IS-GPS-800D (797938), страница 5
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Thus octal 5111 corresponds tothe generator polynomial P1(x) = 1 + x3 + x6 + x9 + x11.** The initial 11 bits also represent the initial condition, n11, ……, n1, for each PRN signalnumber. (See Figure 3.2-2)“*** Note: PRNs 38-63 are required per this Table if a manufacturer chooses to include thesePRNs in their receiver design.†The initial and the final bit values are obtained after dropping the initial bit value 0.15IS-GPS-800D24 Sep 2013FIXED LENGTH-10223 LEGENDRE SEQUENCE (INDEXED 0 THROUGH 10222)011110111100101010100101...001011010101011000010000......WEILINDEX (w)⊕⊕⊕WEIL SEQUENCE WITH INDEX wW(0)W(1)W(2)W(10222).
. .INSERTIONINDEX (p)EXPANSIONSEQUENCE:C(0)C(1)C(2)0 1 1 0 1 0 0()LENGTH-10230 RANGING CODE WITH WEIL INDEX w AND INSERTION INDEX pNOTE: WEIL INDICES AND INSERTION INDICES GIVEN IN TABLE 3.2-2Figure 3.2-1. Generation of L1CP-/L1CD-Codes16IS-GPS-800D24 Sep 2013S1 POLYNOMIAL:1 + m1 x + m2 x 2 + · · · + m10 x 10 + x 11STAGEm2m11n102n21m33n32m44n43m55n54m66n65m8m77n78n867m9m109n9810n109m1111n111011TAPINITIALSHIFT DIRECTIONOUTPUTS2 POLYNOMIAL:1 + x 9 + x 111n103n32n2124n435n546n657n768n8710n109n98911n111011NOTE: S2 POLYNOMIAL IS NEEDED ONLY FOR PRN NUMBERS 64 – 210 AS DESCRIBED IN SECTION 6.3.1.2NOTE: S1 POLYNOMIAL COEFFICIENTS AND INITIAL CONDITIONS ARE GIVEN IN TABLE 3.2-3MSB OF INITIAL CONDITION GIVEN IN TABLE 3.2-3 IS IN STAGE 11FIRST BIT OF THE OUTPUT IS THE MSB OF THE OUTPUT SEQUENCEFOR S1 POLYNOMIAL, m11 IS EQUAL TO 1Figure 3.2-2.
L1CO-Code Generator Configuration17IS-GPS-800D24 Sep 20133.2.2.2 Non-Standard CodesThe non-standard codes, used to protect the user from tracking an anomalous navigation signal,are not for utilization by the user and, therefore, are not defined in this document. In addition tothe SV’s capability to autonomously initiate the broadcast of non-standard codes, the SVs shallalso be capable of initiating and terminating the broadcast of NSCP and/or NSCD code(s)independently of each other, in response to a Control Segment (CS) command.3.2.3 Message CharacteristicsThe following defines the overall message structure of the L1C message, DL1C(t).
The datacontent of the L1C message is defined in Section 3.5.3.2.3.1 L1C Message StructureThe message modulated onto the L1CD signal consists of subframes and frames, as shown inFigure 3.2-3. A frame is divided into three subframes of varying length. Multiple frames arerequired to broadcast a complete data message set to users.Each frame shall consist of 9 bits of “Time of Interval” (TOI) data in subframe 1, 600 bits of“non-variable” clock and ephemeris data with Cyclic Redundancy Check (CRC) in subframe 2,and 274 bits of “variable” data with CRC in subframe 3. The content of subframe 3 nominallyvaries from one frame to the next and is identified by a page number.
The content of subframe 2is nominally non-variant over a period of multiple frames.Subframe 1 provides 9-bit TOI data that corresponds to the SV time epoch at the start (leadingedge) of the next following frame (reference paragraph 3.5.2).
The 9-bit TOI data shall beencoded into 52-symbol code using Bose, Chaudhuri, and Hocquenghem (BCH) code as definedin paragraph 3.2.3.2.Subframes 2 and 3 shall utilize 24-bit CRC parity algorithm as defined in paragraph 3.2.3.3 witha separate CRC for each subframe.Each of the two subframes (2 and 3) shall be further encoded using Low Density Parity Check(LDPC) Forward Error Correction (FEC) code as defined in paragraph 3.2.3.4.The FEC encoded symbols shall be interleaved, as defined in paragraph 3.2.3.5, prior to beingmodulo-2 added to L1CD-code.The resulting 1800 symbols, DL1C(t), representing one message frame, shall be broadcast at 100symbols per second.18IS-GPS-800D24 Sep 2013Figure 3.2-3.
L1C Message Structure3.2.3.2 Time of Interval Data EncodingNine bits of TOI data are channel encoded using BCH (51, 8) code. The eight Least SignificantBits (LSBs- the rightmost bits) of nine-bit TOI data are encoded using the generator polynomialof 763 (octal). This code generator is conceptually described in Figure 3.2-4 using an 8-stagelinear shift register generator. TOI data bits 1 to 8 (8 LSBs) are loaded into the generator, MostSignificant Bit (MSB) first, as initial conditions of the registers, which is then shifted 51 times togenerate 51 encoded symbols.
The ninth bit of TOI data (MSB) shall be modulo-2 added to the51 encoded symbols and it shall also be appended as the MSB of the 52-symbol TOI message.The first output symbol of the generator (after modulo-2 added to the ninth bit of TOI data) shallbe the second MSB of the 52-symbol TOI message.The following provides an example decoding technique to decode the TOI data.
The 52 UEreceived soft decisions are stored as sign/magnitude and correlated, respectively, with the 52symbols of a TOI code word hypothesis corresponding to MSB = 0. (A SV transmitted 0 isexpected to produce a sign of 0.) For each soft decision, the correlation computation adds themagnitude if the sign agrees with the code word hypothesis and subtracts the magnitude19IS-GPS-800D24 Sep 2013otherwise. The correlation computation is repeated for all 256 TOI code word hypotheses. Thedecision on the eight LSBs corresponds to the TOI code word hypothesis producing the largestabsolute value of the correlation.
The decision on the MSB is 0 if this largest correlation ispositive and 1 otherwise.Figure 3.2-4. BCH (51, 8) Code Generator3.2.3.3 Cyclic Redundancy CheckTwenty-four bits of CRC will provide protection against burst as well as random errors with aprobability of undetected error ≤ 2-24 = 5.96×10-8 for all channel bit error probabilities ≤ 0.5.The CRC word is calculated in the forward direction on a given message using a seed of 0. Thesequence of 24 bits (p1,p2,...,p24) is generated from the sequence of information bits(m1,m2,...,mk) (MSB to LSB sequence) in a given message. This is done by means of a code thatis generated by the polynomial24g(X ) = ∑ gi X ii =0where20IS-GPS-800D24 Sep 2013g i = 1for i = 0,1,3,4,5,6,7,10,11,14,17,18,23,24= 0otherwiseThis code is called CRC-24Q.
The generator polynomial of this code is in the following form(using binary polynomial algebra):g ( X ) = (1 + X ) p( X )where p(X) is the primitive and irreducible polynomialp( X ) = X 23 + X 17 + X 13 + X 12 + X 11 + X 9 + X 8 + X 7 + X 5 + X 3 + 1When, by the application of binary polynomial algebra, the above g(x) is divided into m(X)X24,where the information sequence m(x) is expressed asm( X ) = mk + mk −1 X + mk − 2 X 2 + ⋅ ⋅ ⋅ + m1 X k −1.The result is a quotient and a remainder R(X) of degree < 24. The bit sequence formed by thisremainder represents the CRC sequence. CRC bit pi, for any i from 1 to 24, is the coefficient ofx24-i in R(X).This code has the following characteristics:It detects all single bit errors per code word.It detects all double bit error combinations in a codeword because the generatorpolynomial g(X) has a factor of at least three terms.It detects any odd number of errors because g(X) contains a factor 1+X.It detects any burst error for which the length of the burst is ≤ 24 bits.It detects most large error bursts with length greater than the CRC length r = 24 bits.
Thefraction of error bursts of length b > 24 that are undetected is:21IS-GPS-800D24 Sep 20132-24 = 5.96 × 10-8, if b > 25 bits2-23 = 1.19 × 10-7, if b = 25 bits3.2.3.4 Low Density Parity Check (LDPC) CodeSubframe 2 and subframe 3 are separately encoded using rate ½ LDPC codes.
Subframe 2 has atotal of 600 bits consisting of 576 bits for Clock and Ephemeris and 24 bits for CRC. Subframe3 has a total of 274 bits consisting of 250 bits for Variable Data and 24 bits for CRC. As a resultof rate ½ LDPC encoding, there are 1200 symbols (coded bits) for Subframe 2 and 548 symbolsfor Subframe 3 as described in Figure 3.2-3.The LDPC encoder structure is based on a parity-check matrix H(m, n) of m rows and ncolumns. For Subframe 2, m = 600, n=1200 and for Subframe 3, m = 274, n = 548. H(m, n) isfurther decomposed into 6 submatrices A, B, T, C, D, and E as shown in Figure 3.2-5 (seereference document [1]). Each element of matrix H(m, n) is either a value of “0” or “1”.22IS-GPS-800D24 Sep 2013Figure 3.2-5. Parity Check Matrix H for LDPC CodeTables 6.2-2, 6.2-3, 6.2-4, 6.2-5, 6.2-6, and 6.2-7 shall define the coordinates of elements withvalue “1” in each of the submatrices A, B, C, D, E, and T, respectively, for Subframe 2.Tables 6.2-8, 6.2-9, 6.2-10, 6.2-11, 6.2-12, and 6.2-13 shall define the coordinates of elementswith value “1” in each of the submatrices A, B, C, D, E, and T, respectively, for Subframe 3.The inverse of T is not included in this document, however T is a lower triangular matrix andtherefore, the inverse of T can be easily identified.The rate ½ LDPC encoder shall use the given matrices A, B, T, C, D, and E of Section 6.2.4 togenerate the encoded symbols using the following algorithm:p1t = −φ−1 ⋅ (−E ⋅ T−1 ⋅ A + C) ⋅ s tp2t = −Τ−1 ⋅ (A ⋅ s t + B ⋅ p1t)where,φ = −E ⋅ T−1 ⋅ B + D,23IS-GPS-800D24 Sep 2013s = subframe 2 or subframe 3 data,[ ] t indicates transpose,and elements of matrices p1 and p2 are modulo 2 numbers.The encoded symbols for broadcast are comprised of (s;p1;p2) where s is the systematic portionof the codeword, and {p1, p2} comprise the combined parity bits.3.2.3.5 InterleavingThe 1748 encoded symbols of subframes 2 and 3 are combined and interleaved using a blockinterleaver.
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