kopia lustrzana https://github.com/M17-Project/M17_spec
Begins reorganization of Physical and Data Link Layers
This is a work in progress. Items not part of the actual Physical layer have been moved to placeholder spots in the Data Link Layer document. A first pass at Physical layer reordering, slight rewording, and an attempt to use consistent formatting (especially with bytes and symbols).pull/101/head
Jay Francis
rodzic
933e260c13
commit
26c65f56b1
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@ -5,12 +5,12 @@ taxonomy:
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- docs
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simple-responsive-tables:
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active: true
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media_order: 'convolutional.svg,frame_encoding.svg,link_setup_frame_encoding.svg,packet_frame_encoding.svg'
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media_order:
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---
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### 4FSK generation
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### 4-level Frequency-shift Keying Modulation (4FSK)
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M17 standard uses 4FSK modulation running at 4800 symbols/s (9600
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M17 standard uses 4FSK running at 4800 symbols/s (9600
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bits/s) with a deviation index h=0.33 for transmission in 9 kHz
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channel bandwidth. Channel spacing is 12.5 kHz. The symbol stream is
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converted (upsampled) to a series of impulses which pass through a
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@ -18,6 +18,8 @@ root-raised-cosine (alpha=0.5) shaping filter before frequency modulation
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at the transmitter and again after frequency demodulation at the
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receiver.
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!!! Do we need to specify minimal/recommended upsampling rates and minimal/recommended number of RRC taps? !!!
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[mermaid]
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graph LR
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id1[Dibits Input] --> id2[Upsampler] --> id3[RRC Filter] --> id4[Frequency Modulation] --> id5[4FSK Output]
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@ -28,7 +30,11 @@ graph LR
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style id5 fill:#ffffffff,stroke:#ffffffff,stroke-width:0px
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[/mermaid]
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The bit-to-symbol mapping is shown in the table below.
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### Dibit, Symbol, and Frequency-shift
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Each of the 4-level frequency-shifts can be represented by dibits (2-bit values) or symbols, as shown in the table below.
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In the case of dibits, the most significant bits are sent first. For example, the four dibits contained in the byte 0xB4 (0b 10 11 01 00) would be sent as the symbols (-1, -3, +3, +1).
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<table>
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<caption><span>Table 1 </span><span>Dibit symbol mapping to 4FSK deviation</span></caption>
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@ -71,204 +77,39 @@ The bit-to-symbol mapping is shown in the table below.
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</tbody>
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</table>
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The most significant bits are sent first, meaning that the byte 0xB4 (= 0b10'11'01'00) in type 4 bits (see [bit types](#bit-types)) would be sent as the symbols -1 -3 +3 +1. All data fields utilize big-endian order of bytes unless specified otherwise.
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### Preamble
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Every transmission starts with a preamble, which shall consist of at least 40 ms of alternating outer symbols. This is equivalent to 40 milliseconds of a 2400 Hz tone. The last symbol transmitted within the preamble shall be -3 for all modes except BERT. This is to avoid unnecessary long constant symbol runs and increase zero-crossing rate.
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Every transmission shall start with a preamble, which shall consist of at least 40 ms of alternating outer symbols (+3, -3) !!! maximum duration recommendation? !!!. This is equivalent to 40 milliseconds of a 2400 Hz tone. The last symbol transmitted within the preamble shall be -3 for all modes except BERT. !!! check? don't understand !!! This is to avoid unnecessary long constant symbol runs and increase zero-crossing rate.
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### Bit types
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### Frame
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The bits at different stages of the error correction coding are referred to with bit types, given in the following table.
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A frame shall be composed of a Sync Burst followed by a Payload. There are four frame types: Link Setup Frames (LSF), Stream Frames, Packet Frames, and
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Bit Error Rate Test (BERT) frames.
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Type | Description
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---- | -----------
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Type 1 | Data link layer bits
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Type 2 | Bits after appropriate encoding
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Type 3 | Bits after puncturing (only for convolutionally coded data, for other ECC schemes type 3 bits are the same as type 2 bits)
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Type 4 | Decorrelated and interleaved (re-ordered) type 3 bits
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### Synchronization Burst (Sync Burst)
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Type 4 bits are used for transmission over the RF. Incoming type 4 bits shall be decoded to type 1 bits, which are then used to extract all the frame fields.
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All frames shall be preceded by 16 bits (8 symbols) of *synchronization burst*.
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### Error correction coding schemes and bit type conversion
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* LSF shall be preceded with 0x55F7 (+3, +3, +3, +3, -3, -3, +3, -3)
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* Stream frames shall be preceeded with 0xFF5D (-3, -3, -3, -3, +3, +3, -3, +3)
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* Packet frames shall be preceeded with 0x75FF (+3, -3, +3, +3, -3, -3, -3, -3)
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* BERT frames shall be preceeded with 0xDF55 (-3, +3, -3, -3, +3, +3, +3, +3)
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Two distinct ECC/FEC schemes are used for different parts of the transmission.
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The Sync Burst codings are based on [Barker codes](https://en.wikipedia.org/wiki/Barker_code). !!! need reference for 4-level Barker Sequences !!!
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#### Link setup frame (LSF)
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### Payload
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The Payload consists of 368 bits (192 symbols).
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240 DST, SRC, TYPE, META and CRC type 1 bits are convolutionally coded using rate 1/2 coder with constraint K=5. 4 tail bits are used to flush the encoder’s state register, giving a total of 244 bits being encoded. Resulting 488 type 2 bits are retained for type 3 bits computation. Type 3 bits are computed by puncturing type 2 bits using a scheme shown in chapter 4.4. This results in 368 bits, which in conjunction with the synchronization burst gives 384 bits (384 bits / 9600bps = 40 ms).
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#### Randomizer
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Interleaving type 3 bits produce type 4 bits that are ready to be transmitted. Interleaving is used to combat error bursts.
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To avoid transmitting long sequences of constant symbols (e.g. +3, +3, +3, ...), a simple randomizing algorithm is used. At the transmitter, all 368 payload bits shall be XORed with a pseudorandom predefined stream before being converted to symbols. At the receiver, payload symbols are converted to bits and are
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again passed through the same XOR algorithm to obtain the original payload bits.
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#### Subsequent frames
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!!! algorithm should be here !!!
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### End of Transmission marker (EoT)
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A 40-bit (type 1) chunk of the LSF along with a 3-bit modulo 6 counter (LICH_CNT) and 5 reserved bits (see Table 7) is partitioned into 4 12-bit parts and encoded using Golay (24, 12) code. This produces 96 encoded bits of type 2. These bits are used in the Link Information Channel (LICH).
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Every transmission ends with a distinct symbol stream, which shall consist of at least 40 ms !!! but not longer than??? !!! of a repeating 0x555D (+3, +3, +3, +3, +3, +3, -3, +3) pattern.
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16-bit FN and 128 bits of payload (144 bits total) are convolutionally encoded in a manner analogous to that of the link setup frame. A total of 148 bits is being encoded resulting in 296 type 2 bits. These bits are punctured to generate 272 type 3 bits.
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96 type 2 bits of LICH are concatenated with 272 type 3 bits and re-ordered to form type 4 bits for transmission. This, along with 16-bit sync in the beginning of frame, gives a total of 384 bits
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The LICH chunks allow for late listening and indepedent decoding to check destination address. The goal is to require less complexity to decode just the LICH and check if the full message should be decoded.
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#### Packet Frame Encoding
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#### End of Transmission marker (EoT)
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Every transmission ends with a distinct symbol stream, which shall consist of at least 40 ms of repeating +3, +3, +3, +3, +3, +3, -3, +3 pattern, or 0x555D in hexadecimal notation.
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#### Extended Golay(24,12) code
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The extended Golay(24,12) encoder uses generating polynomial g given below to generate the 11 check bits. The check bits and an additional parity bit are appended to the 12 bit data, resulting in a 24 bit codeword. The resulting code is systematic, meaning that the input data (message) is embedded in the codeword.
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\(g(x) = x^{11} + x^{10} + x^6 + x^5 + x^4 + x^2 + 1\)
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This is equivalent to 0xC75 in hexadecimal notation. Both the generating matrix \(G\) and parity check matrix \(H\) are shown below.
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\(
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\begin{align}
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G = \begin{bmatrix} I_k | P \end{bmatrix} = & \begin{bmatrix}
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1&0&0&0&0&0&0&0&0&0&0&0&1&1&0&0&0&1&1&1&0&1&0&1\\
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0&1&0&0&0&0&0&0&0&0&0&0&0&1&1&0&0&0&1&1&1&0&1&1\\
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0&0&1&0&0&0&0&0&0&0&0&0&1&1&1&1&0&1&1&0&1&0&0&0\\
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0&0&0&1&0&0&0&0&0&0&0&0&0&1&1&1&1&0&1&1&0&1&0&0\\
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0&0&0&0&1&0&0&0&0&0&0&0&0&0&1&1&1&1&0&1&1&0&1&0\\
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0&0&0&0&0&1&0&0&0&0&0&0&1&1&0&1&1&0&0&1&1&0&0&1\\
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0&0&0&0&0&0&1&0&0&0&0&0&0&1&1&0&1&1&0&0&1&1&0&1\\
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0&0&0&0&0&0&0&1&0&0&0&0&0&0&1&1&0&1&1&0&0&1&1&1\\
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0&0&0&0&0&0&0&0&1&0&0&0&1&1&0&1&1&1&0&0&0&1&1&0\\
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0&0&0&0&0&0&0&0&0&1&0&0&1&0&1&0&1&0&0&1&0&1&1&1\\
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0&0&0&0&0&0&0&0&0&0&1&0&1&0&0&1&0&0&1&1&1&1&1&0\\
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0&0&0&0&0&0&0&0&0&0&0&1&1&0&0&0&1&1&1&0&1&0&1&1\\
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\end{bmatrix}
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\newline\newline
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H = \begin{bmatrix} P^T | I_k \end{bmatrix} = & \begin{bmatrix}
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1&0&1&0&0&1&0&0&1&1&1&1&1&0&0&0&0&0&0&0&0&0&0&0\\
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1&1&1&1&0&1&1&0&1&0&0&0&0&1&0&0&0&0&0&0&0&0&0&0\\
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0&1&1&1&1&0&1&1&0&1&0&0&0&0&1&0&0&0&0&0&0&0&0&0\\
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0&0&1&1&1&1&0&1&1&0&1&0&0&0&0&1&0&0&0&0&0&0&0&0\\
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0&0&0&1&1&1&1&0&1&1&0&1&0&0&0&0&1&0&0&0&0&0&0&0\\
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1&0&1&0&1&0&1&1&1&0&0&1&0&0&0&0&0&1&0&0&0&0&0&0\\
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1&1&1&1&0&0&0&1&0&0&1&1&0&0&0&0&0&0&1&0&0&0&0&0\\
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1&1&0&1&1&1&0&0&0&1&1&0&0&0&0&0&0&0&0&1&0&0&0&0\\
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0&1&1&0&1&1&1&0&0&0&1&1&0&0&0&0&0&0&0&0&1&0&0&0\\
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1&0&0&1&0&0&1&1&1&1&1&0&0&0&0&0&0&0&0&0&0&1&0&0\\
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0&1&0&0&1&0&0&1&1&1&1&1&0&0&0&0&0&0&0&0&0&0&1&0\\
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1&1&0&0&0&1&1&1&0&1&0&1&0&0&0&0&0&0&0&0&0&0&0&1\\
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\end{bmatrix}
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\end{align}
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\)
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The output of the Golay encoder is shown in the table below.
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Field | Data | Check bits | Parity
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----- | ---- | ---------- | ------
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Position | 23..12 | 11..1 | 0 (LSB)
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Length | 12 | 11 | 1
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Four of these 24-bit blocks are used to reconstruct the LSF.
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Sample MATLAB/Octave code snippet for generating \(G\) and \(H\) matrices is shown below.
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```
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P = hex2poly('0xC75');
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[H,G] = cyclgen(23, P);
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G_P = G(1:12, 1:11);
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I_K = eye(12);
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G = [I_K G_P P.'];
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H = [transpose([G_P P.']) I_K];
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```
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### Convolutional encoder
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The convolutional code shall encode the input bit sequence after appending 4 tail bits at the end of the sequence. Rate of the coder is R=½ with constraint length K=5. The encoder diagram and generating polynomials are shown below.
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\(
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\begin{align}
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G_1(D) =& 1 + D^3 + D^4 \\
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G_2(D) =& 1+ D + D^2 + D^4
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\end{align}
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\)
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The output from the encoder must be read alternately.
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### Code puncturing
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Removing some of the bits from the convolutional coder’s output is called code puncturing. The nominal coding rate of the encoder used in M17 is ½. This means the encoder outputs two bits for every bit of the input data stream. To get other (higher) coding rates, a puncturing scheme has to be used.
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Two different puncturing schemes are used in M17 stream mode:
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1. \(P_1\) leaving 46 from 61 encoded bits
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2. \(P_2\) leaving 11 from 12 encoded bits
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Scheme \(P_1\) is used for the *link setup frame*, taking 488 bits of encoded data and selecting 368 bits. The \(gcd(368, 488)\) is 8 which, when used to divide, leaves 46 and 61 bits. However, a full puncture pattern requires the puncturing matrix entries count to be divisible by the number of encoding polynomials. For this case a partial puncture matrix is used. It has 61 entries with 46 of them being ones and shall be used 8 times, repeatedly. The construction of the partial puncturing pattern \(P_1\) is as follows:
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\(
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\begin{align}
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M = & \begin{bmatrix}
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1 & 0 & 1 & 1
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\end{bmatrix} \\
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P_{1} = & \begin{bmatrix}
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1 & M_{1} & \cdots & M_{15}
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\end{bmatrix}
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\end{align}
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\)
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In which \(M\) is a standard 2/3 rate puncture matrix and is used 15 times, along with a leading \(1\) to form \(P_1\), an array of length 61.
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The first pass of the partial puncturer discards \(G_1\) bits only, second pass discards \(G_2\), third - \(G_1\) again, and so on. This ensures that both bits are punctured out evenly.
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Scheme \(P_2\) is for frames (excluding LICH chunks, which are coded differently). This takes 296 encoded bits and selects 272 of them. Every 12th bit is being punctured out, leaving 272 bits. The full matrix shall have 12 entries with 11 being ones.
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The puncturing scheme \(P_2\) is defined by its partial puncturing matrix:
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\(
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\begin{align}
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P_2 = & \begin{bmatrix}
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1 & 1 & 1 & 1 & 1 & 1 \\
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1 & 1 & 1 & 1 & 1 & 0
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\end{bmatrix}
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\end{align}
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\)
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The linearized representations are:
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```
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P1 = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1,
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1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
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0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]
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P2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
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```
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One additional puncturing scheme \(P_3\) is used in the packet mode. The puncturing scheme is defined by its puncturing matrix:
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\(
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\begin{align}
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P_3 = & \begin{bmatrix}
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1 & 1 & 1 & 1 \\
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1 & 1 & 1 & 0
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\end{bmatrix}
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\end{align}
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\)
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The linearized representation is:
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```
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P3 = [1, 1, 1, 1, 1, 1, 1, 0]
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```
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### Interleaving
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For interleaving a Quadratic Permutation Polynomial (QPP) is used. The polynomial \(\pi(x)=(45x+92x^2)\mod 368\) is used for a 368 bit interleaving pattern QPP. See appendix sec-interleaver for pattern.
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To avoid transmitting long sequences of constant symbols (e.g. 010101…), a simple algorithm is used. All 46 bytes of type 4 bits shall be XORed with a pseudorandom, predefined stream. The same algorithm has to be used for incoming bits at the receiver to get the original data stream. See decorr-seq for sequence.
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Przed Szerokość: | Wysokość: | Rozmiar: 20 KiB Po Szerokość: | Wysokość: | Rozmiar: 20 KiB |
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@ -3,7 +3,7 @@ title: 'Data Link Layer'
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taxonomy:
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category:
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- docs
|
||||
media_order: M17_stream.png
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media_order: 'M17_stream.png,convolutional.svg,frame_encoding.svg,link_setup_frame_encoding.svg,packet_frame_encoding.svg'
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---
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The Data Link layer is split into three modes:
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@ -26,18 +26,6 @@ encoded in big endian byte order.
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In Stream Mode, an *indefinite* amount of payload data is sent continuously without breaks in the physical layer. The *stream* is broken up into parts, called *frames* to not confuse them with *packets* sent in packet mode. Frames contain payload data interleaved with frame signalling (similar to packets). Frame signalling is contained within the **Link Information Channel (LICH)**.
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#### Sync Burst
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All frames are preceded by a 16-bit *synchronization burst*.
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* Link setup frames shall be preceded with 0x55F7.
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* Stream frames shall be preceeded with 0xFF5D.
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* Packet frames shall be preceeded with 0x75FF.
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* BERT frames shall be preceeded with 0xDF55.
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All syncwords are type 4 bits.
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These sync words are based on [Barker codes](https://en.wikipedia.org/wiki/Barker_code).
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#### Link setup frame
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@ -255,3 +243,201 @@ Bits | Meaning
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When sending packets, the sender is reponsible for ensuring the channel is clear before transmitting. CSMA is used to minimize collisions on a shared network. Specifically, P-persistent access is used. Each time slot is 40ms (one packet length) and the probability SHOULD default to 25%. In terms of the values used by the KISS protocol, these equate to a slot time of 4 and a P-persistence value of 63.
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The benefit of this method is that it imposes no penalty on uncontested networks.
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### Bit types
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The bits at different stages of the error correction coding are referred to with bit types, given in the following table.
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Type | Description
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---- | -----------
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Type 1 | Data link layer bits
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Type 2 | Bits after appropriate encoding
|
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Type 3 | Bits after puncturing (only for convolutionally coded data, for other ECC schemes type 3 bits are the same as type 2 bits)
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Type 4 | Decorrelated and interleaved (re-ordered) type 3 bits
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Type 4 bits are used for transmission over the RF. Incoming type 4 bits shall be decoded to type 1 bits, which are then used to extract all the frame fields.
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### Error correction coding schemes and bit type conversion
|
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|
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Two distinct ECC/FEC schemes are used for different parts of the transmission.
|
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|
||||
#### Link setup frame (LSF)
|
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|
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|
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|
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240 DST, SRC, TYPE, META and CRC type 1 bits are convolutionally coded using rate 1/2 coder with constraint K=5. 4 tail bits are used to flush the encoder’s state register, giving a total of 244 bits being encoded. Resulting 488 type 2 bits are retained for type 3 bits computation. Type 3 bits are computed by puncturing type 2 bits using a scheme shown in chapter 4.4. This results in 368 bits, which in conjunction with the synchronization burst gives 384 bits (384 bits / 9600bps = 40 ms).
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|
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Interleaving type 3 bits produce type 4 bits that are ready to be transmitted. Interleaving is used to combat error bursts.
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|
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#### Subsequent frames
|
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|
||||
|
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|
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A 40-bit (type 1) chunk of the LSF along with a 3-bit modulo 6 counter (LICH_CNT) and 5 reserved bits (see Table 7) is partitioned into 4 12-bit parts and encoded using Golay (24, 12) code. This produces 96 encoded bits of type 2. These bits are used in the Link Information Channel (LICH).
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|
||||
16-bit FN and 128 bits of payload (144 bits total) are convolutionally encoded in a manner analogous to that of the link setup frame. A total of 148 bits is being encoded resulting in 296 type 2 bits. These bits are punctured to generate 272 type 3 bits.
|
||||
|
||||
96 type 2 bits of LICH are concatenated with 272 type 3 bits and re-ordered to form type 4 bits for transmission. This, along with 16-bit sync in the beginning of frame, gives a total of 384 bits
|
||||
|
||||
The LICH chunks allow for late listening and indepedent decoding to check destination address. The goal is to require less complexity to decode just the LICH and check if the full message should be decoded.
|
||||
|
||||
#### Packet Frame Encoding
|
||||
|
||||
|
||||
|
||||
|
||||
All data fields utilize big-endian order of bytes unless specified otherwise.
|
||||
|
||||
|
||||
#### Extended Golay(24,12) code
|
||||
|
||||
The extended Golay(24,12) encoder uses generating polynomial g given below to generate the 11 check bits. The check bits and an additional parity bit are appended to the 12 bit data, resulting in a 24 bit codeword. The resulting code is systematic, meaning that the input data (message) is embedded in the codeword.
|
||||
|
||||
\(g(x) = x^{11} + x^{10} + x^6 + x^5 + x^4 + x^2 + 1\)
|
||||
|
||||
This is equivalent to 0xC75 in hexadecimal notation. Both the generating matrix \(G\) and parity check matrix \(H\) are shown below.
|
||||
|
||||
\(
|
||||
\begin{align}
|
||||
G = \begin{bmatrix} I_k | P \end{bmatrix} = & \begin{bmatrix}
|
||||
1&0&0&0&0&0&0&0&0&0&0&0&1&1&0&0&0&1&1&1&0&1&0&1\\
|
||||
0&1&0&0&0&0&0&0&0&0&0&0&0&1&1&0&0&0&1&1&1&0&1&1\\
|
||||
0&0&1&0&0&0&0&0&0&0&0&0&1&1&1&1&0&1&1&0&1&0&0&0\\
|
||||
0&0&0&1&0&0&0&0&0&0&0&0&0&1&1&1&1&0&1&1&0&1&0&0\\
|
||||
0&0&0&0&1&0&0&0&0&0&0&0&0&0&1&1&1&1&0&1&1&0&1&0\\
|
||||
0&0&0&0&0&1&0&0&0&0&0&0&1&1&0&1&1&0&0&1&1&0&0&1\\
|
||||
0&0&0&0&0&0&1&0&0&0&0&0&0&1&1&0&1&1&0&0&1&1&0&1\\
|
||||
0&0&0&0&0&0&0&1&0&0&0&0&0&0&1&1&0&1&1&0&0&1&1&1\\
|
||||
0&0&0&0&0&0&0&0&1&0&0&0&1&1&0&1&1&1&0&0&0&1&1&0\\
|
||||
0&0&0&0&0&0&0&0&0&1&0&0&1&0&1&0&1&0&0&1&0&1&1&1\\
|
||||
0&0&0&0&0&0&0&0&0&0&1&0&1&0&0&1&0&0&1&1&1&1&1&0\\
|
||||
0&0&0&0&0&0&0&0&0&0&0&1&1&0&0&0&1&1&1&0&1&0&1&1\\
|
||||
\end{bmatrix}
|
||||
\newline\newline
|
||||
H = \begin{bmatrix} P^T | I_k \end{bmatrix} = & \begin{bmatrix}
|
||||
1&0&1&0&0&1&0&0&1&1&1&1&1&0&0&0&0&0&0&0&0&0&0&0\\
|
||||
1&1&1&1&0&1&1&0&1&0&0&0&0&1&0&0&0&0&0&0&0&0&0&0\\
|
||||
0&1&1&1&1&0&1&1&0&1&0&0&0&0&1&0&0&0&0&0&0&0&0&0\\
|
||||
0&0&1&1&1&1&0&1&1&0&1&0&0&0&0&1&0&0&0&0&0&0&0&0\\
|
||||
0&0&0&1&1&1&1&0&1&1&0&1&0&0&0&0&1&0&0&0&0&0&0&0\\
|
||||
1&0&1&0&1&0&1&1&1&0&0&1&0&0&0&0&0&1&0&0&0&0&0&0\\
|
||||
1&1&1&1&0&0&0&1&0&0&1&1&0&0&0&0&0&0&1&0&0&0&0&0\\
|
||||
1&1&0&1&1&1&0&0&0&1&1&0&0&0&0&0&0&0&0&1&0&0&0&0\\
|
||||
0&1&1&0&1&1&1&0&0&0&1&1&0&0&0&0&0&0&0&0&1&0&0&0\\
|
||||
1&0&0&1&0&0&1&1&1&1&1&0&0&0&0&0&0&0&0&0&0&1&0&0\\
|
||||
0&1&0&0&1&0&0&1&1&1&1&1&0&0&0&0&0&0&0&0&0&0&1&0\\
|
||||
1&1&0&0&0&1&1&1&0&1&0&1&0&0&0&0&0&0&0&0&0&0&0&1\\
|
||||
\end{bmatrix}
|
||||
\end{align}
|
||||
\)
|
||||
|
||||
The output of the Golay encoder is shown in the table below.
|
||||
|
||||
Field | Data | Check bits | Parity
|
||||
----- | ---- | ---------- | ------
|
||||
Position | 23..12 | 11..1 | 0 (LSB)
|
||||
Length | 12 | 11 | 1
|
||||
|
||||
Four of these 24-bit blocks are used to reconstruct the LSF.
|
||||
|
||||
Sample MATLAB/Octave code snippet for generating \(G\) and \(H\) matrices is shown below.
|
||||
|
||||
```
|
||||
|
||||
P = hex2poly('0xC75');
|
||||
[H,G] = cyclgen(23, P);
|
||||
|
||||
G_P = G(1:12, 1:11);
|
||||
I_K = eye(12);
|
||||
G = [I_K G_P P.'];
|
||||
H = [transpose([G_P P.']) I_K];
|
||||
```
|
||||
|
||||
### Convolutional encoder
|
||||
|
||||
The convolutional code shall encode the input bit sequence after appending 4 tail bits at the end of the sequence. Rate of the coder is R=½ with constraint length K=5. The encoder diagram and generating polynomials are shown below.
|
||||
|
||||
\(
|
||||
\begin{align}
|
||||
G_1(D) =& 1 + D^3 + D^4 \\
|
||||
G_2(D) =& 1+ D + D^2 + D^4
|
||||
\end{align}
|
||||
\)
|
||||
|
||||
The output from the encoder must be read alternately.
|
||||
|
||||
|
||||
|
||||
### Code puncturing
|
||||
|
||||
Removing some of the bits from the convolutional coder’s output is called code puncturing. The nominal coding rate of the encoder used in M17 is ½. This means the encoder outputs two bits for every bit of the input data stream. To get other (higher) coding rates, a puncturing scheme has to be used.
|
||||
|
||||
Two different puncturing schemes are used in M17 stream mode:
|
||||
|
||||
1. \(P_1\) leaving 46 from 61 encoded bits
|
||||
2. \(P_2\) leaving 11 from 12 encoded bits
|
||||
|
||||
Scheme \(P_1\) is used for the *link setup frame*, taking 488 bits of encoded data and selecting 368 bits. The \(gcd(368, 488)\) is 8 which, when used to divide, leaves 46 and 61 bits. However, a full puncture pattern requires the puncturing matrix entries count to be divisible by the number of encoding polynomials. For this case a partial puncture matrix is used. It has 61 entries with 46 of them being ones and shall be used 8 times, repeatedly. The construction of the partial puncturing pattern \(P_1\) is as follows:
|
||||
|
||||
\(
|
||||
\begin{align}
|
||||
M = & \begin{bmatrix}
|
||||
1 & 0 & 1 & 1
|
||||
\end{bmatrix} \\
|
||||
P_{1} = & \begin{bmatrix}
|
||||
1 & M_{1} & \cdots & M_{15}
|
||||
\end{bmatrix}
|
||||
\end{align}
|
||||
\)
|
||||
|
||||
In which \(M\) is a standard 2/3 rate puncture matrix and is used 15 times, along with a leading \(1\) to form \(P_1\), an array of length 61.
|
||||
|
||||
The first pass of the partial puncturer discards \(G_1\) bits only, second pass discards \(G_2\), third - \(G_1\) again, and so on. This ensures that both bits are punctured out evenly.
|
||||
|
||||
Scheme \(P_2\) is for frames (excluding LICH chunks, which are coded differently). This takes 296 encoded bits and selects 272 of them. Every 12th bit is being punctured out, leaving 272 bits. The full matrix shall have 12 entries with 11 being ones.
|
||||
|
||||
The puncturing scheme \(P_2\) is defined by its partial puncturing matrix:
|
||||
|
||||
\(
|
||||
\begin{align}
|
||||
P_2 = & \begin{bmatrix}
|
||||
1 & 1 & 1 & 1 & 1 & 1 \\
|
||||
1 & 1 & 1 & 1 & 1 & 0
|
||||
\end{bmatrix}
|
||||
\end{align}
|
||||
\)
|
||||
|
||||
The linearized representations are:
|
||||
|
||||
```
|
||||
P1 = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1,
|
||||
1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
|
||||
0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]
|
||||
|
||||
P2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
|
||||
```
|
||||
|
||||
One additional puncturing scheme \(P_3\) is used in the packet mode. The puncturing scheme is defined by its puncturing matrix:
|
||||
|
||||
\(
|
||||
\begin{align}
|
||||
P_3 = & \begin{bmatrix}
|
||||
1 & 1 & 1 & 1 \\
|
||||
1 & 1 & 1 & 0
|
||||
\end{bmatrix}
|
||||
\end{align}
|
||||
\)
|
||||
|
||||
The linearized representation is:
|
||||
|
||||
```
|
||||
P3 = [1, 1, 1, 1, 1, 1, 1, 0]
|
||||
```
|
||||
|
||||
### Interleaving
|
||||
|
||||
For interleaving a Quadratic Permutation Polynomial (QPP) is used. The polynomial \(\pi(x)=(45x+92x^2)\mod 368\) is used for a 368 bit interleaving pattern QPP. See appendix sec-interleaver for pattern.
|
||||
|
||||
|
|
|
|||
|
Przed Szerokość: | Wysokość: | Rozmiar: 16 KiB Po Szerokość: | Wysokość: | Rozmiar: 16 KiB |
|
Przed Szerokość: | Wysokość: | Rozmiar: 14 KiB Po Szerokość: | Wysokość: | Rozmiar: 14 KiB |
|
Przed Szerokość: | Wysokość: | Rozmiar: 12 KiB Po Szerokość: | Wysokość: | Rozmiar: 12 KiB |
Ładowanie…
Reference in New Issue