結合非均等錯誤保護與時空編碼技術於高速無線多媒體通訊之研究---理論建構與硬體實現(III)

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行政院國家科學委員會專題研究計畫成果報告

結合非均等錯誤保護與時空編碼技術於高速無線多媒體通

訊之研究---理論建構與硬體實現(3/3)

計畫類別：個別型計畫計畫編號： NSC94-2213-E-009-048- 執行期間： 94 年 08 月 01 日至 95 年 07 月 31 日執行單位：國立交通大學電信工程學系(所) 計畫主持人：王忠炫計畫參與人員：賴俊池，黃慶和，張雲量，陳宗保，共同主持人：曾恕銘報告類型：完整報告報告附件：出席國際會議研究心得報告及發表論文處理方式：本計畫可公開查詢

中華民國 95 年 10 月 31 日

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Abstract

Wireless transmission is rapidly growing and has gradually replaced traditional wired solution in many applications, e.g., personal communications and local area networks, on account of the advantages of mobility and ease of installation. Due to the demand for multimedia services, the trend toward high data rate transmission is also inevitable. This 3-year project combines the powerful unequal error protection (UEP) and space-time coding schemes for channel coding of high-rate wireless multimedia communications. The first year of the project is devoted to studying the UEP capability of space-time coding and establish-ing the related theoretical fundamentals. In the second year, research efforts are focused on combining the puncturing technique with conventional space-time codes to construct a new class of rate-compatible punctured space-time codes for UEP. In the third year, we develop an efficient decoder of the proposed UEP schemes from a soft-defined radio perspective. Its DSP/FPGA implementation is also conducted. The obtained results are expected to be beneficial to both theoreticians and practical engineers, and will promote more UEP space time codes for use in wireless communication systems and networks.

Keywords : Wireless multimedia communications, space-time coding, unequal error pro-tection, soft-defined radio.

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4.6 M=5 p=5D£<g[ã`èDÝý0£ . . . 49

4.7 (a) 1q#[FaìÝ-ý0£(b) 4q#[FaìÝ-ý0£ . . . 50

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5.17 éÿa®l . . . 79 5.18 VirtexII System . . . 80

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4.9 D£<g[ã`èD-Memory=3nT = 3 p=2,3, QPSK . . . 58 4.10 D£<g[ã`èD-Memory=3nT = 3 p=4, QPSK . . . . 58 4.11 D£<g[ã`èD-Memory=3nT = 3 p=5, QPSK . . . . 59 4.12 D£<g[ã`èD-Memory=4nT = 3 p=2,3, QPSK . . . 59 4.13 D£<g[ã`èD-Memory=4nT = 3 p=4, QPSK . . . . 60 4.14 D£<g[ã`èD-Memory=4nT = 3 p=5, QPSK . . . . 60 4.15 rank criterion-Memory=2nT = 2QPSK . . . 61 4.16 rank criterion-Memory=3nT = 2QPSK . . . 61 4.17 rank criterion-Memory=4nT = 2QPSK . . . 62 4.18 rank criterion-Memory=5nT = 2QPSK . . . 62

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DÓÝfì×ðàÝý0?ÑD9'WEXbíá-èºíý0 1|¾tDû(minimum distance)t;ÝêÝEyî9ª;GÙu )2àGjE×1mOèºý0?ÑÝFÙ;¼_DÙ 1iÌb´ {ý0A£]ÝÑ@PTÄ©óC_D£´±;ýæ´úÝý0?ÑD ; 8E2ôÞ»¦;¼_DXm´ª±£]ÝFí£.h×Ë´b[£ Ý;¼_D]PÎÈµAFí£]¥PÝ!èº&XmÝ1æÇÌn XÛ&íý01(unequal error protection, UEP)Ý

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2.1 `èDÙÚx

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...

Modu la t ion Modu la t ion j i, α T X0 T Xn-1 RX0 RXm -1 Infor m at i on souce t

c

% 2.1: `èDÙÚx%

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3` t `FX*rÝ£]-íá_D LAì: ct= (c1t, c 2 t..., c m t ) _D Þ9°íáÝ£]-¿à MPSK Ý]P®ß nT ÍFX*rã nT qFXFaFXFX*r xt=(x1t,x2t...,x nT t )Í xit ` t `Ï i qFXFa XFXÝ*r1 ≤ i ≤ nT' FX*r`åÕ;¼<ÊÝÅ(&Æ|Þ3 ` t Ï j q#[Fa[ÕÝ*rîAì: rj_t = nT X i=0 αi,jxit+ n j t Í nj t Î3` t v3Ï j q#[FaîXåÕÓG¸Î¿íÂ 0v£

HÛÐó N0 Ý}ñPç{úÓG(additive white Gaussian noise, AWGN) αi,j ÎÏ i qFXFaÕÏ j q#[FaÝ5¦Ç(path gain)

3DÝI5';¼Î¿%<[(quasi-static flat fading)(39Ëµ

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Â ëv²ó N0/28EÝ »ð!Go`αi,jÞº;';¼Ï

V£G(channel state information) Î§Ý#½|¿àtPD]°; #[*rÝf^£ÿÕ decision metric FX5îÝ decision metric ÕÝ ÂÎtÝX£?FXÝ*rdecision metric AìXî

nR X j=1 rj_t − nT X i=1 αi,jxˆit 2 (2.1) Íˆxi t #[ £?FXÝDCÐrð1&Æ|¿àù©fÕ°(Viterbi

algorithm)¼ÕN×f"D5(survivor) metricÂt¡&ÆóC=btá metric ÂÝ"D5 ®Dí

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2.2 `èDî°

&ÆÞÜ×Í»+Û`èDÝÚx¬v|¿àhÚxÕ`èD_D¿ ÇTà´Ü Tarokh ß[2]XèÌb°ÍÏVÝ`èD¬v¸à2qFXF aC 4-PSK ]PÍ_D Ýó.î°Aì (s1_t, s2_t) = bt−1(2, 0) ⊕4at−1(1, 0) ⊕4bt(0, 2) ⊕4at(0, 1) Í°Ðr ⊕4 Îÿó-4 (module-4) Ý°ºÕÍ¸ Î ⊕2 T ⊕8 J5½î ÿó-2 (module-2) õÿó-8 (module-8) Ý°ºÕh»`èD¸à 4-PSK ]PETÕ*rÏ2FîÝÐr { 0123 }A% 2.2(b) XîX|`èD3 'î¸àÿó-4ÝºÕDCÐrÞ|ayhP«Í Î¸à 8-PSK ]PJÎ;àÿó-8Ý°ºÕ (s1 t, s2t) 3` t `5½ãÏ×qÏÞq FXFaXFXÝDCÐr(bt, at) 3` t `5½íáy_D ÞÍíáH -3Ìb°ÍÏVÝ`èD_D bÞÍõD Í (bt−1, at−1) Ç Î3` t `;DyõD Ý-ô|Õ ` t `ÝÏVT3 t − 1 `íá ÝÞÍ-¨²btatbt−1at−1 5½ET8¶Ý®ß;ó(generator coefficent) (2,0)(1,0)(0,2)(0,1)|¸`èDÊ Ý_D¡ÿ´·Ý1æ |h`èD »Í`èDÉÜ-% 4-PSK *rÏ2F%A% 2.2(a) 2.2(b) XîÍNÍÏVKb°f5YqAíá-Ý!5½=Õì×Í` Ý °ÍÏV|3` t @ÏV S0 » &Æíá- (bt, at) = (1, 1)Jí DCÐr (s1 t, s2t) = (0, 3)3` t ÝÏVJã S0 ; ÏV S3

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0 0 0 1 1 0 1 1 ) , (a₂ a₁ (0, 0) (0, 1) (1, 0) (1, 1) 0 0 0 1 1 0 1 1 ) , (a₄ a₃ input bits codeword symbols state bits Ant.1 Ant.2 00/00/S₀ 01/01/S₁ 02/10/S₂ 03/11/S₃ 10/00/S0 11/01/S1 12/10/S2 13/11/S3 20/00/S₀ 21/01/S₁ 22/10/S₂ 23/11/S₃ 30/00/S0 31/01/S1 32/10/S2 33/11/S3 state ) , (b_t₋₁a_t₋₁ 1 S 2 S 0 S 3 S state) )/(next , /( ) , (s1_t s_t2 b_t a_t codeword symbol : : : : (a) 0 1 2 3 2 4 2 (b) % 2.2: (a)`èDÉÜ-(b)4-PSK*rÏ2F%

2.3 `èD['ãJ

'§;¼ÏV£GìvFX£]ÝGo LFXÝ*r|î Aì: x = x1₁x2₁· · · xnT 1 x 1 2x 2 2· · · x nT 2 · · · x 1 Lx 2 L· · · x nT L

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3#[ÐD ¿àtPD(maximal likelihood decoding)DÝ*r| îAì: ˆ x = ˆx1₁xˆ2₁· · · ˆxnT 1 xˆ 1 2x 2 2· · · ˆx nT 2 · · · ˆx 1 Lxˆ 2 L· · · ˆx nT L '` t ETÝ;¼Îp(channel matrix)îAì: Ht =      αt_1,1 αt_2,1 · · · αt_n_T_,1 αt 1,2 αt2,2 · · · αtnT,2 .. . ... . .. ... αt_1,n_R αt_2,n_R · · · αt_n_T_,n_R      ¬vH = (H1, H2, · · · , HL) D ÞFX*r x ¾\W ˆx Ý^£Ì WEý0^£ (pairwise error probability)|îW:

P (x → ˆx|H) ≤ 1 2exp −d2_{(x, ˆ}_x) Es 4N0 (2.2) Í d2(x, ˆx) = nR X j=1 L X t=1 nT X i=1

αt_i,j(xi,t− ˆxi,t) 2 (2.3) LDCÐr-²Îp(codeword difference matrix) B(x, ˆx)

B(x, ˆx) =      x1 1− ˆx11 x12− ˆx12 · · · x1L− ˆx1L x2 1− ˆx21 x22− ˆx22 · · · x2L− ˆx2L .. . ... . .. ... xnT 1 − ˆx nT 1 x nT 2 − ˆx nT 2 · · · x nT L − ˆx nT L     

#½&Æ| ñ ×Í nT × nT ÝDCÐrûÒÎp(codeword distance matrix) A(x, ˆx)LAì:

A(x, ˆx) = B(x, ˆx) · BH(x, ˆx)

Í H ÎEÎp7»H. A(x, ˆx) ÎÑA{©Îp(nonnegative definite Hermitian matrix)ÇA(x, ˆx) = AH_{(x, ˆ}_x)_{X|ºD3×ÍóÑÎp(unitary matrix)}

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V¬v|ÿÕìP:

V A(x, ˆx)VH = 4

V Ý'{v1, v2, · · · , vnT} Î A(x, ˆx) Ý©Ç'¬v3 N-îÝ'è Î

ÑøÃ9(complete orthonormal basis) 4 Î×ÍE;ÝÎpÎp/ÝE-ô λi, i = 1, 2, · · · , nTÇ A(x, ˆx) Ý©ÇÂ(eigenvalue)Îp 4 |îAì:

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2.3.1 `èD3{rn

R

ìÝ'ãJ

Ê3 Rayleigh <ÊÝ;¼ìvE®3{GÓfÝìý0£î\& ×M;Aì[12]: P (x → ˆx) ≤ 1 4exp −nR 4N0 r X i=1 λi ! (2.6) ÌDîP|s¨WEý0£Ýî&Îp A(x, ˆx) Ý©ÇÂÀõbnã©ÇÂ õ8 yÞEÎp 4 /ÝE-ôÀÌ ÎpÝªóÂ(trace of the matrix) |îAì: tr (A(x, ˆx)) = r X i=1 λi = nT X i=1 Ai,i (2.7) Í Ai,i îEÎpE-ô Ai,j = L X t=1 xi_t− ˆxi_t xj_t − ˆxj_t∗ (2.8) Þ(2.8)á(2.7)t¡|ÿÕ tr(A(x, ˆx)) = nT X i=1 L X t=1 (xi_t− ˆxi_t 2 (2.9) (2.9)P|ÌDÎp A(x, ˆx) ÝªóÂy x õ ˆx Ý¿]Ã¦ÆûÒ .h¯ A(x, ˆx) ÝªóÂt;8 y¯ x õ ˆx Ý¿]Ã¦ÆûÒt; 9øÝ'ãJÌ ªóãJ(trace criterion).h3 rnR≥ 4 v¿c Rayleigh <Ê ;¼(ì`èD'ãJ|J§Aì:

•èãJ(rank criterion):Îp A(x, ˆx) ÝèÄ6@1 rnR≥ 4Wñt?Ý è nTnR

• ªóãJ(trace criterion): EyXbÝ x õ ˆx (x 6= ˆx) ¼¸ A(x, ˆx) Ýªó Â t

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2.3.2 `èD3±rn

R

ìÝ'ãJ

rnR < 4Ê3 Rayleigh <ÊÝ;¼v3{GÓfìWEý0£Ýî\&B ã.0|;Aì[12]: P (x → ˆx) ≤ r Y i=1 λi !−nR 1 4N0 −rnR (2.10)

Í r ÎÎp A(x, ˆx) Ýè λ1λ2· · · λr JÎ A(x, ˆx) &ëÝ©ÇÂP

(2.10)|:3{GÓfÝì rnR Ýt¶Eý0£bÝÅ(3h

L rnR 5/¦Ç(diversity gain)¬vL_n¦Ç(coding gain): Gc =

(λ0λ1· · · λr−1)1/r d2

u Í d2

uîÎBÄ_DÙÝ¿]Ã¦ÆûÒ (squared Euclidean distance)¥

Õ(2.10)PrnR ÎGÓfÝ¼óEý0£b´ÝÅ(.h ÙÝ rnR Â÷ `¾Õ´Ý5/¦Çºf¾Õ´Ý_n¦Ç? ¥ |î5|J§3 rnR < 4 v¿c Rayleigh <Ê;¼ì`èD' ãJAì: • èãJ:3 rnR < 4 ÝìÎp A(x, ˆx) ÝèÝtt?Ý è nTnR

•PãJ(determinant criterion): EyXbÝ x õ ˆx (x 6= ˆx) ¼¸ A(x, ˆx) ETÝ©ÇÂ¶t

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2.4 `èD-ý0£

&Æá¼`èDÝt·D]°ÎÉÜ%_ÕFXÝDCÐr5.h D sßý0ÝÇ D XÝ5FX5!ý0|%2.3 î 39Í%D 3Ï j Í` Fsßý0ÇÑ@5BÄ l Í` F ê/ÕÑ@5Þ9Ëý0LWý0¯ ej,l,iÍ ej,l,i3Ï j Í`Ñs ßý0 l Í` Fê¥±/ÕÑ@5î!Ý l 5½ºETÕ i fý0 5 j _j₊_l C i l j e _,_, correct path incorrect path % 2.3: Ñ@5 l Ýý05 ×¼1`èDÎaPÝDX|&ÆÄ6jEXbsßÝÑ@5 ¿í¼OÿD 3Ï j Í` FÝÙýÝ¿íý0^£ P (E|j) ≤ X C P (C)X l X i Pr(ej,l,i|C, j) = X C P (C)X l X i Pr(C → Xj,l,i|C, j) (2.11)

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£3h&Æ| rnR≥ 4 Ýµ5 2.3.1 ;Ý.0|á¼WEý0^£ ¿]Ã¦ÆûÒ Ýn=P.h|;¶ (2.11) WìP: P (E|j) ≤ X C P (C)X l X i Pr(C → Xj,l,i|C, j) = X d2 k∈Γ A_d2 kPd2k (2.12) Í Pd2 k îD óC¿]Ã¦ÆûÒ d 2 k Ýý05^£Ad2 k îÍ5 ûÒ d2 k XETÝ5¿íÍóΓ = {d2(c, ˜c)|∀ c 6= ˜c ∈ C}&ÆÌP§WE(infinity pairs)/) {d2, Ad2} hDXETûÒH(distance spectrum)[11]¸|à¼¾\

`èDÝ?û #½D¡-ý0£ ×Íý0¯sß`9Íý0¯XETÕÝ£G -¬×ºýì«Ü»1'b×fëÑ@DCÐr5 X ý0 53Õ-ý0£`Ä6:9Íý0¯ºý¿Í-00 53Õ-ý0£`Ä6:9Íý0¯ºý¿Í-00 53Õ-ý0£`Ä6:9Íý0¯ºý¿Í-00 53Õ-ý0£`Ä6:9Íý0¯ºý¿Í-00 10 01 ₀₀ X 00 01 ) X ( P 2 1 r ) X ( P 2 1 r ) X ( P 2 1 r ) X ( P 2 0 r input bits ´Lý0¯^£ÎPr(X)î%|:3Ï×Í` FýÝ×Í- ETÕÝý0£|¶W 1 2Pr(X)X||9Í»¼1-ý0£|îAì:

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Pr{ bit error } = Pr{e1 [ e2· · · [ el} ≤ 1/2 l X i=1 #(ei) ! Pr{X}

ÍeiÎÏ i Í branch XETÝý0¯#(ei) Îý0¯ ei XETÝý0-ó #½ÞG«.0¼Ýý0¯^£Õ-ý0£Ý.0|ÿÕ|ìÝ

L Pb : -ý0£(bit error probability) Pb ≤

1 k

X i=1

(numbe of erroneous bits) · Pr{Ei}

= 1 k X d2 i∈Γ b · A_d2 iPd2i = 1 k X d2 i∈Γ B_d2 iPd 2 i (2.13) Í k N` íá-ÍóBd2 i = b · Ad2i !§ Ê rnR < 4 Ýµ Λ = {r(c, ˜c)|∀ c 6= ˜c ∈ C}-ý0£|àì Pî: Pb ≤ 1 k X r∈Λ Br r Y i=1 λi !−nR 1 4N0 −rnR (2.14) Í Br’s ÎETÝûÒH Bã|îÝ.05|á¼ rnR ≥ 4`T¸ÿÎp A(c, ˆc) ¾Õ èÂvªóÂtÊ¿í-¥ó Bd2 i TJ¿íDý0£º÷ rnR< 4 Ýµìm¸ÿÎp A(c, ˆc) ¾ÕèÂvPÂtÊ

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¿í-¥ó Br TJ¿íDý0£º÷.h'`èDÝãJè ãJPãJªóãJ|ÿÕJ@¬v|¢ã¿í-¥ó¢ó¯&Æ? Þ@Ý£?D ÙýÝ¿í^£

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Ï 3 a

&íý01`èD

3.1 &íý01`èD'ãJ

3&íý01]ID[13][14]¸à5Ò'¢ó S(G) ¢|ÝEyNÍ íáXEèº&íý01æÝ9>&Æs¨Ey`èDôbv«Ý&íý 01æEy£]íá_D Ý!HùbÍETt¿]Ã¦ÆûÒ Ý&íý01æ#½&ÆÞ¿àîZÝD¿íý0£î&§ .0_D NÍíáHXETD¿íý0£î&§ ´Ê rnR ≥ 4 `Ýµ&ÆqAÏ (2.12) P¿à¯ý0^£Ý5] °Þ;¶D Ï γ ÍíáHXETÝ¯ý0^£ P(γ) ≤ X i(d2 i∈Γ) A(γ)_d2 i P_d2 i Í A(γ) d2 i Ï γ ÍíáHXETÝ¿í5¥óÇÎÏ γ íáHsßDý0 CW d2 i [ûÒÝ5Íó #½&Æ|qAÏ(2.13)P¼àÍÏ γ íáHET-ý0£î&§

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îAì Pb (γ) ≤ X i(d2 i∈Γ) B_d(γ)2 i P_d2 i (3.1) Í B(γ) d2 i JÎN×ÍíáHXETÝ¿í-¥óÇÎ¿íý05îETÕÏ γ íáHsßDý0Ý-¡ÝÍóÞÍî B_d(γ)2 i = b(γ)_d2 i A(γ)_d2 i Í b(γ) d2 i î3¿]Ã§ÆûÒ d 2 i fìÏ γ íáHsßDý0Ý-Í óãÏ(3.1)PÌDÿá©¸ÿN×ÍíáHXETt¿]Ã¦ÆûÒ d2_i ÷µ|¸ÿN×ÍíáHETý0£÷±.hN×ÍíáHXE Tý0£ãt¿]Ã¦ÆûÒ d2 i xÝ¢óÍETXbÑ @5ý05CWt¿]Ã¦ÆûÒÍó gÝ¢ó#½& ÆLÝ&íý01Dx¢óãJ L: `èD C b k ÍíáH nT qFXFaíáÞ£G u = (uit∀ i, t) _D ®ßÝFXDCÐr c = (ci t ∀ i, t)D£?DCÐr ˆc = (ˆcit ∀ i, t)[è' î R(G) = (rmin,1, rmin,2, · · · , rmin,k)ÍÞ£Gíá_D Ï γ HX ETtèîAì

rmin,γ = min {∀c6= ˆc∈C}

{rank (A(c, ˆc)) | ∃t uγ_t 6= ˆuγ_t} for 1 ≤ γ ≤ k.

Í ˆuγ

t 3` t `EyÏ γ íáHD£G2Xb[è't

ÝÇ J¿íÝèÂ

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L: '3 rnR ≥ 4 ``èD C b k ÍíáH nT qFXFaíáÞ £G u = (ui

t ∀ i, t)_D ®ßÝFXDCÐr c = (cit ∀ i, t) D£?DCÐ r ˆc = (ˆci

t ∀ i, t)[5Ò'î E(G) = (d2min,1, d2min,2, · · · , d2min,k) ÍÞ-£Gíá_D Ï γ HXETt¿]Ã¦ÆûÒîAì d2_min,γ = min {∀c6= ˆc∈C}      nT X i=1 L X t=1 |ci t− ˆcit|2 ∃t u γ t 6= û γ t      for 1 ≤ γ ≤ k. ÍFX` L ûγ t 3` t ÈyÏ γ íáHD£G2X b5Ò'tÝÇ [¿]Ã¦ÆûÒTÌ [ûÒ d2_min = min {1≤γ≤k}d 2 min,γ &Æ|¿à[ûÒ `èDD 3 rnR≥ 4`Ý¿íDý0£ÝÝýã • rnR≥ 4&íý01D'ãJ: Ey¢!ÝDC c õ ˆcT¸ £]íá_D ÝNÍHXET rmin,γ ¾Õè¬v!`¸ÿ[5Ò' N×Í[ûÒ d2 min,γ t¢|è{`èDN×ÍíáXETDC Ýt ¿]Ã¦ÆûÒÿ´{Ý5/¦Ç_D¦Ç L: '3 rnR < 4 ``èD C b k ÍíáH nT qFXFaíáÞ £G u = (ui t ∀ i, t)_D ®ßÝFXDCÐr c = (cit ∀ i, t) D£?DCÐ r ˆc = (ˆci

t ∀ i, t)[5PÂî D(G) = (detmin,1, detmin,2, · · · , detmin,k) ÍN×ÍíáHXETtPÂîAì

detmin,γ = min {∀c6= ˆc∈C}      det L X t=1 (c1_t − ˆc1_t, . . . , cnT t − ˆc nT t ) H (c1_t − ˆc1_t, . . . , cnT t − ˆc nT t ) ! ∃t uγ_t 6= ˆuγ_t      for 1 ≤ γ ≤ k.

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ÍFX` L ˆuγ

t 3` t `EyÏ γ íáHD£GXb[

5ÒPÂtÝÇ tPÂ detmin = min

{1≤γ≤k}detmin,γ &Æ|¿àtPÂ `èDD 3 rnR < 4 `Ý¿íDý0£ÝÝ ýã • rnR< 4&íý01D'ãJ: Ey¢!ÝDC c õ ˆcT¸ £]íá_D ÝNÍHXET rmin,γ ¼¬v!`¸ÿ[5Ò PÂN×Í detmin,γ Â tÿ´{Ý5/¦Ç_D¦Ç

3.2 &íý01`èDóx

`èÉÜD|à&9!PîÍ_D ÚxêGt\ã Tarokh Seshadri õ Calderbank ß3- 1998 OèEÌP`èDÝÉÜ-P[2]#½ - 2000 OGozail Brianõ WoernerßèTà Calderbank-Mazo Õ°[15] ¸à @óÐóÝ]°|Õ`èDÝó.îP!`ô|¿àhÕ°Þ`èD ã×_D Úx 5Wã;¼_D Ù¬v2à9¥FaÞ·ùÚx Q¡3- 2001 O Vucetic õ Yuan ßqA Tarokh ß'`èDÝÃFè

M -PSK `èÉÜ_D 3ÍO&ÆèËËÚx|xÌbú&í

ý01æÝ`èDÍ×&Æ;[13][15]è§¡'ãaPÞ-]ID ) M-PSKÙ9¥FaÚx`èÉÜD©»¨²&ÆÑ;ãChen VuceticõYuanßèt·`èÉÜ_D Úx[12][16]¾Õt·&íý01 æt¡TàXÿÝ!ÿÝé\¨´&íý01`èD

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3.2.1 ]ID) M-PSK Ù9¥FXFaÚx`èD

'Þ- G (n, k, m) ]ID_D ®ßÎpÍ n _D íÍ ó k _D íáÍó m õD Íó ; ¨²3` t `ÍíÎpî xt = (x1t, x2t, · · · , xnt)#ì¼&ÆL×Gr7 Îp(signal mapping matrix) ¿àhÎp]IDíÎp¶Þ]IDí7 Õ*rÏ2%(signal constellation)îJ&ÆÿÕ3` t`èÉÜDDCÐrA%3.1XîÇ Í_D î L: ×Í (n × nT) M -PSKGr7 ÎpMîAì M =                              2(log2M )−1 ₀ · · · ₀ 2(log2M )−2 ₀ · · · ₀ .. . ... . .. ... 20 0 · · · 0 0 2(log2M )−1 · · · ₀ 0 2(log2M )−2 · · · ₀ .. . ... . .. 0 0 20 · · · 0 0 0 . .. 0 .. . ... . .. ... 0 0 · · · 2(log2M )−1 0 0 · · · 2(log2M )−2 .. . ... . .. ... 0 0 · · · 20                              (3.2) Í nT FXFaÍó n ]IDíÍóã(3.2)PLMÞ]IDí 7 Õ*rÏ2%Íî°Aì (s1_t, s2_t, ..., snT t ) = (x1t, x2t, · · · , xnt)M Ísi t 3` tãÏiqFXFaXÝDCÐr

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Expamle : ×Í (4, 2, 2) ]ID®ßÎp¸à 2×4 4-PSK Gr7 Îp MJ ET`èÉÜDDCÐrî (s1_t, s2_t) = (x1_t, x2_t, x3_t, x4_t)     2 0 1 0 0 2 0 1     h_DÙt¡ÞDCÐr si t Bã (modulator)Ç `èÉÜDÙ FXGr Convolutional Code Encoder 4PSK Mapper input data H L H L 4PSK Mapper switch % 3.1: )Gr7 ]ID2à4PSK]PÞqFXFa`è_D

3.2.2 `èÉÜD&íý01n;

êGt·`èÉÜD_D ¢å[12]Xî3[12]Vuceticßè_D õD Ý4]PÝ§×AìP vp = b v + p − 1 log₂M c. ¬ÎBãîZXLÝ[5Ò'ÝÝýã¡s¨9_D Úx);àFÙÝ ÃF©èº×1æ Ý'&íý01`èÉÜD_D Úx&Æ è3üõD (register)Íóì¢½;_D õD Ý4]°g)&í 1DãJ Ý&íý01æÝýãìÇ0Ít·&íý01D

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3.3 &íý01`èDé\¨´

3.3.1 ±Ó&íý01`è_Dé\¨´]°

ãÏ;3.2.1XL`èD©»î°èº&Æ×±ÓÝ&íý01` èD¨´]°´3üÌb?Ý&íý0]ID®ßÎpì[14]&Æ| ¢½;Gr7 Îp¾Õ×_D &íý01êÝ.h¥P´{Ý -Çÿ´·1¥P±Jgï&Æ©0XbGr7 Îp PÞ]IDíGr7 Îp×E×(one-to-one)ETA%3.1Xîq A[5Ò'ÝÝýãÇ|ÿ[ý&íý01`èDh²ã yXbGr7 Îpóê´K&Æ|3´±ÓìW&íý01D é\¨´| 4-PSK ¸à ÞqFXFa »ÍGr7 ÎpÍó©b 4! = 24 Ë #½Þ1A¢;Gr7 Îp &Æã%3.1_D Úxì5G«Xó.óÚx)&Æ' ×øð ÞN×Í]IDNÍí5½ET×Gr7 Ý×ÍíáhêÝÎÞ] IDí7 ÕGrÏ2%îÿÕ`èÉÜDDCÐr&Æ|¢½6ðø ð ]IDí×E×ET;Gr3Ï2è îÝHh]°ó. î°8ñT|îZÜExampleu&Æøð 6ð½Þ]IDÏ×Íí ÏÞÍíEÏ×ÍGr7 î{±-!86ðÍµÇ!JAì: ;Gr7 ÎpãJ: (1);Gr7 ÎpM-ôîìH (2)EyN×©b×-ô ë

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î»t¡ÿÕÝ (s1_t, s2_t) = (x1_t, x2_t, x3_t, x4_t)     1 0 2 0 0 2 0 1     ¿à9Ë']Pb[£Ýÿ[ýÝ&íý01D¬vÝª ±é\¨´Ó|ì&Æ¿à?Ý&íý01]ID[16]Ü×°ÍET t·Gr7 ÎpA3.23.33.43.53.23.3 ¸à24]I D)4-PSKGr7 `è_D3.43.5 ¸à34]ID)4-PSKG r7 `è_D]ID®ßÎp|âî

3.3.2 {Ó&íý01`èÉÜDé\¨´]°

ãÿa@~s¨|Vuceticß'Ý`è_D Úx[12]3üõD Íó ì&Æ|¢½;õD ÝXbÝ4]°Q¡;N×ÍõD XET ÕÝ®ß;ógp q,i ∈ 0, 1, · · · , M − 1 &íý01`èÉÜDÝ¨´P µA[5Ò'&íý01D'ãJÝ¡ óEyNÍíáHè ºt·Ý&íý01æ|ìÞ+Û&íý01`èÉÜDÍ¨´]°X µÇM»: &íý01`èÉÜDÍ¨´M»: (1)óÙ M-PSK FXFaó nT (2)óõD Àóv¬v4Í×ËP (3)0XbõD XETÝ®ß;óÝP Í¨´Ý_D î° (4)N0×ËÝ_D î°ÇÕÍETÝ[5Ò' (5)f´[5Ò'ót·Ý&íý01`èÉÜD

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Expamle : '&Æ¨´üËÍõD ËÍíá¬v¸à4-PSKÙ ËqFXFaìÌbt·&íý01æÝ`èÉÜD´0õD b ËË4]PÍ× FÙÝ_D PA%3.2Í_D Ý®ß]PîAì (s_t1, s2_t) = I_t−11 (g_1,11 , g_1,21 ) ⊕4It−12 (g 2 1,1, g 2 1,2) ⊕4It1(g 1 0,1, g 1 0,2) ⊕4It2(g 2 0,1, g 2 0,2) #½&Æ0NÍõD XbETÕÝ®ß;óÇ|0Xb_D Ý P 48 _{ËQ¡ÞXb_D BÄ[5Ò'ýãÝ¡s¨t·[5Ò'} E(G) = (10, 10)3õD 3EÌ4ÝPì¬Ìn{[Ý&íý01 æA%3.3Xî üËÍõD ìÝÏÞËî°Þ_D Ý®ß]P îAì (s_t1, s2_t) = I_t−22 (g_2,12 , g_2,22 ) ⊕4It−12 (g 2 1,1, g 2 1,2) ⊕4It1(g 1 0,1, g 1 0,2) ⊕4It2(g 2 0,1, g 2 0,2) µî]°0Xb_D ¡BÄ[5Ò'ýãÝ¡s¨t·[5Ò' E(G) = (4, 14)A3.2Xî3üËÍõD ì2`èÉÜD|è º!mOÝ9ª£G&íÝý01æÍÏ2ÍíáH38!Ó ì|èº?·Ý1æÏ×ÍíáHJgt¡&ÆÞêG0Ýt ·&íý01`èÉÜDy3.2 ∑ ) , ( 1 0,2 1 0,1g g mod 4 2 t I 1 t I 1 1 -t I 2 1 -t I ) , (1 2 t t s s ) , ( 1 1,2 1 1,1g g ) , ( 2 0,2 2 0,1g g ) , ( 2 1,2 2 1,1g g % 3.2: FÙÞíáÞõD `èÉÜD_D

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) , ( 1 0,2 1 0,1g g mod 4 2 t I 1 t I 2 2 -t I 2 1 -t I ) , (1 2 t ts s ) , ( 2 2,2 2 2,1g g ) , ( 2 0,2 2 0,1g g ) , ( 2 1,2 2 1,1g g ∑ % 3.3: ±P&íý01ÞíáÞõD `èÉÜD_D

3.4 &íý01`èDÿaD¡

h;&ÆÞÜ1ãé\ÿa×8Ý&íý01`èDÝ[ 3h¡ZÝXbÿaÝ('3¿%è¿<ÊÝ;¼Ê 3.1 ¸à 4PSK ]PËFXFa (nT = 2) vËÍõD (v = 2) Ý&íý01`èÒÜD ®ßîAì g1 = [(2, 0)] g2 = [(1, 2), (1, 3), (0, 2)] Íhà&íý01`èÒÜDETÝ[5Ò' E(G) = (4, 14) Ï×Ííá HXETÝ[ûÒ 4ÏÞÍíáHXETÝ[ûÒ 14¸àé\ÿ a¼Ý-ý0£Ý`a5µA% 3.4 Xî&ÆÜ Vucetic ¸àªóã JXèÝt·`èÒÜD×f´®ßîAì

g1 = [(0, 2), (1, 2)] g2 = [(2, 3), (2, 0)]

Íhà`èÒÜDXETÝ[5Ò' E(G) = (10, 10)ÿa¼Ý-ý0 £Ý`a5µA% 3.5 Xî% 3.5 ¸à input 1 input 2 Ýî°5½Ï ×ÍíáHÏÞÍíáHXîÝ`a

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èÒÜD@@|qA¸_D íáÝH!èº!Ýý01æÏÞ àt·`èÒÜD¬Ìb&íý0Ý1æ#½&Æ|5½E9ËàD Ï×ÍíáHETÝ-ý0£`af´2s¨% 3.5 f 3.4 ?EÏ ÞÍí áHXEÝ-ý0£f´J% 3.4 f 3.5 ?Q¡&Æ5½E9Ë à`èÒÜDÌbÝ[5Ò'f´ô|z½s¨ÏÞàDÝÏ×Ííá HETÝ[ûÒfÏ×àÏÞÍíáHJDãG«a;Ý5& Æ|ÿáN×ÍíáHXETÝ[ûÒ÷ÍETÝý0£Jº÷±¢ ã|îÝÌD&Æ|ÿÕ?ÝTJ[5Ò'@@|à¼ÉNÍíá HXETÝý01æ #½&ÆÞÜ»1 [ûÒ8`&ÆA¢f´ËïÝ[?ûÊ 3.2 ¸à 4PSK ]P2FXFa2ÍõD õ3ÍíáÝ&íý01`è D®ßÎpîAì G =   0 0 1 2 0 1 1 1 3 0 2 3   0 2 4 6 8 10 12 14 16 18 20 10−5 10−4 10−3 10−2 10−1

Bit Error Probability

SNR (dB) Average BER Nonessential data, d2 1,min=4 Essential data, d2 2,min=14 % 3.4: 4-ÏV 4PSK k = 2 nT = 2 nR = 2 &íý01`èÉÜDÝ-ý0£

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0 2 4 6 8 10 12 14 10−5 10−4 10−3 10−2 10−1

SNR (dB) Average BER input 1, d2 1,min=10 input 2, d22,min=10 % 3.5: 4-ÏV 4PSK k = 2 nT = 2 nR= 2 Ë&íý01æÝ`èÉÜDÝ-ý0£ Í¸àÝGr7 ÎpîAì M =     2 0 1 0 0 1 0 2    

hà&íý01`èDETÝ[5Ò' E(G) = (6, 4, 6)&Æs¨Ï×Íí áHXETÝ[ûÒ 6ÏëÍíáHXETÝHô 6¸Æ5½ET Ý¿í-¥ó B(1) d2 min = 5 B_d(2)2 min = 0.33&Æ|s¨4QÏ×ÍíáÏëÍ íáHXETÝ[ûÒ×ø¬Î5½ETÕÝ¿í-¥óÏëÍíáHf Ï×ÍíáHETÕÝA%3.6Xî%&Æs¨@@ÏëÍíáHÿa ¼Ý-ý0£@@fÏ×ÍíáHÝ±.h&Æ|ã9»ÿÕTJ¾ ½DÝ[?û`Ê[ûÒ¢¿í-¥ó|ï£hàDÝ[A %3.7XîJÎè{FXFaÍó 4 qÿÕ´{Ý5/¦Çô|?z½Ý5 ½5½ETÕÝ-ý0£Ý{±

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0 2 4 6 8 10 12 14 16 18 20 10−5 10−4 10−3 10−2 10−1

SNR (dB) input 1, d21,min=6, Bd2 min =5 input 2, d2_2,min=4, B_d2 min =5 input 3, d23,min=6, Bd2 min =0.33 % 3.6: 4-ÏV 4PSK k = 3 nT = 2 nR= 2 &íý01`èDÝ-ý0£ 0 1 2 3 4 5 6 7 8 9 10−5 10−4 10−3 10−2 10−1

SNR (dB) input 1, d2 min,1=6, Bd2 min =5 input 2, d2_min,1=4, B_d2 min =5 input 3, d2 min,1=6, Bd2 min =0.33 % 3.7: 4-ÏV 4PSK k = 3 nT = 2 nR= 4 &íý01`èDÝ-ý0£

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3.5 +

3ÍÏ×O&Æ)&íý01`è_D*èãè Ì Fì5]°[ãËï8F|'Ê)yPaFí;¼_DÙh]°x Î"D`è_DÍ&íý01æqA£]íá`è_D H! DÌÍ1æ!¬vãgEý0£5.3 rnR ≥ 43 rnR< 4 ` Ý`èDý01æË¢óLEyÍ!íáET[5Ò' [5ÒPÂ¢hÝ`è_D&íý01æh²&ÆèËËÚ x|xÌbú&íý01æÝ`èDÍ×&Æ;[8]è§¡' ãaPÞ-]ID) M-PSKÙ9¥FaÚx`èÉÜD©»¨ ²&ÆÑ;ãChenVuceticõYuanßèt·`èÉÜ_D Úx[9]¾Õt ·&íý01æt¡TàXÿÝ!ÿÝé\¨´&íý01 `èD

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3.1: ×8&íý01`èÉÜD¸à4PSK]PÞqFXFa v n_T Generator sequences E(G) 2 d A B_d2 A_d(12) ) 2 ( 2 d A (1₂) d B B_d(22) 2 2 g 1 =[(2,0)] g2=[(1,2), (1,3),(0,2)] 4 14 1 0.5 1 4 1 4 2 3 g 1 =[(2,0)] g2=[(1,2), (0,2),(1,3),(0,2)] 4 18 1 0.5 1 4 1 4 2 3 g 1 =[(2,2)] g2=[(3,3), (1,0),(1,3),(2,0)] 8 14 1 0.5 1 8 1 8 2 4 g 1 =[(2,0)] g2=[(1,0), (1,3),(1,2),(0,1),(3,2)] 4 20 1 0.5 1 62 1 92 2 4 g 1 =[(2,2)] g2=[(2,0), (3,1),(1,1),(1,0),(0,2)] 8 18 1 0.5 1 24 1 40 2 5 g 1 =[(0,2)] g2=[(2,0), (2,3),(2,1),(3,0),(0,1),(2,3)] 4 24 1 0.5 1 15.5 1 32 2 5 g 1 =[(2,2)] g2=[(2,0), (3,1),(1,0),(1,3),(0,2),(2,1)] 8 20 1 0.5 1 36 1 60 2 5 g 1_{=[(1,0),(2,0)]} g2=[(2,2),(0,2),(1,3),(1,2),(2,1)] 12 18 1 0.5 1 16 1 24 2 6 g 1 =[(0,2),(2,3)] g2=[(3,0),(2,2),(1,0),(1,1),(2,1),(1,3)] 12 20 1 0.5 1 24 1 40 2 6 g 1 =[(2,2)] g2=[(1,1), (3,0),(3,3),(2,1),(1,3),(2,0),(1,3)] 8 24 1 0.5 1 48 1 64

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3.2: ×TàGr7 Îp8&íý01`èD¸à 4PSK nT = 2 k = 2 n k m Canonical PGM Fornry indices S(G) M T E(G) A_d2 B_d2 ) 1 ( 2 d A A_d(22) ) 1 ( 2 d B B_d(22) 0 1 2 0 1 0 0 2 4 8 1 0.5 1 2 1 2 4 2 1 3 2 0 3 0 0 1 1 0 1 2 5 0 0 1 2 1 2 0 0 2 10 1 0.5 1 1 1 1 4 2 2 0 5 7 7 1 0 0 1 0 2 2 8 0 0 2 1 1 2 0 0 4 14 1 0.5 1 3 1 4 1 0 2 0 0 1 0 2 4 18 1 0.5 1 4 1 4 4 2 3 17 15 0 13 0 0 1 1 0 3 2 10 2 0 0 1 0 2 1 0 8 14 1 0.5 1 8 1 8 4 2 3 7 1 5 6 0 3 2 1 1 2 4 8 0 1 0 2 2 0 1 0 6 14 1 0.5 1 2 0.5 3 0 1 2 0 1 0 0 2 8 16 1 0.5 1 32 1 48 4 2 3 3 1 7 4 2 2 3 3 1 2 6 7 0 2 1 0 1 0 0 2 10 12 1 0.5 1 2 1 2 4 2 4 0 32 17 25 1 1 1 1 0 4 4 10 2 1 0 0 0 0 2 1 4 20 1 0.5 1 52 1 120 1 0 2 0 0 2 0 1 4 20 1 0.5 1 16 1 32 4 2 4 0 37 33 25 1 0 0 1 0 4 2 12 2 0 1 0 0 1 0 2 8 18 1 0.5 1 15 1 16 1 0 2 0 0 2 0 1 4 24 1 0.5 1 24 1 40 4 2 5 0 55 57 45 1 0 0 1 0 5 2 13 2 0 1 0 0 1 0 2 8 18 1 0.5 1 16 1 16

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3.3: ;3.2 n k m Canonical PGM Fornry indices S(G) M T _E(G) 2 d A B_d2 (12) d A A_d(22) ) 1 ( 2 d B B_d(22) 0 2 0 1 2 0 1 0 10 18 1 0.5 1 4 1 6 4 2 5 5 15 13 14 6 7 0 1 2 3 6 10 0 2 1 0 2 0 0 1 12 16 1 1 1 1 2 2 4 2 5 0 66 51 37 1 1 1 1 0 5 4 12 1 0 2 0 0 2 0 1 4 22 1 0.5 1 1 32 32 4 2 5 3 6 7 5 15 3 16 0 3 2 8 9 0 1 2 0 1 0 0 2 18 14 1 0.5 7 1 14 1 0 2 0 1 2 0 1 0 12 18 1 0.5 1 1 1 1 4 2 6 20 35 11 35 1 7 5 0 2 4 6 11 0 0 1 2 1 2 0 0 14 16 1 0.5 1 2 1 3 2 0 0 1 0 2 1 0 4 26 1 0.5 1 8 1 8 0 1 0 2 2 0 1 0 6 22 1 0.5 1 1 1 1 4 2 6 0 165 167 113 1 1 0 0 0 6 2 15 1 0 2 0 0 1 0 2 8 20 1 0.5 1 8 1 8 2 0 1 0 0 1 0 2 4 24 1 0.5 1 44 1 56 4 2 6 40 25 67 63 1 2 1 2 1 5 4 13 2 1 0 0 0 0 1 2 12 20 1 0.5 1 9 1 12 34

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3.4: ×TàGr7 Îp8&íý01`èD¸à 4PSK nT = 2 k = 3 n k m Canonical PGM Fornry indices S(G) M T E(G) 2 d A 2 d B (1) 2 d A (22) d A A_d(32) ) 1 ( 2 d B B_d(22) ) 3 ( 2 d B 4 3 2 3 2 0 3 1 1 1 0 2 1 0 0 1 0 1 2 3 4 2 1 0 0 0 0 2 1 6 4 6 1 0.33 1 5 3 0.33 5 5 4 3 3 0 0 13 16 0 1 1 0 1 0 1 0 0 0 3 2 2 6 0 2 1 0 2 0 0 1 6 2 10 1 0.33 1 1 4 1 1 4 4 3 3 0 4 3 5 0 1 3 2 1 1 1 1 0 1 2 4 4 5 0 1 0 2 2 0 1 0 4 8 8 1 0.33 1 14 14 1 18 18 4 3 4 0 0 31 27 0 1 0 1 1 0 0 1 0 0 4 2 2 7 2 0 1 0 0 2 0 1 6 2 12 1 0.33 1 1 12 1 1 16 4 3 4 0 7 4 3 0 4 1 7 1 1 1 1 0 2 2 4 5 5 0 0 2 1 2 1 0 0 4 10 10 1 0.33 1 21 17 1 37 26 4 3 4 0 15 5 16 0 3 2 1 1 1 1 1 0 1 3 4 4 6 2 1 0 0 0 0 2 1 4 8 8 1 0.33 1 4 4 1 12 4 4 3 5 0 6 15 15 0 7 4 3 1 1 1 1 0 2 3 4 6 6 0 0 1 2 2 1 0 0 4 10 10 1 0.33 1 8 24 1 16 56 4 3 5 0 0 65 37 1 0 1 0 0 1 0 1 0 0 5 2 2 8 1 0 0 2 0 1 2 0 4 4 12 1 0.67 1 1 8 1 1 8

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3.5: ;3.4 n k m Canonical PGM Fornry indices S(G) M T E(G) A_d2 B_d2 (12) d A (22) d A (3) 2 d A B_d(12) ) 2 ( 2 d B B_d(32) 4 3 5 0 31 11 36 0 3 2 1 1 1 1 1 0 1 4 4 4 7 0 0 1 2 2 1 0 0 4 10 1 0 1 0.33 1 4 6 1 18 4 0 0 2 1 2 1 0 0 2 12 12 1 0.33 1 6 4 1 12 4 4 3 6 0 37 13 26 0 3 6 7 1 1 0 0 0 2 4 2 6 7 1 0 0 2 0 2 1 0 6 10 10 1 0.33 1 4 5 1 7 5 4 3 6 0 147 0 135 0 0 1 1 1 1 0 0 0 0 6 2 2 10 2 0 1 0 0 1 0 2 4 4 12 1 0.67 1 1 16 1 1 48 4 3 6 0 21 40 57 0 2 1 3 1 1 1 1 0 1 5 4 4 8 2 0 0 1 0 2 1 0 4 10 12 1 0.33 1 2 4 1 2 4

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Ï 4 a

D£<g[ã`èD

4.1 [ã`èDÝ_D

Ê nT qFXFanR q#[FaÝ`èDÙ'FXÝ*rÎ L L ci t 3` tÏ i qFXFaXFXÝ*rÍ ∀1 ≤ t ≤ L∀1 ≤ i ≤ nT Þ[ãÝ*Tày`èDÇPÝÀtØqFaîÝ*r ci tBã9øÝ) '×±Ý_DÙÌ [ã`èD [ã`èDÝ*Î¿à×Í[ã(punctured table)ÞDCP2Àt L×Í[ã pÝ[ã AA Î×Í nT × pÝÎpÎp/Ý-ô| ax,y î ∀ax,y ∈ 0, 13` t `FXÝ*rA ai,tmodp = 1*rFXDA

ai,tmodp= 0JÎFXBãîÝ[ã^× [ãÝ-ô ax,y = 1 Ýó ÷K`ºETÕ´-Ý1æ3hL`èDÝD£ FX×Í*rºµ£ ]-Ýóê.h'ÒDÎËqFXFaÝ`èD¬v¸à QPSK ]P ÍD£|îW 1 -/FX*rAb×Í 2 Ý[ãAì: A = 1 1 0 1 Bã[ã A XÿÕÝDÍETÝD£ºÎ 4/3 -/FX*r.h×¼1

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E×ÍÌb φ Í&ë-ôÝ[ã|®ßD£ nTp/φ ÝD

4.2 [ã`èDÝD

L xi

t [ãD3` F tÏ i qFXFaXFXÝ*r'FX;¼

ÎX>¿%<[(slowly flat fading)Ï j q#[FaÝ#[*r rj

tj = 1, 2, ..., nR |îAì: r_tj = nT X i=1 αi,j· xit+ n j t

Í αi,j Ï i qFXFaÕÏ j q#[FaÝ5¦Ç njt J ¿íÂ ë

NÍî²ó N0/2 Ýç{úÓG(AWGN)';¼ÏV£GÎ§ÝÇ

αi,j, i = 1, 2, · · · , nT, j = 1, 2, · · · , nR Ey#[ÐÎáÝfìqAtPD (Maximum likelihood decoding)¶W

Pr{r_tj ∀j, t | ˆxi_t, αi,j ∀ i, j, t} = Y t Y j 1 πN0 exp − r_tj−P iαi,j · ˆxit 2 N0 !

¿àtPÕ°|ÿÕ decision metric Aì.h decision metric tÝ

`ÎD £?FXÝ*rˆxi t X t X j rj_t −X i αi,j· ˆxit 2 (4.0) ˆci t Î8Ey ˆxit^bBÄ[ãÝÒDXFXÝ*r.h (4.0) P|¶W: X t X j rj_t −X i

αi,j· ai,t mod p· ˆcit 2 (4.1) ÞîP^b®[ãÝÒDD metric f´ X t X j rj_t −X i αi,j· ˆcit 2

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Bãf´¡|s¨[ãDÒDÝtPDÝ metric Ý-½3y[ãD9

Ý ai,t mod p.hæÍàyÒDÝD |E×Ý[ãDD

4.3 [ã`èDÝ'ãJ

3Ï 2.4 ;&Æ5Ý`èDÝ-ý0£Ê rnR ≥ 4`Ýµã(2.12)P á¼D Dý0Ý¿íý0^£ P (E|j) ≤ X d2 i∈Γ A_d2 iPd2i (4.1) ã (2.13)P|á¼[ãD¿í-ý0£î& Pb ≤ 1 k X d2 i∈Γ B_d2 iPd2i (4.2) QEy[ã`èDãy[ãD«` Ý8nP.h[ãEy¯ ý0£ºbXÅ('[ã p&ÆÞ[ã p Í` Ú ×Í±Ý` ¿í¯ý0^£¿í-ý0^£|;¶Aì: ¿í¯ý0^£ P (E|j) ≤ 1 p X d2 i∈Γ A_d2 iPd2i (4.3) ¿í-ý0^£ Pb ≤ 1 pk X d2 i∈Γ B_d2 iPd2i (4.4) |îËÍP|:Ad2 iBd2iED Ùý^£ÝÅ(Ç9ËÍ¢óÎ[ã`è D'ãJ8Dé\¨´Ý¥¢µA Ê×ÒD C Bã[ã A ÿÕ[ãD ˆC^bBÄ[ãÝËÍDCÐr õ ˜c = (˜c BÄ[ã A ¡ÿÕÝDCÐr x = (x õ

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˜ x = (˜xi t ∀ i, t)qA (4.1)PD ÞFX*r c ¾\W ˜c ÝWEý0^£î\& ¶ Pr{x → ˜x | ∀ αi,j} ≤ 1 2exp   −1 4N0 L X t=1 nR X j=1 nT X i=1

αi,j· ai,t mod p· (ci,t− ˜ci,t) 2  (4.5) L×nT × Lb[DC-²Îp(effective codeword difference matrix) BA(c, ˜c)

BA(c, ˜c) =     a1,1(c1,1− ˜c1,1) a1,2(c1,2− ˜c1,2) · · · a1,L mod p(c1,L− ˜c1,L) a2,1(c2,1− ˜c2,1) a2,2(c2,2− ˜c2,2) · · · a2,L mod p(c2,L− ˜c2,L) .. . ... . .. ... anT,1(cnT,1− ˜cnT,1) anT,2(cnT,2− ˜cnT,2) · · · anT,L mod p(cnT,L− ˜cnT,L)    

#½b[DCûÒÎp(effective codeword distance matrix)QA(c, ˜c) Q_A(c, ˜c) = BA(c, ˜c) · BHA(c, ˜c) ¢ 2.3 ;Ý.0(4.5) P|;¶W Pr{x → ˜x | ∀ αi,j} ≤ 1 2exp −1 4N0 nR X j=1 nT X i=1 λi|βi,j|2 ! . (4.6)

L rA(c, ˜c) Îp QA(c, ˜c) ÝèÌ b[è(effective rank)Ê;¼Î Rayleigh <Êv3{GÓfÝµì(4.6) |;W Pr{x → ˜x} ≤   rA(c,˜c) Y i=1 λi Es   −nR E_s 4N0 −rA(c,˜c)nR (4.7) QEy rA(c, ˜c)nR≥ 4ÝµÏ (4.6) PÝ P nR j=1 PnT i=1λi|βi,j| 2 _|«W{ú ^óWEý0£Ýî&t¡|;W [2] Pr{x → ˜x} ≤ 1 4exp −nR 4N0 nT X i=1 λi ! (4.8) LBÄ[ã A ¡ c õ ˜c Ýb[ûÒ(effective distance) d2_A(c, ˜c) = L X t=0 nT X i=1

|ai,t mod p· (ci,t− ˜ci,t)| 2

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BãÌD&Æá¼ PnT i=1λi = d 2 A(c, ˜c), .hÏ (4.8) P|;¶W Pr{x → ˜x} ≤ 1 4exp −n_R 4N0 d2_A(c, ˜c) (4.9) G«Ý+Û&Æá¼qA rA(c, ˜c)nR ÂÝºETÕËË!ÝWEý0^ £îP rmin( ˆC) [ãD ˆC tÝb[èîAì rmin( ˆC) = min ∀ c6=˜c∈CrA(c, ˜c)

|ìË;&ÆÞ+Ûµ rmin( ˆC)nR Â!XETÕÝËË[ã`èDÝ'ãJ

4.3.1 r

min

( ˆ

C)n

R

< 4

5

Λ = {rA(c, ˜c)|∀ c 6= ˜c ∈ C}[ãD ˆC Ý-ý0£î&îAì: Pb( ˆC) ≤ X r∈Λ Br r Y i=1 λi Es !−nR Es 4N0 −rnR (4.8) Í Br’s ÝÎûÒHtb[Pî°Aì

detmin( ˆC) = min

{∀c6=˜c∈C|rA(c,˜c)=rmin( ˆC)} rmin( ˆC) Y i=1 λi Es .

ÌD (4.3.1)P|á¼3{GÓfÝµ[ãDÝ[?û|ãrmin( ˆC), detmin( ˆC), Brmin( ˆC)

X rmin( ˆC) õ detmin( ˆC) ÷`[ãD ˆC ºÌb´?Ý[;uÎ!Ý[ ãDÌb8!Ý rmin( ˆC) õ detmin( ˆC)JÎf´ Brmin( ˆC)÷J[÷?.h3

¨´´?Ý[ãD`[ãÄ6'W¯[ãDÝ rmin( ˆC) õ detmin( ˆC) ÷|C B_r min( ˆC) ÷÷?

4.3.2 r

min

( ˆ

C)n

R

≥ 4

5

qA(4.9)P[ãD ˆC Ý-ý0£î&|¶W Pb( ˆC) ≤ X Bd2exp −m · d 2 (4.7)

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Í Γ = {d2 A(c, ˜c) | ∀ c 6= ˜c ∈ C} Bd2’s ÎûÒHL[ãD ˆC Ýtb[û ÒAì d2_min( ˆC) = min ∀ c6=˜c∈Cd 2 A(c, ˜c) ÌD (4.3.2)P|á¼3{GÓfÝµ[ãDÝ[?û|ãd2_min( ˆC), B_d2 min( ˆC) X d2 min( ˆC)÷`[ãD ˆC ºÌb÷?Ý[;uÎ!Ý[ãDÌb8!Ý d2_min( ˆC)JÎf´ B_d2 min( ˆC)÷J[÷?.h3¨´´?Ý[ãD`[ã Ä6'W¯[ãDÝ d2 min( ˆC)÷|CBd2 min( ˆC) ÷÷?

4.4 Tà[ã`èDy&íý01

FX£]¥!T;¼(º;`ÙmÌn&íý01Ý ó×`èD|óã!Ý[ãñ×Ìb!1æÝ[ã Dv×DK|¿àÒDÝ_D D _DD.h[ã` èD&ðÊ)&íý01 'FXÝ£]-Àb N Íµï!ÝFX-b!Ý1mOÞ £]-5 W ÍËvÝ£]ÙSlN×ÍËvETÕ!Ý-ý0£ Pb,l 1 ≤ l ≤ WÍPb,1 ≥ Pb,2 ≥ · · · ≥ Pb,WvPW_l=1Sl = N ¨3Bá¼1ÝËvb W Ë.hm W Í!Ý[ã®ßÝD´&ÆóC×Íý01æ´· Ý`èÒD CóCÊ Ý[ã A(l) |®ß×Ìb!ý01æÝD ˆ Cl¬v&Í!ÝDÝ d2 min( ˆCl), Bd2 min( ˆCl) £]XETÝ-ý0£ Pb,l [ã|µïíá£]XmÝý01æV2óC6ðA%4.1

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Enc oder of the P arent Code A(1) for S1 A(2) for S2 A(W ) for Sw to Channel

P unc utring Unit

M

% 4.1: 6ð[ã^× Q3V6ð[ã`ºCWïÝb[ûÒª´0lP°¾ ÕFX£]XmÝý01æÜ»¼1Ê×ËÍ[ã[ãÝ`èD[ ãAìXî: A(1) = 0 0 0 1 1 1 1 1 and A(2) = 1 1 1 1 1 0 0 1 . (4.6)

'bËÍDCÐr c = (ci,t ∀ i, t) õ ˜c = (˜ci,t ∀ i, t)vDC-²ûpîAì e_0,0 e0,1 e0,2 e0,3 0 0 0 e0,7

e1,0 0 0 0 e1,4 e1,5 e1,6 e1,7

(4.6)

Í ei,t = ci,t− ˜ci,tî3` t `Ï i qFaÐr Ý-û ÒD[ã A(1) X[ãqA (4.3)DCÐr c = (ci,t ∀ i, t)õ ˜c = (˜ci,t ∀ i, t) Ýb[ûÒ

d2_A(1)(c, ˜c) = |e0,3|2+ |e0,7|2|e1,0|2+ |e1,4|2+ |e1,5|2+ |e1,6|2+ |e1,7|2

ÒD[ã A(2) X[ãDCÐr c = (ci,t ∀ i, t) õ ˜c = (˜ci,t ∀ i, t) Ýb[ ûÒJ

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' 3` 0 ≤ t ≤ 3 ¸à[ã A(1)Q¡3` 4 ≤ t ≤ 7 6ðÕ[ã A(2)h `(4.4)PÝ-²ÎpºWìP × × × e0,3 0 0 0 e0,7 e1,0 0 0 0 e1,4 × × e1,7 ETÕÝb[ûÒ d2_A(1)|A(2)(c, ˜c) = |e0,3|2+ |e0,7|2+ |e1,0|2 + |e1,4|2+ |e1,7|2 9Í»&Æs¨ d2 A(1)|A(2)(c, ˜c) f d 2 A(1)(c, ˜c) õ d 2 A(2)(c, ˜c) K¼ÿãy6ð [ãsßÝb[ûÒÝÇCWý01æª±.h&Æ¹9Ë Ýsß Ý¹36ð[ãÝÄsßb[ûÒÝÝ&ÆXó CÝ[ã D£<gãJ(rate-compatible criterion)[17]:

if ax,y(i) = 1, then ax,y(j) = 1, for all x, y and 1 ≤ i < j ≤ W (4.6)

Í ax,y(i) [ ã A(i) Ï x Ï j Í û Ý - ô 3 D £ < g ã J ì { D £ D X F X Ý D C Ð r 3± D £ Ý D ô º F X .h | 1 J d2

min( ˆCi) ≤ d2min( ˆCi+1)¬vA3[ã A(i) õ A(j) 6ðXETÝb[ûÒK Î min(d2

min( ˆCi), d2min( ˆCj))(¢§×)

&ÆBá¼3FX£]`ºÞ£]µ¥Ý!5W!ÝN Þ9°Nà)W×£]GoA%4.2£]Go/Ý!N Ýb[ûÒ ý0£Ýn;|à%4.3î[17]

(56)

S uper F ram e 3 S uper F ram e 2 S uper F ram e 1 Enc oder of punc ture s pac e-tim e trellis c ode

00....000 . . . . . . w S S2 S1 % 4.2: G>£]N/Úx S1 S2 S_W 0 0 index l l b P_, _{-BE R} 1 , b P < 2 , b P < W b P_, 1 2 W 2 min d dmin2 (CˆW)≥ (ˆ2)≥ 2 minC d (ˆ1) 2 min C d M ze r o s to p r o p e r ly te r min a te th e e n c o d e r me mo r y . . . . . . . . . . . . . % 4.3: FÙÝG>-4Úx 39ø*ì3£]Go@¡mFXÈÝ”0”-zèõD /Ý- QBãJ(¢§×)s¨ [ãÝ»ðÎ A(l) Õ A(l +1) TÎ A(l +1) to A(l)DCÐr c ˜c Ýb[ûÒKºy d2

min( ˆCl).h£]GoÝ4] P|'WA%4.4Xî¿à9Ë4]PGÝ£]Gof´|s¨& ÆÄ3£]Go FX”0”-9øÝ']PÎÊàyXbÝ[ãDÙÝ

S uper F ram e 3 S uper F ram e 2 S uper F ram e 1 Enc oder of punc ture

s pac e-tim e trellis c ode

. . . 1

S S₂ . . . S_W SW S2 S1

(57)

§×:

Ê×Ìb nT qFXFaÝ`èD C'[ãÎ p A(1) = (ax,y(1))_{0≤x<n,0≤y<p} õ A(2) = (ax,y(2))_{0≤x<n,0≤y<p}vhËÍ[ã D£<gãJÇA ax,y(1) = 1Jax,y(2) = 1 ∀ x, yLFXÝDCÐrc,DÝDCÐr˜c,Í c = (ci,t ∀ i, t) ˜ c = (˜ci,t ∀ i, t)|bì min c6=˜c∈Cd 2 A(1)(c, ˜c) ≤ min c6=˜c∈Cd 2 A(2)(c, ˜c)

J: e = (ei,t ∀ i, t)ÎDCÐr c õ ˜c Ý-ÂÍ ei,t = ci,t− ˜ci,t ÒD[ã A(1) X[ã`ÍETÝb[ûÒ

d2_A(1)(c, ˜c) =X t

X i

ai,t mod p(1) · |ei,t|2 (4.7)

¸à[ã A(2)`

d2_A(2)(c, ˜c) =X t

X i

ai,t mod p(2) · |ei,t|2 (4.8)

.h

d2_A(2)(c, ˜c) − d2_A(1)(c, ˜c) = X t

X i

ai,t mod p(2) · |ei,t|2− X

t X

i

ai,t mod p(1) · |ei,t|2

= X

t X

i

(58)

ãyD£<gÝ§×:ax,y(2) − ax,y(1) ≥ 0 ∀ x, y.h(4.8)P|ÿÕ min c6=˜c∈Cd 2 A(1)(c, ˜c) ≤ min c6=˜c∈Cd 2 A(2)(c, ˜c) #½ÊÒD[ã A(1) X[ã3` F t06ð[ã A(2)J d2_A(1)|A(2)(c, ˜c) |îAì d2_A(1)|A(2)(c, ˜c) =X t<t0 X i

ai,t mod p(1) · |ei,t|2+ X t≥t0

X i

ai,t mod p(2) · |ei,t|2 (4.8)

ÕìP

d2_A(1)|A(2)(c, ˜c) − d2_A(1)(c, ˜c) = X t<t0

X i

ai,t mod p(2) · |ei,t|2 !

−X t

X i

= X

t≥t0

X i

(ai,t mod p(2) − ai,t mod p(1)) · |ei,t|2 ≥ 0

.h|ÿÕ|ì min c6=˜c∈Cd 2 A(1)(c, ˜c) ≤ min c6=˜c∈Cd 2 A(1)|A(2)(c, ˜c) #½D¡[ã A(2) 6ð A(1) Ýv6ðÝ` F×øÎ t0 d2_A(2)|A(1)(c, ˜c) =X t<t0 X i

X i

ÕìP

d2_A(2)|A(1)(c, ˜c) − d2_A(1)(c, ˜c) = X t<t0

X i

ai,t mod p(1) · |ei,t|2 !

−X t

X i

(59)

.h|ÿÕ|ì min c6=˜c∈Cd 2 A(1)(c, ˜c) ≤ min c6=˜c∈Cd 2 A(2)|A(1)(c, ˜c)

4.5 ÿa

Ê×®ß g1 _{= [(1, 2), (1, 3), (3, 2)]} _{v g}2 _{= [(2, 0), (2, 2), (2, 0)]} _ÝÒD[ã 4;¼ ¿% Rayleigh <Ê#[Fa 4 q|1J rm ≥ 4°Í[ã 5½Aì A(1) = 1 1 1 1 0 1 0 0 A(2) = 1 1 1 1 1 1 0 0 A(3) = 1 1 1 1 1 1 1 0 A(4) = 1 1 1 1 1 1 1 1 ÒDBã9°Í[ã¡ETÝb[ûÒ5½ 6,8,12,16ÌD%4.5|s¨ b[ûÒ÷`¸XETÝ-ý0£º÷± 0 2 4 6 8 10 12 10−5 10−4 10−3 10−2 10−1 100 BER E b/N0(dB) d2 min=6 d2 min=8 d2 min=12 d2 min=16 % 4.5: M=4 p=4 D£<g[ã`èDÝý0£

(60)

#½Ey rm < 4 Ý&ÆÊ×®ß g1 _{= [(2, 0), (2, 3), (0, 2)]} v g2 = [(2, 2), (1, 0), (1, 2), (2, 2)] ÝÒD[ã 5;¼ ¿% Rayleigh <ÊX¸ àÝ[ãC&ETÝèPÂAìXî: A(1) = 0 0 1 1 1 0 0 1 1 1 , rmin( ˆC), det min( ˆC) = (1, 4) A(2) = 0 0 1 1 1 0 1 1 1 1 ,rmin( ˆC), det min( ˆC) = (1, 6) A(3) = 0 1 1 1 1 0 1 1 1 1 ,rmin( ˆC), det min( ˆC) = (2, 8) A(4) = 0 1 1 1 1 1 1 1 1 1 , rmin( ˆC), det min( ˆC) = (2, 12)

ÌD%4.6|s¨ rmin( ˆC), detmin( ˆC) @@| £?ÙÝ×ÍÉý ã 0 5 10 15 20 25 30 35 40 10−5 10−4 10−3 10−2 10−1 100 BER E b/N0(dB) r

min=1, detmin=4 r

min=1, detmin=6 r

min=2, detmin=8 r

min=2, detmin=12

% 4.6: M=5 p=5 D£<g[ã`èDÝý0£

(61)

ÝÒDóã|ìËÍ[ã: A(1) = 1 1 1 1 1 1 0 0 and A(2) = 0 0 1 1 1 1 1 1 BÄ9ËÍ[ãÝD5½ C1 õ C2ETÝèb[ûÒÂ5½ : d2min(C1) = 8 & rmin(C1) = 1 õ d2min(C2) = 6 & rmin(C2) = 2jE9ËàD&Æÿa×q#[F a°q#[FaÝÿaA%4.7Xî: 0 5 10 15 20 25 30 35 40 10−5 10−4 10−3 10−2 10−1 100 BER E b/N0(dB) C1 C 2 0 2 4 6 8 10 12 10−5 10−4 10−3 10−2 10−1 100 BER Eb/N0(dB) C1 C2 (a) (b)

% 4.7: (a) 1q#[FaìÝ-ý0£(b) 4q#[FaìÝ-ý0£

ÌDÿa&Æ|s¨ 3±¦ÇÝÝìÙ[ºãtb[ èÂXX; D3{¦ÇÝÝìÙ[ºãtÝb[ûÒXX

3Ï 4.4 ;&ÆD¡ÝA¢Þ-[ã*Tà3`èD&íý01 ¬v5ÝËË!£]4Úx:A%4.2%4.43h&ÆjEhËË!Úx ÿa¸Ý[Ê×®ß g1 _{= [(0, 2), (1, 2)]} _{v g}2 _{= [(2, 3), (2, 0)]} _ÝÒDÐ)

(62)

D£<gæJÝ×[ãAìXî: A(1) = 1 1 1 1 0 1 0 0 A(2) = 1 1 1 1 1 1 0 0 A(3) = 1 1 1 1 1 1 0 1 A(4) = 1 1 1 1 1 1 1 1 Ð)D£<gæJÝ°Í[ãJ A0(1) = 1 1 1 1 1 0 0 0 A0(2) = 0 1 0 1 1 1 1 1 A0(3) = 1 0 1 1 1 1 1 1 A0(4) = 1 1 1 1 1 1 1 1 39ËÝ[ãÌb8!&ë-ôÝ[ãXETÝb[ûÒKÎ×øÝ .h3[ã»ð ?&:D£<gãJE[ÝÅ('ÙÌb 4 q#[ FaGÓf 8 dBÿaAì: 5 10 15 20 25 30 10−5 10−4 10−3 Average BER Bit Number S 1 S2 S3 S4 Not Rate−Compatible Rate−Compatible % 4.8: ×£]4]PETÝý0£ ÌDÿa|s¨Ð)D£<gãJÝ[ã3»ð ºCW[Ê ;ÝÐ)D£<gãJÝ[ã3»ð Jb[Ê;Ýsß

(63)

10 20 30 40 50 60 10−5 10−4 10−3 Average BER Bit Number S₁ S₂ S₃ S₄ S₄ S₃ S₂ S₁ Not Rate−Compatible Rate−Compatible % 4.9: ±l£]4]PETÝý0£ t¡f´hËË!Ý£]4]PA%4.103Ð)D£<gãJìÝ [:3[ã»ðÝÄhËË]°E[ÝÅ(&ð8«Q¥ 2&ÆXèÝ±l£]4]P3£]Go ¬mFXÜ²Ý- 5 10 15 20 25 30 10−5 10−4 10−3 Average BER Bit Number S₁ S₂ S₃ S₄ Bitonic Scheme Monotonic Scheme % 4.10: !£]4]PETÝ[f´

(64)

4.6 +

3Ía&Æ)`èD-[ã*Tày&íý01ñÌ&í ý01[;¼_DÙ¬vTà3PaFí<Ê;¼&Æ'¨ ´8`èD`X¢ÝãJ¯&Æÿ|ñ×8Ý&íý01D ¾Õ ÙèºÄPÝý01^×ÝêÝ rmin( ˆC)nR ≥ 4`&Æá¼ b[û Ò´-ý0J¥÷`ºb´?Ýý01æ; rmin( ˆC)nR< 4`J è ÂPÂ´PET;ó´`ºb´?Ýý01æ3&íý 01Tà`3Ía&Æ1ËËFX£]4Ý]Pf´FÙ]P±Ý] P|s¨Ëï[8¬±Ý]°3£]Go ¬mFXÜ²Ý-.h |Ìb´{Ý£]Fí£t¡¿àé\Ý¨´jE!ÝB7C! Ý[ã0ETÝ×8[ã|èºÂ½ÝTà

(65)

4.1: D£<g[ã`èD-Memory=2nT = 2QPSK g1 = [(0, 2), (2, 2)] g2 = [(2, 1), (1, 1)] , (d2 min(C), Bd2 min(C), rmin(C)) = (10, 1.500, 2) p A (d2 min( ˆC), Bd2

min( ˆC), rmin( ˆC)) mmin

2 1 0 1 1 (6, 1.142, 2) 2 3 0 0 1 1 1 1 (4, 0.500, 1) 4 0 1 1 1 1 1 (6, 0.500, 2) 2 4 0 0 0 1 1 1 1 1 (4, 0.953, 1) 4 0 1 0 1 1 1 1 1 (6, 1.145, 2) 2 0 1 1 1 1 1 1 1 (6, 0.375, 2) 2 5 0 0 0 0 1 1 1 1 1 1 (4, 1.295, 1) 4 0 1 0 0 1 1 1 1 1 1 (4, 0.300, 1) 4 0 1 0 1 1 1 1 1 1 1 (6, 0.763, 2) 2 0 1 1 1 1 1 1 1 1 1 (6, 0.303, 2) 2 1 4.2: D£<g[ã`èD-Memory=3nT = 2QPSK g1 = [(2, 2), (2, 2)] g2 = [(1, 1), (1, 3), (1, 1)] , (d2 min(C), Bd2 min(C), rmin(C)) = (12, 1.091, 2) p A (d2 min( ˆC), Bd2

2 0 1 1 1 (8, 0.653, 1) 4 3 1 0 1 0 1 1 (8, 2.567, 2) 2 1 1 1 0 1 1 (8, 0.030, 2) 2 4 1 0 0 1 0 1 1 1 (4, 0.016, 1) 4 1 1 0 1 0 1 1 1 (8, 0.655, 2) 2 1 1 1 1 0 1 1 1 (8, 0.012, 2) 2 5 1 0 0 0 1 0 1 1 1 1 (4, 0.077, 1) 4 1 0 1 0 1 0 1 1 1 1 (8, 1.376, 1) 4 1 0 1 1 1 0 1 1 1 1 (8, 0.575, 2) 2 1 1 1 1 1 0 1 1 1 1 (8, 0.005, 2) 2 54

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4.3: D£<g[ã`èD-Memory=4nT = 2QPSK g1 = [(1, 2), (1, 3), (3, 2)] g2 = [(2, 0), (2, 2), (2, 0)] , (d2 min(C), Bd2 min(C), rmin(C)) = (16, 1.27, 2) p A (d2 min( ˆC), Bd2

2 1 1 0 1 (8, 0.188, 1) 4 3 1 1 1 0 1 0 (8, 0.288, 1) 4 1 1 1 0 1 1 (12, 0.777, 1) 4 4 1 1 1 1 0 1 0 0 (6, 0.094, 1) 4 1 1 1 1 1 1 0 0 (8, 0.020, 1) 4 1 1 1 1 1 1 1 0 (12, 0.516, 1) 4 5 1 1 1 1 1 0 0 0 0 1 (6, 0.163, 1) 4 1 1 1 1 1 0 1 0 0 1 (8, 0.172, 1) 4 1 1 1 1 1 0 1 1 0 1 (8, 0.075, 1) 4 1 1 1 1 1 0 1 1 1 1 (12, 0.327, 1) 4 1 4.4: D£<g[ã`èD-Memory=5nT = 2QPSK g1 = [(0, 2), (2, 2), (2, 2)] g2 = [(3, 0), (2, 1), (3, 1), (3, 3)] , (d2 min(C), Bd2 min(C), rmin(C)) = (16, 0.400, 2) p A (d2 min( ˆC), Bd2

2 1 1 0 1 (8, 0.010, 2) 2 3 0 0 1 1 1 1 (8, 0.079, 1) 4 0 1 1 1 1 1 (12, 0.202, 2) 2 4 1 1 1 1 0 0 0 1 (6, 0.013, 1) 4 1 1 1 1 0 0 1 1 (8, 0.015, 1) 4 1 1 1 1 0 1 1 1 (12, 0.085, 1) 4 5 1 1 1 0 0 0 0 1 1 1 (6, 0.062, 1) 4 1 1 1 0 1 0 0 1 1 1 (8, 0.065, 2) 2 1 1 1 0 1 1 0 1 1 1 (10, 0.045 2) 2 1 1 1 1 1 1 0 1 1 1 (12, 0.064, 1) 4 55

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4.5: D£<g[ã`èD-Memory=6nT = 2QPSK g1 = [(0, 2), (3, 1), (3, 3), (3, 2)] g2 = [(2, 2), (2, 2), (0, 0), (2, 0)] , (d2 min(C), Bd2 min(C), rmin(C)) = (18, 0.157, 2) p A (d2 min( ˆC), Bd2

2 1 1 0 1 (12, 0.152, 2) 2 3 0 1 1 1 1 0 (8, 0.0034, 2) 2 0 1 1 1 1 1 (12, 0.095, 2) 2 4 1 0 1 1 0 1 0 1 (6, 0.009, 2) 2 1 0 1 1 0 1 1 1 (8, 0.008, 1) 4 1 1 1 1 0 1 1 1 (12, 0.002, 2) 2 5 1 1 1 0 0 0 0 1 1 1 (6, 0.016, 1) 4 1 1 1 0 1 0 1 0 1 1 (8, 0.028, 2) 2 1 1 1 1 1 0 1 0 1 1 (10, 0.009 2) 2 1 1 1 1 1 0 1 1 1 1 (14, 0.038, 2) 2 1 4.6: D£<g[ã`èD-Memory=2nT = 3 p=2,3, QPSK g1 = [(0, 2, 2), (1, 2, 3)] g2 = [(2, 3, 3), (2, 0, 2)] , (d2 min(C), Bd2 min(C), rmin(C)) = (16, 2.00, 2) p A (d2 min( ˆC), Bd2

2   1 1 0 1 0 0   (4, 0.156, 1) 4   1 1 1 1 0 0   (10, 1.000, 2) 2   1 1 1 1 1 0   (12, 0.500, 2) 2 3   1 1 0 0 1 1 0 0 0   (4, 0.552, 1) 4   1 1 1 0 1 1 0 0 0   (6, 0.391, 1) 4   1 1 1 1 1 1 0 0 0   (10, 1.00, 2) 2   1 1 1 1 1 1 0 0 1   (10, 0.333, 2) 2   1 1 1 1 1 1 0 1 1   (12, 0.333, 2) 2 56

(68)

4.7: D£<g[ã`èD-Memory=2nT = 3 p=4, QPSK g1 = [(0, 2, 2), (1, 2, 3)] g2 = [(2, 3, 3), (2, 0, 2)] , (d2 min(C), Bd2 min(C), rmin(C)) = (16, 2.00, 2) p A (d2 min( ˆC), Bd2

4   1 1 0 0 0 1 1 1 0 0 0 0   (2, 0.125, 1) 4   1 1 0 1 0 1 1 1 0 0 0 0   (4, 0.078, 1) 4   1 1 0 1 0 1 1 1 0 0 1 0   (6, 0.250, 1) 4   1 1 0 1 1 1 1 1 0 0 1 0   (8, 0.125, 2) 2   1 1 0 1 1 1 1 1 0 0 1 1   (10, 0.500, 2) 2   1 1 0 1 1 1 1 1 0 1 1 1   (12, 0.989, 2) 2   1 1 1 1 1 1 1 1 0 1 1 1   (12, 0.250, 2) 2 1 4.8: D£<g[ã`èD-Memory=2nT = 3 p=5, QPSK g1 = [(0, 2, 2), (1, 2, 3)] g2 = [(2, 3, 3), (2, 0, 2)] , (d 2 min(C), Bd2 min(C), rmin(C)) = (16, 2.00, 2) p A (d2 min( ˆC), Bd2

5   0 0 1 0 1 1 1 0 0 0 0 0 1 1 0   (2, 0.227, 1) 4   1 0 1 0 1 1 1 0 0 0 0 0 1 1 0   (4, 0.297, 1) 4   1 0 1 0 1 1 1 0 0 0 0 1 1 1 0   (4, 0.200, 1) 4   1 0 1 1 1 1 1 0 0 0 0 1 1 1 0   (6, 0.200, 1) 4   1 0 1 1 1 1 1 0 0 1 0 1 1 1 0   (8, 0.300, 2) 2   1 1 1 1 1 1 1 0 0 1 0 1 1 1 0   (8, 0.100, 2) 2   1 1 1 1 1 1 1 1 0 1 0 1 1 1 0   (10, 0.400, 2) 2   1 1 1 1 1 1 1 1 1 1 0 1 1 1 0   (10, 0.200, 2) 2   1 1 1 1 1 1 1 1 1 1 1 1 1 1 0   (12, 0.200, 2) 2 57

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4.9: D£<g[ã`èD-Memory=3nT = 3 p=2,3, QPSK g1 = [(2, 2, 2), (2, 1, 1)] g2 = [(2, 0, 3), (1, 2, 0), (0, 2, 2)] , (d2 min(C), Bd2 min(C), rmin(C)) = (20, 2.625, 2) p A (d2 min( ˆC), Bd2

2   0 1 1 1 0 0   (4, 0.156, 1) 4   1 1 1 1 0 0   (12, 0.563, 2) 2   1 1 1 1 1 0   (14, 0.250, 2) 2 3   0 1 1 1 1 0 0 0 0   (4, 0.102, 1) 4   0 1 1 1 1 1 0 0 0   (6, 0.055, 1) 4   1 1 1 1 1 1 0 0 0   (12, 0.563, 2) 2   1 1 1 1 1 1 0 0 1   (14, 0.589, 2) 2   1 1 1 1 1 1 0 1 1   (16, 0.354, 2) 2 1 4.10: D£<g[ã`èD-Memory=3nT = 3 p=4, QPSK g1 = [(2, 2, 2), (2, 1, 1)] g2 = [(2, 0, 3), (1, 2, 0), (0, 2, 2)] , (d2 min(C), Bd2 min(C), rmin(C)) = (20, 2.625, 2) p A (d2 min( ˆC), Bd2

4   1 0 0 0 1 0 0 0 0 1 1 1   (4, 0.009, 2) 2   1 0 0 1 1 0 0 0 0 1 1 1   (6, 0.125, 2) 2   1 1 0 1 1 0 0 0 0 1 1 1   (8, 0.125, 2) 2   1 1 0 1 1 0 0 1 0 1 1 1   (10, 0.195, 2) 2   1 1 0 1 1 0 1 1 0 1 1 1   (12, 0.195, 2) 2   1 1 1 1 1 0 1 1 0 1 1 1   (14, 0.266, 2) 2   1 1 1 1 1 1 1 1 0 1 1 1   (16, 0.266, 2) 2 58

(70)

4.11: D£<g[ã`èD-Memory=3nT = 3 p=5, QPSK g1 = [(2, 2, 2), (2, 1, 1)] g2 = [(2, 0, 3), (1, 2, 0), (0, 2, 2)] , (d 2 min(C), Bd2 min(C), rmin(C)) = (20, 2.625, 2) p A (d2 min( ˆC), Bd2

5   0 0 1 0 1 1 1 0 0 1 0 0 0 1 0   (2, 0.045, 1) 4   0 1 1 0 1 1 1 0 0 1 0 0 0 1 0   (4, 0.040, 1) 4   0 1 1 0 1 1 1 1 0 1 0 0 0 1 0   (6, 0.095, 1) 4   1 1 1 0 1 1 1 1 0 1 0 0 0 1 0   (8, 0.1125, 2) 2   1 1 1 0 1 1 1 1 1 1 0 0 0 1 0   (10, 0.125, 2) 2   1 1 1 1 1 1 1 1 1 1 0 0 0 1 0   (12, 0.225, 2) 2   1 1 1 1 1 1 1 1 1 1 0 0 1 1 0   (12, 0.1125, 2) 2   1 1 1 1 1 1 1 1 1 1 0 1 1 1 0   (14, 0.225, 2) 2   1 1 1 1 1 1 1 1 1 1 1 1 1 1 0   (16, 0.213, 2) 2 1 4.12: D£<g[ã`èD-Memory=4nT = 3 p=2,3, QPSK g1 = [(1, 2, 1), (1, 3, 2), (3, 2, 1)] g2 = [(2, 0, 2), (2, 2, 0), (2, 0, 2)] , (d2 min(C), Bd2 min(C), rmin(C)) = (24, 0.891, 2) p A (d2 min( ˆC), Bd2

2   1 1 0 1 0 0   (8, 0.187, 1) 4   1 1 1 1 0 0   (16, 1.271, 1) 4   1 1 1 1 1 0   (16, 0.063, 2) 2 3   1 1 0 0 1 0 0 0 1   (8, 0.364, 1) 4   1 1 0 0 1 0 1 0 1   (10, 0.221, 2) 2   1 1 0 0 1 1 1 0 1   (12, 0.042, 2) 2   1 1 1 0 1 1 1 0 1   (16, 0.224, 2) 2   1 1 1 0 1 1 1 1 1   (20, 0.578, 2) 2 59

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4.13: D£<g[ã`èD-Memory=4nT = 3 p=4, QPSK g1 = [(1, 2, 1), (1, 3, 2), (3, 2, 1)] g2 = [(2, 0, 2), (2, 2, 0), (2, 0, 2)] , (d2 min(C), Bd2 min(C), rmin(C)) = (24, 0.891, 2) p A (d2 min( ˆC), Bd2

4   0 1 1 1 1 0 0 0 0 0 0 1   (4, 0.015, 1) 4   0 1 1 1 1 0 0 0 0 1 0 1   (8, 0.103, 1) 4   0 1 1 1 1 0 0 0 1 1 0 1   (10, 0.094, 1) 4   0 1 1 1 1 0 0 1 1 1 0 1   (12, 0.031, 2) 2   0 1 1 1 1 1 0 1 1 1 0 1   (16, 0.376, 2) 2   0 1 1 1 1 1 0 1 1 1 1 1   (18, 0.383, 2) 2   0 1 1 1 1 1 1 1 1 1 1 1   (20, 0.191, 2) 2 1 4.14: D£<g[ã`èD-Memory=4nT = 3 p=5, QPSK g1 = [(1, 2, 1), (1, 3, 2), (3, 2, 1)] g2 = [(2, 0, 2), (2, 2, 0), (2, 0, 2)] , (d2 min(C), Bd2 min(C), rmin(C)) = (24, 0.891, 2) p A (d2 min( ˆC), Bd2

5   1 1 1 1 1 0 0 0 0 1 0 0 0 0 0   (6, 0.162, 1) 4   1 1 1 1 1 1 0 0 0 1 0 0 0 0 0   (6, 0.075, 1) 4   1 1 1 1 1 1 1 0 0 1 0 0 0 0 0   (8, 0.016, 1) 4   1 1 1 1 1 1 1 1 0 1 0 0 0 0 0   (12, 0.327, 1) 4   1 1 1 1 1 1 1 1 1 1 0 0 0 0 0   (16, 1.271, 1) 4   1 1 1 1 1 1 1 1 1 1 0 0 0 1 0   (16, 0.397, 2) 2   1 1 1 1 1 1 1 1 1 1 0 0 1 1 0   (16, 0.100, 2) 2   1 1 1 1 1 1 1 1 1 1 0 1 1 1 0   (18, 0.228, 2) 2   1 1 1 1 1 1 1 1 1 1 1 1 1 1 0   (20, 0.203, 2) 2 60

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4.15: rank criterion-Memory=2nT = 2QPSK

g1 = [(0, 2), (1, 0)]

g2 = [(2, 2), (0, 1)] , (detmin(C), Bdetmin(C), rmin(C)) = (8, 2.000, 2)

p A (detmin( ˆC), Bdetmin( ˆC), rmin( ˆC))

2 1 0 1 1 (4, 2.000, 1) 3 0 0 1 1 1 1 (2, 1.000, 1) 0 1 1 1 1 1 (4, 1.500, 1) 4 0 1 0 1 0 1 1 1 (2, 1.500, 1) 0 1 0 1 0 1 1 1 (2, 1.000, 1) 0 1 1 1 1 1 1 1 (4, 1.500, 1) 5 0 0 0 0 1 1 1 1 1 1 (2, 2.25, 1) 0 1 0 1 1 0 1 1 1 1 (2, 1.500, 1) 0 1 0 1 1 1 1 1 1 1 (4, 1.375, 1) 0 1 1 1 1 1 1 1 1 1 (4, 1.160, 1)

(a) Parent code of memory 2

1

4.16: rank criterion-Memory=3nT = 2QPSK g1 = [(0, 2), (2, 0)]

g2 = [(2, 1), (1, 2), (0, 2)]

, (detmin(C), Bdetmin(C), rmin(C)) = (16, 0.250, 2) p A (detmin( ˆC), Bdetmin( ˆC), rmin( ˆC))

2 1 1 1 0 (4, 0.250, 1) 3 0 0 1 1 1 1 (4, 0.52, 1) 0 1 1 1 1 1 (4, 0.344, 1) 4 0 0 1 1 1 0 1 1 (4, 0.504, 1) 0 0 1 1 1 1 1 1 (4, 0.418, 1) 1 0 1 1 1 1 1 1 (4, 0.180, 1) 5 0 0 1 1 1 1 0 0 1 1 (2, 0.500, 1) 0 0 1 1 1 1 0 1 1 1 (4, 0.425, 1) 0 0 1 1 1 1 1 1 1 1 (4, 0.317, 1) 1 1 1 1 1 0 1 1 1 1 (4, 0.191, 1)

(b) Parent code of memory 3

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g1 = [(0, 2), (1, 2), (2, 2)]

g2 = [(2, 0), (1, 1), (0, 2)]

, (detmin(C), Bdetmin(C), rmin(C)) = (32, 0.372, 2)

2 ₁ ₁ 1 0 (8, 0.183, 2) 3 ₀ ₁ ₁ 0 1 1 (8, 0.561, 2) ₀ ₁ ₁ 1 1 1 (8, 0.156, 2) 4 1 0 1 1 0 1 0 1 (8, 0.308, 1) ₁ ₁ ₁ ₁ 0 1 0 1 (8, 0.184, 2) 1 1 1 1 0 1 1 1 (8, 0.126, 2) 5 ₀ ₀ ₁ ₁ ₁ 0 0 1 1 1 (4, 0.482, 1) ₀ ₀ ₁ ₁ ₁ 0 1 1 1 1 (6, 0.173, 1) 0 1 1 1 1 0 1 1 1 1 (8, 0.423, 2) 0 1 1 1 1 1 1 1 1 1 (8, 0.142, 2)

(c) Parent code of memory 4

1

g1 = [(2, 0), (2, 3), (0, 2)]

g2 = [(2, 2), (1, 0), (1, 2), (2, 2)]

, (detmin(C), Bdetmin(C), rmin(C)) = (36, 0.029, 2)

2 1 1 0 1 (8, 0.063, 2) 3 0 1 1 1 0 1 (8, 0.078, 2) 0 1 1 1 1 1 (16, 0.052, 2) 4 0 1 1 1 0 1 1 0 (8, 0.069, 1) 0 1 1 1 0 1 1 1 (8, 0.076, 2) 0 1 1 1 1 1 1 1 (12, 0.023, 2) 5 0 0 1 1 1 0 0 1 1 1 (4, 0.082, 1) 0 0 1 1 1 0 1 1 1 1 (6, 0.095, 1) 0 1 1 1 1 0 1 1 1 1 (8, 0.086 2) 0 1 1 1 1 1 1 1 1 1 (12, 0.021, 2)

(d) Parent code of memory 5

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結合非均等錯誤保護與時空編碼技術於高速無線多媒體通訊之研究---理論建構與硬體實現(III)

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