducing the peak to average power ratio or the mean power of the constellation; Arrangements for increasing the shape gain of a signal set
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
    • H03M13/1165—QC-LDPC codes as defined for the digital video broadcasting [DVB] specifications, e.g. DVB-Satellite [DVB-S2]

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Error Detection And Correction (AREA)
  • Detergent Compositions (AREA)
  • Digital Transmission Methods That Use Modulated Carrier Waves (AREA)

Description

133.4295 九、發明說明： 【發明所屬之技術領域】 本發明涉及數位通信’且具體地涉及用於LDPC編碼的 32APSK系統的位元映射方法。 【先前技術】 通信系統使用前向差錯控制（Forward Error Control，FEC )編 碼以保證資料經雜訊通信通道的可靠傳輸。基於香農（shannon) 的理論，這些通信通道在球定的信號雜訊比（Signal to Noise Ratio , SNR)下具有以位元每符碼（symbol)表示的確定的容量，這被 定義為香農限（Shannon limit)。通信和編碼理論中研究領域之一 涉及以合理的複雜度設計提供逼近香農限性能的編碼方法。已經 表明，使用置信傳播（Belief Propagation，BP)解碼的低密度奇偶 校驗碼(Low Density Parity Check Code, LDPC)具有可控的編碼和 解碼複雜度，並能提供接近香農限的性能。 在最近Yan Li和William Ryan所著，發表於IEEE Communications Letters，vol. 9，no. 1，January 2005 的 “Bit-Reliability Mapping in LDPC-Codes Modulation systems” (LDPC碼調變系統中的位元可靠性映射）的論文中，作者研究 了具有8PSK的LDPC編碼的調變系統的性能。通過作者提出的 位元可靠性映射策略’實現了超過非交錯方案（n〇n_intedeaving scheme)大約0_15 dB的性能改進。而且作者還表明，格雷映射 比其他映射方法，比如自然映射，更加適於高階調變。 【發明内容】 、本發明的多種實施例涉及32APSK調變系統中的位元映射^ 法。這些實施例的技術特別適合於與LDPC碼一起使用。、 (LDm:種^於32apsk調變系統中低密度奇偶校厚 (LDPC)、、扁碼位π的位χ映射方法^所公開的位元映射方法提$ 133.4295 LDPC碼的良好門檻值。另外，位元映射方法能夠促進32APSK 調變系統中交錯設置的設計。 為提出用於LDPC編碼的32APSK系統的位元映射方法。所 公開的位元映射為LDPC編碼的32APSK系統提供良好性能，且 簡化32APSK系統中的交錯設置。 &、、,根據^發明的多種實施例，一種數位通信系統包括：發射器， 發送數位信號；其中該數位信號利用具有FEc編碼的32APSK系
，，且使用格雷映射位元映射該信號，且基於來自通信通道的對 數似然比的值對該數位信號的位元排序。 ，FEC碼是規貝丨J LDPC碼。-’ FEC碼是非規則LDPC碼。 ’ FEC碼是規則重複累積碼。 ’ FEC碼是非規則重複累積碼。 根據本發明的多種實施例 根據本發明的多種實施例 根據本發明的多種實施例 根據本發明的多種實施例 【實施方式】 示你附圖：其提供根據本發明多種實施例的使用LDPC碼的 Jr生、扁碼位元映射方法的詳細描述。 在發明是通過LDPC碼描述的，但是應該認識到可同樣 碼季使用該位元映射方法。另外，應該理解，可以在非編 1示統中貫現該方法。 常逼!在6〇年代首先描述了 LDPC碼。LDPC碼的性能非 碼由限。具有碼長度N和維度尺的（N，K)二進位1^1^ 元素N-列的奇偶校驗矩陣Η定義。矩陣Η的大多數 行表、數兀素是一，因此矩陣Η是稀疏的。矩陣Η的每 所描’而每列表示變數，例如，位元或符碼。Manager 的行重碼是關的，也就是，奇偶校驗祕^有恒定 133.4295 規則LDPC碼能夠擴展形成非規則LDPC碼，其中行重和列 重是變化的。非規則LDPC碼由分別定義變數和校驗.節點度分佈 的度分佈多項式（degree distribution polynomial) v(x)和 c(x)指定。 更加具體地說’非規則LDPC碼可以定義如下： 和
ν(χ)
(2) 其中變數^vmax和尤max分別是最大變數節點度和校驗節點 度’且v;.(c;)表示從度j的變數（校驗）節點發出的邊（)的 分數（fraction)/雖然非規則LDPC碼在表示和/或實現上比規則 LDPC碼更加複雜，但是理論上和經驗上都表明，具有適當選擇 的度分佈的非規則LDPC碼優於規則LDPC碼。〃圖1說明了編石今 ^codeword) 如果位元 的。通常’假定-對節點以υ:為匕們是鄰近或相_ 圖2說明了如圖i所示的非規則LDPC碼的二分圖表示。 二雖=於奇偶校驗矩陣中具有相對高的列 DPC碼（例如，歐幾里彳__和投影 133.4295 數邏輯解碼需要最小的複 迭代解碼方法因為它們更杯二且貝現相當不錯的差錯性 到了更多的關注。不闭认々f性能對複雜度取捨（tradeo
到了更多的關注。不同= f複雜度取捨（tradeoffs) 的約束條件，通過對所接收，，迭代解碼基於定義碼型 靠性。在第一次迭代尹，二f = 3痛處理來提高每個符碼的可 並對每個符碼產生可靠性輸出。碼益僅使用通道輸出作為輸入， 性度量結寺對解碼符碼輸出的可靠 結束，之後基於來自最後迭代直到滿足停止條件時 作出崙诒、五—,θ^5久送代的解碼符碼輸出的可靠性度詈 iiii^S〇fldeCiSi〇n) (hybrid decision) „ ## (BP) (weighted bit-flipping, WBF) ^ J ； ΐί 當相應的⑽打圖是非迴圈時，BP演算法能夠 貫見取大似;、、〈、解碼，因而其成為最流行的解碼方法。 ^DPC碼的BP是一種資訊傳遞解碼（message passing jco mg)。沿著圖的邊發送的資訊是和對應於編碼字位元的變數 ^點相巧聯的對數似然比（log-likelihood ratio, LLR) log也。在 $個運具式中，凡和几分別表示相關位元值是〇或〗的機晕。Bp ，碼通常，括兩個步驟，水平步驟和垂直步驟。在水平步驟中， 每個校驗^點Cm將基於除了來自位元匕外所有進入校驗q的“位 元到校驗’’ （bit-to-check)資訊計算而得的“校驗到位元” (check-to-bit)資訊’發送到相鄰節點匕。在垂直步驟中，每個 位元節點，^將基於除了來自校驗節點〜外所有進入位元匕的“校 驗到^元資訊計算而得的“位元到校驗”資訊，發送到相鄰的 校驗節點C(n。重複這兩個步驟直到找到可用的編碼字或達到最大 的迭代次數。 因為p其利用BP解碼的顯著性能，非規則LDPC碼對於很多 應用是最好的選擇之一。對於多種通信和存儲標準，比如 1334295 DVB-S2/DAB，有線線路 ADSL，IEEE802.11n 和 IEEE802.16 等， 已經採用或正在考慮··採t用多種非規則ldpc碼。 LDPC碼的門檻值（threshold)被定義為最小SNR值，在該 值下當編碼子長度趨於無窮時，能夠使位元差錯機率任意小。 LDPC碼門檻值的數值能夠由被稱為密度演化的分析工具確~定。 密度演化的概念也能夠回溯到Gallager的結果。為確定BF 解碼的性能，Gallager推導了作為在迭代開始時的輸入位元錯誤 率(Bit Error Rate, BER)的函數’每次迭代的輸出BER的計算公 式，進而可迭代地計算出在給定迭代次數處的BER。對於連續的 字元表（alphabet)，計算更加複雜。需要逐次計算出在位元和校 驗節點之間交換的置信信息的機率密度函數（pdf)，再基於這些 pdf f出每次迭代的平均BER。在校驗節點處理和位元節點處^ 中，每個出向置信息（outgoing belief message)是入向置信作·、 (incoming belief messages)的函數。對於度《的校驗節點，‘二 出向資訊能夠由4—1個入向資訊的函數表示， U = K(',V2，…,Vdy) 其中，K表示從BP解碼確定的校驗節點處理函數。類似 對於度4的位元節點，每個出向資訊r能夠由個入向 、、’ 道置彳§ ^訊的函數表示， 、 通
V 其中，6表示位元節點處理函數。雖然對於校驗和 處理，對於給定解碼演算法，可以基於入向資訊的pdf =黑 貧訊j pdf，但是存在指數級的大量的入向資訊的可能形出# 此，密度演化處理看起來很難。幸運的是，已經證明，二 資訊傳遞演算法和雜訊通道，如果滿足一些對稱條件’声： BER獨立於發送序列，。也就是說，基於對稱假定，全 列χ = ι的解碼BER和任意隨機選擇的序列的相同，因此能& 1334295 硬化的推導。高效密度演化所需的對稱條件是通道對 H aBL:輯稱和位元節崎稱。密度演化W，假歧Tanner 圖疋非迴圈（cyclic free)的。 田苎亡疋，到位元和校驗節點的入向資訊是獨立的，且 新夕Τηρί著簡化出向資訊的pdf的推導。對於具有實際作用的 ^雙碼，相應的Ta職圖包括迴圈1 LDPC碼的丁3崎 ΐΐΐΐ或圍長（帥10)的最小長度等於4x1時，那麼在利用 &定、二!時t第1個解碼迭代之後獨立假定不成立。但是，對 杜込ΐ數，s碼長度增加時，對於增加的迭代數能夠滿足獨 所^ “、2,此’密度演化可以預測一組LDPC碼的漸近性能，且 所明漸近特性需就碼長度的意義而言。 rnpr圖^ ί根據本發明的多種實施例，採用具有32APSK調變的 sm吝信系統的示例圖。通信系統包括發射器501，發射器 號波形經通信通道502到接收器503。發射器501包i 生離散的一組可能的資訊的資訊源。這些資訊均對應於一 ΐΐίϊ 5被雜訊破壞。採用ldpc碼以減
編碼的位元轉換為錢^形且㈣32魏調變方法以將LDPC 用LD圖圖5的通信系統中的示例性發射器，該發射器採 的資句你馬和iPSK調變。LDPC編碼器602將來自資訊源6〇1 4字的映字。從每個資訊塊到每個LDpc編 ^子射由LDPC碼的奇偶校驗矩陣（或等效的生成矩陣 U 2 /調變器6〇3基於32APSK位元映射方法將LDPC編 並ϋίΪΞ變為信號波形。這些信號波形被發送到發射天線_ I傳播到如圖7所示的接收器。 和5 Ιϊΐ例性接收器，該接收器採用[腦碼 创站·^ 解調為。由接收天線701接收信號波形，並將豆分於 ^調⑸解交錯器702。由解調器解調並由解交錯器解交^信^ 《n將其分發到迭代地解碼接收到的消息的咖。解碼器u ，亚輸出對發送的編碼字的估計。解調器/解交錯器702採用 1334295 的32APSK解調規則應該和交 變規則匹配。 乂錯裔/凋變器603採用的32APSK調 . ' * ^ 碼映種實施例’如圖3所示’ 32APSK位元到符 b5i+4^=^f作可以使駐個位'元賊 b5i+1，b5i+2, b5i+3, 射丄映f到1值和Q值，其中… '、根據本發明多種實施例的位元映射定義如下： 13-34295 (i?2 cos〇r / 4),及2 sin〇 / 4)), (b5i, b5l+x, b5i+2, b5M, b5i+,) = (0,0,0,0,0) (R2 cos{kI\2),R2 sin(^-/12)), (b5i,b5M,b5i+2,b5M,&5i+4) = (0,0,0,0,1) (i?3 cos(n/S),R3 sin(^·/8)), (^5, > bsi+\ ^ b5i+2, b5i+i, b5i+i) = (0,0,0,1,0) (R3,0), (b5i, b5j+1, b5j+2, bSj+3, b5j+4) = (0,0,0,1,1) (i?2 sin(;r /12)，i?2 cos〇 /12))，(b5l, b5M, b5i+2, b5i+3, b5l+4) = (0,0,1,0,0) (孕 cos(;r / 4)，昇 sin〇 / 4)), (b5i, b5l+i, b5i+2, b5i+3, b5l+4) = (0,0,1,0,1) (/?3 sin(;r / 8)，i?3 cos(?r / 8))， (bSi, b5M, b5i+2, b5M, b5M) = (0,0,1,1,0) (R3 cos(^/4),i?3 sin(^/4)), (b5i, b5M, b5i+2, b5i+3, b5i+4) = (0,0,1,1,1) (R2 cos(^/4),-i?2 sin(^·/4)), (b5i, b5M, b5i+2, b5l+3, b5l+4) = (0,1,0,0,0) (i?2 cos〇/12)，-i?2 sin(7r/12))，(b5i, b5M, b5i+2, b5i+3, b5i+4) = (0,1,0,0,1) (R3 cos(k/4),-R, sin(^·/4)), (b5i, b5M, b5i+2, b5M, b5i+A) = (0,1,0,1,0) (T?3 cos〇 / 8)，-及3 sin(;r / 8))， (b5i, b5l+l, b5i+2, b5i+3, b5i+4) = (0,1,0,1,1)
(R2 sm(nI\2)-R2 cos(^·/12)), (b5l,b5M,b5i+2,b5i+3,b5i+i) = (0,1,1,0,0) (孕 cos〇r / 4)，-& sin〇 / 4))， (b5i, b5M, b5l+2, b5M, b5i+4) = (0,1,1,0,1) (0-^)= (h / 5 ^5(+15 ^5/+2 5 ^5/+3 5 ^5/+4 =(0,1,1,1,0) (/(〇,0(〇) =
,(Λ3 sin〇 / 8)，-/?3 cos(;r / 8))， (b5i; b5i+l, b5i+2, b5i+i, b5i+A) = (0,1,1,1,1) (~R2 cos{n!A),R2 sin(^/4)), (b5i, b5i+i, b5l+2, b5i+i, b5M ) = (1,0,0,0,0) (-晃 cos〇r /12)，尽 sin〇 /12))，(b5i, b5M, b5i+2, b5l+3, b5l+,) = (1,0,0,0,1) (~R3 cos(^/4),7?3 sin(^·/4)), (b5i, b5M, b5i+2, , b5M) = (1,0,0,1,0) (-i?3 cos(tt / 8), i?3 sin〇 / 8))， (b5i, b5M, b5i+2, b5i+3, b5i+4) = (1,0,0,1,1) (-R2 sm^/\2),R2 cos(^·/12)), (b5i,b5l+],b5l+2,b5l+3,biM) = (1,0,1,0,0) (-& cos(tt / 4)，7?, sin(;r / 4))， (b5i, b5M, b5i+2, b5l+3, b5l+,) = (1,0,1,0,1) (0, R3), (b5i, b5i+l, b5i+2, b5i+3, b5i+i) = (1,0,1,1^0) (-i?3 sin〇 / 8)，i?3 cos(tt / 8))， (b5i, b5i+], b5l+2, bSM, b5l+4) = (1,0,1,1,1) (-i?2 cos(;r / 4)，-i?2 sin〇 / 4)), (b5i, b5M, b5l+2, b5l+i, b5l+i) = (1,1,0,0,0) (-晃 cos(；r /12)，-i?2 sin(;r /12))，（Z?5i, U5,_+2，U5(>4) = (1，1，0,0，1) (-R, cos(^/8),~/?3 sin(^-/8)), (b5i, b5M, b5l+2, b5l+3, b5i+4) = (1,1,0,1,0) (—J?3,0), (b5j, b5l+x, b5j+2, bii+i, b5i+4) = (1,1,0,1,1) (-R2 sin(^-/12)-i?2 cos(^·/12)), (b5i,b5i+],b5i+2,b5l+i,b5i+A) = (l,U,〇,〇) (-Rx cos(^-/4),-i?, sin(^/4)), (b5i, b5l+l, bil+2, b5M, b5i+4) = (1,1,1,0,1) (~R3 sin(^/8),-i?3 cos(^·/8)), (b5l, b5M, b5l+2, b5M, b5M) = (1,1,1,1,0) (-i?3 cos〇r / 4),-i?3 sin(7r / 4))， {b5i, b5M, b5l+2, b5M, b5i+A) = (1,1,1,1,1) 其中，R1是内環的半徑，R2是中間環的半徑，而R3是外環 的半徑。 根據本發明的多種實施例，圖4的位元映射方法可使用格雷 映射，這意味著相鄰點的二進位表示僅有一個位元不同。密度演 化分析表明，給定LDPC編碼的32APSK系統，格雷映射方法能
< S 12 3.3420 夠提供最好的門檻值。圖
道的對數似然比的值_ =70映射方法還以气於來自通信通 系統的交錯方法的設計。、來排列位兀。這種處理簡化了 32APSK 在本本發明，但是應該理解 發明申請專利範圍的改。因此，本 中的這些修改和變更。疋覆盍所有在本發明的真正精神和範圍 【圖式簡單說明】 圖 表示； 疋碼字長度六的示例性非規則LDPC碼的奇偶校驗矩陣 圖2 =明了如圖1所示的非規則LDPC碼的二分圖表示； 位元發明的多種實施例，在32題調變中的 位元明了根據本發明的多種實施例，用於32APSK符碼的 了根據本發明的多種實施例，採用LDPC碼和 32APSK 5胃&的不例性通信系統； 調變Γ二Si本Γ月的多種實施例’採用圖5中的32APSK 調變S = 本發明的多種實施例’採用圖5中的32概 【主要元件符號說明】 發射器501 通信通道502 接收器503 資訊源601 . 13 (£ > 133.4295 LDPC編碼器602 '交錯器/調變器603 發射天線604 天線701 解調器/解交錯器702 LDPC解碼器703

Claims (1)

133.4295 十、申請專利範圍： • / 1、一種32APSK系統中位元映射的方法，該方法包括： 從發射器發送數位信號；和 在接收器接收該數位信號， 其中該數位信號利用32APSK系統，且在發送之前根 據下面公式位元映射該信號： (R2 cos(^· / 4), R2 sin(^· / 4)), (R2 cos(^· /12), R2 sin(^· /12)), (T?3 cos(^ / 8), R3 sin(^· / 8)); 汎，〇)， (R2 sin(^· /12), R2 cos(^· /12))s (7?! cos(^· / 4), ^ sin(^· / 4)), (尺3 sin(;r/8),7?3 cos(;r/8))， (穴3 cos(;z7 4),穴3 sin(;r / 4))， (T?2 cos(^/4)-T?2 sin(^·/4)), (i^2 cos(^/12);-7?2 sin(^·/12)), cos(W4)，-i?3 sin(;r/4))， (尺3 cos(;r/8)，一及3 sin(;r/8))， (片2 sinh/l〗),-/^ cos(;z712)), (^, cos(^/4)5-^, sin(^·/4)), (R2 sin(^/8),-7?3 cos(^/8)), (~R2 cos(^ / 4). R2 sin(^r / 4)), (-7?2 cos(^· /12), sin(^· /12)). (-Λ3 cos(;r / 4),穴3 sin(;r / 4)), (-穴3 cos(;t/8)，_/?3 sin(;r/8))， (-R2 sin(^-/12);R2 cos(^/12)). (-7?, cos(^ / 4), 7?! sin(^· / 4)), (〇,晃)， (-i?3 sin(^· / 8), cos(^· / 8)), (-及2 cos(;r/4)，_/?2 sin(;r/4))， (-T?2 cos(^· /12),-/?2 sin(^·/12)), (-T?3 cos(^r / 8),-/^3 sin(^/8))s (-'〇)， (~R2 sm^/\2)-R2 cos(^/12)), (-% cos(;r / 4)，-& sin(;r / 4))， (-7¾ sin(7r/8)，-T?3 cos(;r/8))， (-^3 cos(^/4);-^3 sin(^/4)X (/(0,6(0) =
(办5, = \+l，办5i+2，办5/+3，^5/+4 ) = (〇,〇,〇,〇,〇) (〜，〜+1，厶5i+2，厶5/+3，办5/+4 ) = (〇,〇,〇,〇，l) (厶5，，办5，+1，\+2=厶5|+3，办5/+4) = (〇,〇,〇，1，〇) (办5i，办5/+1，\+2，\+3，&5,+4 ) : (〇,〇,〇=1，0 05,，U5,+2，\+3 Α+4) = (〇,〇丄〇,〇) (¾ A+l A+2 A+3 , U = (0,0，1，0,1) (b5nb5i+lib5i+2,bSi+3,b5i+4) = (〇AU,〇) (办5ι，办5/+1，办5ί+2，办5|+3，\+4 ) = (〇?〇，1，1，1) (办5,，办5ί+1，办5ΐ+2，办5，+3，办5Ϊ+4 ) = (〇山〇,〇,〇) (b5i; b5i+x, b5u2, bSi+3, b5i+4) = (0,1,0,0,1) (i5l.; b5i+l, b5i+2; Z?3,.+3 ? b5i+4) = (05L0;L0) (办5,，办5i+l，65/+2，&5，.+3，&5，、4 ) = (〇，1，〇，1，1) (办5i，办 5/+1，\+2，办5/+3，^+4 )二(〇-·1，1，〇,〇) (办5/，办5ί+1』5ί+2，办5/+3，&5ί+4 ) = (〇，1，1，〇，1) (\，U5,+2，D5,+4)= (〇，ι,ι，ι，〇) (厶5,-，厶5;.+1，厶 5i+2，办5i+3，厶 5i+4 ) = (〇W) (b5i, b5i+l, b5i+2, b5i+3, b5i+A) = (10,0,0,0) (办5i，办5/+1 =厶5/+2，办5i+3，办5/+4 ) = (l，〇,〇=〇，l) (办5i，办5/+1，办5i+2,办5i+3,办5i+4) z (l，〇,〇，l，〇) (办5,，厶5>+1，办51+2，厶5卜3，厶5，+4) = (1，〇,〇，1，” (\，办5/+1，办5“2，办5>+3，办5/+4) = (1，〇，1，〇,〇) (〜，办5/+1，办5ι>2，办5,+3 =办5/+4 ) = (1，〇，1，〇，1) (厶5，，厶5/+1，办5ί+2,厶5 1+3 5 05,+4) = (1，0，1，1，0) (办5,，办5ί+1，办5,+2，〜+3，办5|+4 ) = (1，〇，1山1) d 办5，+1，厶5ί+2，厶5，+3,厶5，+4) = (1山〇,〇!〇) (办5ι，厶5ί+1，厶5，+2，厶5ί+3，办5ί+4 ) = (1，1，〇,〇，1) (办5,，办5ί+1』5/+2，&5ί+3，&5ί+4 ) = Ο丄〇，1，〇) (〜人+1 Α+2，，心+4 ) = (U，0，1,1) 队 A+1Α+2 Aw Α+4) = (W，0,0) (办5"办5j+l Ai+2，办5!-+3，\+4 ) _ Ο丄 1，〇，1) (〜，厶5ι+1，厶5，+2，厶5/+3，〜+4 ) = (1，1丄1，〇) (^5/ > ^5/+1 = ^5/+2 »^5/+3 ,i5/+4) = (iuu) 其中，R1是内環的半徑，R2是中間環的半徑，而R3 是外環的半徑。 15 133.4295 2、 如申請專利範圍第1項所述之32APSK系統中位元映射的方 法，其中該系統使用FEC碼。 . - 3、 一種數位通信系統，包括： 發送數位信號的發射器； 其中，該數位信號利用具有FEC編碼的32APSK系 統，且使用格雷映射來位元映射該信號，並且基於來自通 信通道的對數似然比的值對該數位信號的位元排序。
4、 如申請專利範圍第3項所述之數位通信系統，其中，該FEC 碼是規則LDPC瑪。 5、 如申請專利範圍第3項所述之數位通信系統，其中，該FEC 碼是非規則LDPC碼。 6、 如申請專利範圍第3項所述之數位通信系統，其中，該FEC 碼是規則重複累積碼。 7、 如申請專利範圍第3項所述之數位通信系統，其中，該FEC 碼是非規則重複累積碼。 8、 一種數位通信系統，包括： 發射器，對於卜0, 1,2, ....，基於下面公式將至少一個 五位元(b5i，b5i+l，b5i+2, b5i+3, b5i+4)的映射組調變為 32APSK 符碼（symbols ): 16 133.4295 (i?2 cos(7T / 4)，i?2 sin〇 / 4)), (bSi, bSi+l, b5t+2, bSi+3, bSi+4) = (0,0,0,0,0) (i?2 cos〇 /12)，sin(;r /12)), (b5i, b5i+l, b5i+2, b5M, bSi+A) (0,0,0,0,1) (/?3 cos〇 / 8)，/?3 sin(;r / 8)), (b5i, biM, biM, b5M, b5i+4) = (0,0,0,1,0) (及3，〇)， (K, b5M, bSi+2, bSM, b5l+4) - (0,0,0,1,1) (R2 sin(^· /12), R2 ο〇ζ(π /12)), (bSi, b5M, b5i+2, b5M, bii+A) = (0,0,1,0,0) cos〇 / 4)，尺 sin〇 / 4))， (bSi, bSM, bSi+2, bSM, b5M ) = (0,0,1,0,1) (i?3 5ΰι(π/8)，Λ3 cos(W8))， (bif,b5M,b5i+2,b5M,b5M) = (0,0,1,1,0) (/?3 cos(?r / 4)，sink / 4))， (b5i, bSM, bSl+2, b5i+}, b5i+A) = (0,0,1,1,1) (R2 cos(z/4),-R2 sin(^·/4)), (bSi, b5M, bSi+2, b5M, bSi+A) = (0,1,0,0,0) (R2 cos{n!\2)-R2 sin(^/12)), (bSi,b5M,bSi+2,bSi+3,b5i+4) = (0,1,0,0,1) (R3 cos(^·/4),-^ sin(^·/4)), (b5i, b5M, έ5ί+2, b5M, b}M) - (0,1,0,1,0) (R, cos(^·/8)-^3 sin(^·/8)), (bSi, bSM, bSi+2, b5M, bSi+A) - (0,1,0,1,1) (i?2 sin〇 /12),-i?2 cos(7r /12)), (b5i, bSi+], bSi+2, bSM, bsl+A) = (0,1,1,0,0)
(A cos(tt/4),-尺 sin〇r/4))， (binbSM,b5i+1,biM,bSi+,) = (0,1,1,0,1) (〇，-及3 )， （H】，U5w, U = (0，1，1，1，0) (/?3 sin(;r / 8)，-/?3 cos(7r / 8))， (b5i, bSM, bSi+2, biM, b5i+4) = (0,1,1,1,1) (~R2 cos(^- / 4), R2 sin(^· / 4)), (bSj, b5M, b5i+2, b}M, b5i+4) = (1,0,0,0,0) (-R2 cos(^· /12), R2 sin(«- /12)), (bSf, bSi+l, bSi+2, b5i+3, b5i+A) = (1,0,0,0,1) (-/?3 cos〇 / 4)，i?3 sin〇 / 4)), (bSi, bSM, b5i+2, bSM, bSi+A) = (1,0,0,1,0) (-cos〇 / 8)，sin(;r / 8)), (bSi, b5M, bs/+2, bSM, bSl+4) = (1,0,0,1,1) (-i?2 sin〇 /12)，i?2 cos(tt /12))，(b5i, b5i+l, b5i+2, b5M, b5i+4) = (l,0,l,〇,〇) (-Λ, cos(^/4),i?, sin(^/4)), (bSi, bSM, b5i+1, b5M, bSi+4) = (1,0,1,0,1) (〇,及3 )， (K，bSi+l, bii+2, b5M, b5i+4) = (1,0,1,1,0) (-尽 sin(；T/8),cos(tt/8)), (bsnbiM,b5i+2,bSi+3,b5i+A) = (1,0,U4) (-/?2 cos〇 / 4),-/?2 sin〇 / 4)), {b5i, bSM, bSi+2, biM, ) = (1,1,0,0,0) (-R2 cos(^· /12),-R2 sin(^· /12)), (bSi, b5i+l, b5l+2, bSj+3, bSi+A) = (1,1,0,0,1) (-i?3 cos〇 / 8)，-i?3 sin〇 / 8)), (ό5/, bim, bii+2, b5i+3, bSl+A) = (1,1,0,1,0) (-/?3，0)， (bSl, bSM, bii+2, bSM, b}i+A) = (1,1,0,1,1)
(-R2 sin(^/12),-/?2 cos(^·/12)), (b5i, bim, b5i+2, biM, biM) = (1,1,1,0,0) (-Λ, cos(^·/4),-^, sin(^·/4)), (bSi, biM, bii+2, biM, biM) - (1,1,1,0,1) (-i?3 sin(7T / 8)，-/?3 cos〇 / 8)), (b5i, b5M, bSi+2, biM, bSi+4) = (1,1,1,1,0) (-i?3 cos〇 / 4)，-J?3 sin〇 / 4))， (bSi, b5i+i, b5i+2, b5M, biM ) = (1,1,1,1,1) 其中，R1是内環的半徑，R2是中間環的半徑，而R3 是外環的半徑。 9、一種數位通信系統，包括： 接收器，其對於i=〇, 1,2, ....，基於下面32APSK定義 將至少一個映射後的32APSK符碼解調為五位元（b5i， b5i+l，b5i+2, b5i+3, b5i+4)的信息組估值： (£ 17 1334295 (R2 cos(^·/4),R2 sin(^·/4)), (b^,b5M,b5i.2,b5M,b5i+4) = (0,0,0,0,0) (R2 cos(^·/12),Λ2 sin(^·/12)), (i5,, 65,+1, bii+2, ί)5ί+3,65i+4) = (0,0,0,0,1) (^3cos(^/8),/?3 sin(^·/8)), (b5i, b5M, 65i+2, bSM, bii+i) = (0,0,0,1,0) (λ3 ,0), (65i, 65i+1, ft5i+2, ί>5,·+3,65,.+4) = (0,0,0,1,1) (R2 sin(^- /12), Λ2 cos(^· /12)), (65i，U5,.+2, U5,-+4) = (0,0,1,0,0) (Λ, cos(^/4),/f,sin(^/4)), (.bSi,b5l+],b5i+2,bSM,b5M) = (0,0,1,0,1) (Λ3 sin(7r/8)，_R3 cos(?r/8))， (b5i,biM,b5i+1,bSM,b5l+A) = (0,0,1,1,0) (Λ3 cos(;r / 4)，/?3 sin(;r / 4)), (b5i, b5i+l, b5i+2, b5M, bSi+i) = (0,0,1,1,1) (R2 cos(^/4),-Λ2 sin(^·/4)), (bs,, bSM, b5M, bSM, t5i+4) = (0,1,0,0,0) (R2 cos(^/12)-T?2 sin(^·/12)), (bSi, biM, b5i+2, bSM, ό5ί+4) = (0,1,0,0,1) (R3 cos(^/4),-/?3 sin(^r/4)), (b5i, b}M, b5M, b5M, b5i+4) = (0,1,0,1,0) (Λ3 cos(tt / 8)，-Λ3 sin(;r / 8)), (b5f, bSi+l, b5i+2, b5M, b5l+i) = (0,1,0,1,1) (R2 sin(^/12),-^2 cos(^·/12)), (b5i,b5M,b}i+2,b5M,b5i+A) = (0,1,1,0,0) (Λ】cos〇r/4)，-·/?】 sin〇r/4)), (bSi,biM,bSi+2,b5i+3,bil+4) = (0,1,1,0,1) (〇，—穴3 )， （办5i，办5i+l，办5/+2，&5i+3，办5i+4 ) = (〇，l，l，l，〇)
(/(Ο,β(Ο)=
(Λ3 sin〇78)，-i?3 cos〇r/8))， (b5i,b5M, bSM,bSM,bSi+,) = (0,1,1,1,1) (~R2 οο%{π I A), R2 sin(^·/4)), (bSi, b5M, b5i+2, bs.+3, b5i+A) = (1,0,0,0,0) (-R2 cos(^/12),i?2 sin(^/12)), (bSi, b5M, b5：+2, b5l+}, bSM) = (1,0,0,0,1) (-R3 cos(^/4),7?3 sin(^·/4)), {b5i, bSM, bSM, b5i+3, bii+A) = (1,0,0,1,0) (-R} cos(^/8),/?3 sin(^·/8)), (b5i, biM, bii+2, biM, biM) = (1,0,0,1,1) (-R2 sin(^·/12),Λ2 cos(^·/12)), (b5i, b5M, b5i+2, biM, i5/+4) = (1,0,1,0,0) (-/?, cos(;r / 4)，苹 sin(;r / 4)), {bSi, biM, bSi+2, b5M, b5i+4) = (1,0,1,0,1) (〇,穴3 )， （&5i，办5/+1，&5i+2，办5|.+3，办5'.+4 ) = (1，〇，1，1，〇) (—-^3 sin(;r /8),/^3 cos(tt/8)), (bSj, biM, bSj+2, bii+i, bii+i) = (1,0,1,1,1) (-R2 cos(^/4),-Λ2 sin(^·/4)), (b5l, b5M, bii+1, bSj+3, b5i+4) = (1,1,0,0,0) (-Λ2 cos〇/12)，-/?2 sin〇r/12))，(bs,,bil+l,b5l+2,bSi+3,bSi+,) = (1,1,0,0,1) (-R3 cos(^·/8),-^3 sin(^·/8)), (bSl, bSM, bil+2, bSl+3, bSl+,) = (1,1,0,1,0) (—T?3,0), (bSi, bSM, bij+1, bSi+}, bSi+A) = (1,1,0,1,1) (-R2 sin(^/12),-Λ2 cos(^·/12)), (b5i, biM, b5i+2, b5M, b5i+4) = (1,1,1,0,0) (-Λ, cos(^/4)-/?, sin(^·/4)), (bSi, bSM, biM, bSM, bSi+4) = (1,1,1,0,1) (-i?3 sin(^·/8)-^3 cos(^/8)), (bSi, biM, bSl+2, bSi+3, bSi+A) = (1,1,1,1,0) (-R} cos(^/4)-^3 sin(^·/4)), (bSi, biM, bSM, bSi+), bSi+A) = (1,1,1,1,1) 其中，R1是内環的半徑，R2是中間環的半徑，而R3 是外環的半徑。 10、一種存儲電腦程式的電腦可讀媒體，該電腦程式對i=0，1， 2，....，基於下面公式將至少一個五位元(b5i，b5i+l，b5i+2, b5i+3, b5i+4)組映射為 32APSK 符碼（symbol): 18 133.4295 (办5i 5 办5/+丨，办5(+2，办5，+3，办5/+4 ) = (〇,〇,〇,〇,〇) (^5/5 ^5/+] 5 ^5i+2 5 ^5/+3 5 ^5/+4) ^ (〇5〇3〇?〇5〇 (b5i，bSi+、，b5i+2，b5j+3，b5i+4 ) = (0,0,0,1,0) (△5,，方5/+1，办5/+2，办5，+3，&S/+4 ) = (〇,〇,〇，l，l) (P5i，bSi+'，b5i+2，b5U3，b5i+4 )=(0,0,1,0,0) (Jhi，b5i+'，bSl+2，bSi+3，bSi+4 ) = (0,0,1,0,1) ibsi，bSi+'，bSi+2，b5i+3，b5i+4 ) = (0,0,1,1,0)
(/0),2(0) =
(R2 cos(^ / 4), R2 sin(^r / 4)), (T?2 cos(^· /12), Λ2 sin(^· /12)), (Λ3 cos(^· / 8), i?3 sin(^· / 8)), (&，〇)， (T?2 sin(^/12)5/?2 cos(^/12)), (7?! cos(^/4)57?! sin(^/4))5 (R3 sin(^/8)5J?3 cos(^/8)X (T?3 cos(^/4)s7?3 sin(^·/4)), (R2 cos(^ / 4)5-7?2 sin(^- / 4)), (T?2 cos(;t/12)，-/?2 sin(;r/12))， (T?3 cos(^/4)5-i?3 sin(^-/4)), (T?3 cos(^/8)s-7?3 sin(^·/8)), :(R2 sin(^/12)5-i?2 cos(^-/12)), (i?, cos(^· / 4);-7?, sin(^ / 4)), (0,—矣）， (R3 sin(a / 8)，-Λ3 cos(jt / 8))， (-i?2 cos(;r / 4)，疋 sin(;r / 4)), (-i?2 cos(^/12)57?2 sin(^/12))5 (-i?3 cos(^/4),7?3 sin(^·/4)), (~R2 cos(^/8);7?3 sin(^·/8)), (-i?2 sin(^/12);7?2 cos(^·/12)), cos(;r/4)，7?] sin(;r/4))， (0,^3 )5 (-i?3 sin(^/8)5i?3 cos(^/8)), (-T?2 cos(^ / 4),-7?2 sin(^/4))5 (-i?2 cos(^/12),-i?2 sin(^·/12)), (-i?3 cos(^/8),-7?3 sin(^·/8)), (-〜〇), (~R2 sin(^·/12);-Λ2 cos(^/12))5 (-7?, cos(^ / sin(^/4)), (-i?3 sin(^/8),-7?3 cos(^·/8)), (-T?3 cos(^·/4),-Λ3 sin(^·/4)), (办5/，&5i+l，办5;+2，办Si+3，办5i+4 ) = (〇,〇，l，l，l) (办5,，^5/+1，^5/+2，^5/+3，^5/+4 ) = (〇，l，〇,〇,〇) (办5/ s 办5/.丨，办5'+2，办S“3，厶S，+4 ) = (〇，1，〇,〇，1) (办5,，办5/+1，办5，+2，办5，+3，〜+4 ) = (〇，1，〇，1，〇) (办5/，办5/+丨，厶5/+2, ^5/+3 5 ^5/+4 ) = (0,1,0,1,1) (办5/，办5，+丨，厶5，+2，办5/+3，办5/+4 ) = (〇，1，1，〇,〇) (^5/ 5 ^5i+l 5 ^5/+2 5 ^5/+3 ? ^5/+4 ) = (OJJjOJ) (办5/，办5>+1，办5/+2，办5,十3，办5“4 ) = (〇山1，1，〇) (办5/，》5ί+1，\+2，办5/+3，^5/+4 ) = (〇山 (办5,，办5/+丨，厶5，+2，办5，+3，办5/+4 ) = (1，〇,〇,〇,〇) (办5,，心+1，办5/+2，办5/+3，办5/+4 ) = (1，〇,〇,〇，1) (办5/，办5/+〗，b 5i+2 5 办5/+3，办5)+4 ) = (1，〇,〇，1，〇) (办5ί，办，办5>+2，办5/+3，办5ί+4 ) = 0,〇,〇，1，】） (^5/? ^5/+1 ，办5>+2，办5;+3，厶5，+4 )=(1，0，1,0,0) {b5i,b5j+l,b 5/+2 5 办5/+3，厶5/+4) = (1，〇，1，〇，1) (^5/ ? ^5/+15 ^5/+2 5 ^5/+3 5 ^5/+4 )=(1,0,1,1,0) (办5ί，办5，+1，办5，+2，办5/+3，办5，+4 ) = (1，〇山1，1) (^5/ 5 ^5/+1 5^5/+2 5^5(+3^5/+4 ) = (1,1,0,0,0) (bSi，b5i+l，b5i+2，b5i+3，bSi+4 ) = (1,1,0,0,1) (厶5/，〜+丨，办5，+2，〜+3，办5/+4 )=(1，1，0,1,0) (^5/5 ^5/+1 5 ^5/+2 s ^5/+3 5 ^Si+4) = (办5,，办5，+1，〜+2，办5/+3，办5/+4 ) = (l，H〇,〇) (b5i，b5i+”b5i+2，b5i+3，b5i+4 )=au，〇，i) (bvAM,b 5/+2 5 办5，十3，办Si+4 ) = (l，l，l，l，〇) (办5/，办5/+1，b 5/+2， n)=(i，u,u) 其中，R1是内環的半徑，R2是中間環的半徑，而R3 是外環的半徑。 < £ 19
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