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ft8.py
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ft8.py
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#!/usr/local/bin/python
#
# encode and decode FT8.
#
# for new 77-bit FT8.
# LDPC tables and pack/unpack details from wsjt-x 2.0.
#
# Robert Morris, AB1HL
#
import numpy
import wave
import scipy
import scipy.signal
import sys
import os
import math
import time
import multiprocessing
import threading
import re
import random
import ctypes
import weakaudio
import weakutil
#
# tuning parameters.
#
budget = 2.2 # max seconds of time for decoding.
pass0_fstep = 2 # coarse search granularity, per FFT bin
pass0_tstep = 2 # coarse search granularity, per symbol time
passN_fstep = 2 # coarse search granularity, per FFT bin
passN_tstep = 4 # coarse search granularity, per symbol time
pass0_tminus = 2.2 # start search this many seconds before 0.5
pass0_tplus = 2.7 # end search this many seconds after 0.5
passN_tminus = 1.5
passN_tplus = 1.8
coarse_no = 1 # number of best offsets to use per hz
fine_no = 1 # number of best fine offsets to look at
fine_fstep = 4 # fine-tuning steps per coarse_fstep
fine_tstep = 8 # fine-tuning steps per coarse_tstep
start_adj = 0.1 # signals seem on avg to start this many seconds late.
ldpc_iters = 30 # how hard LDPC should work on pass 0
softboost = 1.0 # log(prob) if #2 symbol has same bit value
do_subtract = 1 # 0 none, 1 once per unique decode, 2 three per unique, 3 once per decode
subgap = 0.8 # extra subtract()s this many hz on either side of main bin
substeps = 16 # subtract phase steps, in 2pi
subpasses = 2 # 0 means no subtraction, 1 means subtract, 2 means another subtraction pass
pass0_frac = 1.0
pass0_hints = True # hints in pass 0 (as well as later passes)?
contrast_weight = 0.5
noise_factor = 0.8 # for strength()
top_high_order = 0 # 0 for cheby, 19 for butter
high_cutoff = 1.05
low_pass_order = 0 # 15
top_down = True
bottom_slow = True
osd_crc = False # True means OSD only accepts if CRC is correct
osd0_crc = True # True means OSD accepts if depth=0 CRC is correct
osd_depth = 6
osd_thresh = -500
already_o = 1
already_f = 1
down200 = False # process1() that down-converts to 200 hz / 32 samples/symbol
use_apriori = True
nchildren = 4
child_overlap = 30
osd_no_snr = False
padfactor = 0.1 # quiet-ish before/after padding
osd_hints = False # use OSD on hints BUT causes lots of false pseudo-juicy CQs!
down_cutoff = 0.45 # low-pass filter cutoff before down-sampling
cheb_cut1 = 0.48
cheb_cut2 = 0.61
cheb_ripple_pass = 0.5
cheb_atten_stop = 50
cheb_high_minus = 40
cheb_high_plus = 60
hint_tol = 9 # look for CQ XXX hints in this +/- hz range of where heard
crc_and_83 = True # True means require both CRC and LDPC
ldpc_thresh = 83 # 83 means all LDPC check-bits must be correct
snr_overlap = 3 # -1 means don't convert to snr, 0 means each sym time by itself
snr_wintype = "blackman"
real_min_hz = 150
real_max_hz = 2900
sub_amp_win = 2
adjust_hz_for_sub = True
adjust_off_for_sub = True
yes_mul = 1.0
yes_add = 0.0
no_mul = 1.0
no_add = 0.0
soft1 = 7
soft2 = 8
soft3 = 4
soft4 = 6
guard200 = 10
order200 = 5
strength_div = 4.0
decimate_order = 8
# FT8 modulation and protocol definitions.
# 1920-point FFT at 12000 samples/second
# yields 6.25 Hz spacing, 0.16 seconds/symbol
# encode chain:
# 77 bits
# append 14 bits CRC (for 91 bits)
# LDPC(174,91) yields 174 bits
# that's 58 3-bit FSK-8 symbols
# gray code each 3 bits
# insert three 7-symbol Costas sync arrays
# at symbol #s 0, 36, 72 of final signal
# thus: 79 FSK-8 symbols
# total transmission time is 12.64 seconds
costas_symbols = [ 3, 1, 4, 0, 6, 5, 2 ] # new FT8
# gray map for encoding 3-bit chunks of the 174 bits,
# after LDPC and before generating FSK-8 tones.
graymap = [ 0, 1, 3, 2, 5, 6, 4, 7 ]
# the CRC-14 polynomial, from wsjt-x's 0x2757,
# with leading 1 bit.
crc14poly = [ 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1 ]
def crc_c(msg):
msgtype = ctypes.c_int * len(msg)
outtype = ctypes.c_int * 14
msg1 = msgtype()
for i in range(0, len(msg)):
msg1[i] = msg[i]
out1 = outtype()
libldpc.ft8_crc(msg1, len(msg), out1)
out = numpy.zeros(14, dtype=numpy.int32)
for i in range(0, 14):
out[i] = out1[i]
return out
#
# thank you, evan sneath.
# https://gist.github.com/evansneath/4650991
#
# generate with x^3 + x + 1:
# >>> xc.crc([1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0], [1, 0, 1, 1])
# array([1, 0, 0])
# check:
# >>> xc.crc([1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0], [1, 0, 1, 1], [1, 0, 0])
# array([0, 0, 0])
#
# 0xc06 is really 0x1c06 or [ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0 ]
#
def crc_python(msg, div, code=None):
"""Cyclic Redundancy Check
Generates an error detecting code based on an inputted message
and divisor in the form of a polynomial representation.
Arguments:
msg: The input message of which to generate the output code.
div: The divisor in polynomial form. For example, if the polynomial
of x^3 + x + 1 is given, this should be represented as '1011' in
the div argument.
code: This is an option argument where a previously generated code may
be passed in. This can be used to check validity. If the inputted
code produces an outputted code of all zeros, then the message has
no errors.
Returns:
An error-detecting code generated by the message and the given divisor.
"""
# Append the code to the message. If no code is given, default to '000'
if code is None:
code = numpy.zeros(len(div)-1, dtype=numpy.int32)
assert len(code) == len(div) - 1
msg = numpy.append(msg, code)
div = numpy.array(div, dtype=numpy.int32)
divlen = len(div)
# Loop over every message bit (minus the appended code)
for i in range(len(msg)-len(code)):
# If that messsage bit is 1, perform modulo 2 multiplication
if msg[i] == 1:
#for j in range(len(div)):
# # Perform modulo 2 multiplication on each index of the divisor
# msg[i+j] = (msg[i+j] + div[j]) % 2
msg[i:i+divlen] = numpy.mod(msg[i:i+divlen] + div, 2)
# Output the last error-checking code portion of the message generated
return msg[-len(code):]
def crc(msg, div):
if True:
return crc_c(msg)
else:
return crc_python(msg, div)
def check_crc(a91):
padded = numpy.append(a91[0:77], numpy.zeros(5, dtype=numpy.int32))
cksum = crc(padded, crc14poly)
if numpy.array_equal(cksum, a91[-14:]) == False:
# CRC failed.
return False
return True
# this is the LDPC(174,91) parity check matrix.
# each row describes one parity check.
# each number is an index into the codeword (1-origin).
# the codeword bits mentioned in each row must xor to zero.
# From WSJT-X's ldpc_174_91_c_reordered_parity.f90
Nm = [
[ 4, 31, 59, 91, 92, 96, 153 ],
[ 5, 32, 60, 93, 115, 146, 0 ],
[ 6, 24, 61, 94, 122, 151, 0 ],
[ 7, 33, 62, 95, 96, 143, 0 ],
[ 8, 25, 63, 83, 93, 96, 148 ],
[ 6, 32, 64, 97, 126, 138, 0 ],
[ 5, 34, 65, 78, 98, 107, 154 ],
[ 9, 35, 66, 99, 139, 146, 0 ],
[ 10, 36, 67, 100, 107, 126, 0 ],
[ 11, 37, 67, 87, 101, 139, 158 ],
[ 12, 38, 68, 102, 105, 155, 0 ],
[ 13, 39, 69, 103, 149, 162, 0 ],
[ 8, 40, 70, 82, 104, 114, 145 ],
[ 14, 41, 71, 88, 102, 123, 156 ],
[ 15, 42, 59, 106, 123, 159, 0 ],
[ 1, 33, 72, 106, 107, 157, 0 ],
[ 16, 43, 73, 108, 141, 160, 0 ],
[ 17, 37, 74, 81, 109, 131, 154 ],
[ 11, 44, 75, 110, 121, 166, 0 ],
[ 45, 55, 64, 111, 130, 161, 173 ],
[ 8, 46, 71, 112, 119, 166, 0 ],
[ 18, 36, 76, 89, 113, 114, 143 ],
[ 19, 38, 77, 104, 116, 163, 0 ],
[ 20, 47, 70, 92, 138, 165, 0 ],
[ 2, 48, 74, 113, 128, 160, 0 ],
[ 21, 45, 78, 83, 117, 121, 151 ],
[ 22, 47, 58, 118, 127, 164, 0 ],
[ 16, 39, 62, 112, 134, 158, 0 ],
[ 23, 43, 79, 120, 131, 145, 0 ],
[ 19, 35, 59, 73, 110, 125, 161 ],
[ 20, 36, 63, 94, 136, 161, 0 ],
[ 14, 31, 79, 98, 132, 164, 0 ],
[ 3, 44, 80, 124, 127, 169, 0 ],
[ 19, 46, 81, 117, 135, 167, 0 ],
[ 7, 49, 58, 90, 100, 105, 168 ],
[ 12, 50, 61, 118, 119, 144, 0 ],
[ 13, 51, 64, 114, 118, 157, 0 ],
[ 24, 52, 76, 129, 148, 149, 0 ],
[ 25, 53, 69, 90, 101, 130, 156 ],
[ 20, 46, 65, 80, 120, 140, 170 ],
[ 21, 54, 77, 100, 140, 171, 0 ],
[ 35, 82, 133, 142, 171, 174, 0 ],
[ 14, 30, 83, 113, 125, 170, 0 ],
[ 4, 29, 68, 120, 134, 173, 0 ],
[ 1, 4, 52, 57, 86, 136, 152 ],
[ 26, 51, 56, 91, 122, 137, 168 ],
[ 52, 84, 110, 115, 145, 168, 0 ],
[ 7, 50, 81, 99, 132, 173, 0 ],
[ 23, 55, 67, 95, 172, 174, 0 ],
[ 26, 41, 77, 109, 141, 148, 0 ],
[ 2, 27, 41, 61, 62, 115, 133 ],
[ 27, 40, 56, 124, 125, 126, 0 ],
[ 18, 49, 55, 124, 141, 167, 0 ],
[ 6, 33, 85, 108, 116, 156, 0 ],
[ 28, 48, 70, 85, 105, 129, 158 ],
[ 9, 54, 63, 131, 147, 155, 0 ],
[ 22, 53, 68, 109, 121, 174, 0 ],
[ 3, 13, 48, 78, 95, 123, 0 ],
[ 31, 69, 133, 150, 155, 169, 0 ],
[ 12, 43, 66, 89, 97, 135, 159 ],
[ 5, 39, 75, 102, 136, 167, 0 ],
[ 2, 54, 86, 101, 135, 164, 0 ],
[ 15, 56, 87, 108, 119, 171, 0 ],
[ 10, 44, 82, 91, 111, 144, 149 ],
[ 23, 34, 71, 94, 127, 153, 0 ],
[ 11, 49, 88, 92, 142, 157, 0 ],
[ 29, 34, 87, 97, 147, 162, 0 ],
[ 30, 50, 60, 86, 137, 142, 162 ],
[ 10, 53, 66, 84, 112, 128, 165 ],
[ 22, 57, 85, 93, 140, 159, 0 ],
[ 28, 32, 72, 103, 132, 166, 0 ],
[ 28, 29, 84, 88, 117, 143, 150 ],
[ 1, 26, 45, 80, 128, 147, 0 ],
[ 17, 27, 89, 103, 116, 153, 0 ],
[ 51, 57, 98, 163, 165, 172, 0 ],
[ 21, 37, 73, 138, 152, 169, 0 ],
[ 16, 47, 76, 130, 137, 154, 0 ],
[ 3, 24, 30, 72, 104, 139, 0 ],
[ 9, 40, 90, 106, 134, 151, 0 ],
[ 15, 58, 60, 74, 111, 150, 163 ],
[ 18, 42, 79, 144, 146, 152, 0 ],
[ 25, 38, 65, 99, 122, 160, 0 ],
[ 17, 42, 75, 129, 170, 172, 0 ],
]
# Mn from WSJT-X's ldpc_174_91_c_reordered_parity.f90
# each of the 174 rows corresponds to a codeword bit.
# the numbers indicate which three parity
# checks (rows in Nm) refer to the codeword bit.
# 1-origin.
Mn = [
[ 16, 45, 73 ],
[ 25, 51, 62 ],
[ 33, 58, 78 ],
[ 1, 44, 45 ],
[ 2, 7, 61 ],
[ 3, 6, 54 ],
[ 4, 35, 48 ],
[ 5, 13, 21 ],
[ 8, 56, 79 ],
[ 9, 64, 69 ],
[ 10, 19, 66 ],
[ 11, 36, 60 ],
[ 12, 37, 58 ],
[ 14, 32, 43 ],
[ 15, 63, 80 ],
[ 17, 28, 77 ],
[ 18, 74, 83 ],
[ 22, 53, 81 ],
[ 23, 30, 34 ],
[ 24, 31, 40 ],
[ 26, 41, 76 ],
[ 27, 57, 70 ],
[ 29, 49, 65 ],
[ 3, 38, 78 ],
[ 5, 39, 82 ],
[ 46, 50, 73 ],
[ 51, 52, 74 ],
[ 55, 71, 72 ],
[ 44, 67, 72 ],
[ 43, 68, 78 ],
[ 1, 32, 59 ],
[ 2, 6, 71 ],
[ 4, 16, 54 ],
[ 7, 65, 67 ],
[ 8, 30, 42 ],
[ 9, 22, 31 ],
[ 10, 18, 76 ],
[ 11, 23, 82 ],
[ 12, 28, 61 ],
[ 13, 52, 79 ],
[ 14, 50, 51 ],
[ 15, 81, 83 ],
[ 17, 29, 60 ],
[ 19, 33, 64 ],
[ 20, 26, 73 ],
[ 21, 34, 40 ],
[ 24, 27, 77 ],
[ 25, 55, 58 ],
[ 35, 53, 66 ],
[ 36, 48, 68 ],
[ 37, 46, 75 ],
[ 38, 45, 47 ],
[ 39, 57, 69 ],
[ 41, 56, 62 ],
[ 20, 49, 53 ],
[ 46, 52, 63 ],
[ 45, 70, 75 ],
[ 27, 35, 80 ],
[ 1, 15, 30 ],
[ 2, 68, 80 ],
[ 3, 36, 51 ],
[ 4, 28, 51 ],
[ 5, 31, 56 ],
[ 6, 20, 37 ],
[ 7, 40, 82 ],
[ 8, 60, 69 ],
[ 9, 10, 49 ],
[ 11, 44, 57 ],
[ 12, 39, 59 ],
[ 13, 24, 55 ],
[ 14, 21, 65 ],
[ 16, 71, 78 ],
[ 17, 30, 76 ],
[ 18, 25, 80 ],
[ 19, 61, 83 ],
[ 22, 38, 77 ],
[ 23, 41, 50 ],
[ 7, 26, 58 ],
[ 29, 32, 81 ],
[ 33, 40, 73 ],
[ 18, 34, 48 ],
[ 13, 42, 64 ],
[ 5, 26, 43 ],
[ 47, 69, 72 ],
[ 54, 55, 70 ],
[ 45, 62, 68 ],
[ 10, 63, 67 ],
[ 14, 66, 72 ],
[ 22, 60, 74 ],
[ 35, 39, 79 ],
[ 1, 46, 64 ],
[ 1, 24, 66 ],
[ 2, 5, 70 ],
[ 3, 31, 65 ],
[ 4, 49, 58 ],
[ 1, 4, 5 ],
[ 6, 60, 67 ],
[ 7, 32, 75 ],
[ 8, 48, 82 ],
[ 9, 35, 41 ],
[ 10, 39, 62 ],
[ 11, 14, 61 ],
[ 12, 71, 74 ],
[ 13, 23, 78 ],
[ 11, 35, 55 ],
[ 15, 16, 79 ],
[ 7, 9, 16 ],
[ 17, 54, 63 ],
[ 18, 50, 57 ],
[ 19, 30, 47 ],
[ 20, 64, 80 ],
[ 21, 28, 69 ],
[ 22, 25, 43 ],
[ 13, 22, 37 ],
[ 2, 47, 51 ],
[ 23, 54, 74 ],
[ 26, 34, 72 ],
[ 27, 36, 37 ],
[ 21, 36, 63 ],
[ 29, 40, 44 ],
[ 19, 26, 57 ],
[ 3, 46, 82 ],
[ 14, 15, 58 ],
[ 33, 52, 53 ],
[ 30, 43, 52 ],
[ 6, 9, 52 ],
[ 27, 33, 65 ],
[ 25, 69, 73 ],
[ 38, 55, 83 ],
[ 20, 39, 77 ],
[ 18, 29, 56 ],
[ 32, 48, 71 ],
[ 42, 51, 59 ],
[ 28, 44, 79 ],
[ 34, 60, 62 ],
[ 31, 45, 61 ],
[ 46, 68, 77 ],
[ 6, 24, 76 ],
[ 8, 10, 78 ],
[ 40, 41, 70 ],
[ 17, 50, 53 ],
[ 42, 66, 68 ],
[ 4, 22, 72 ],
[ 36, 64, 81 ],
[ 13, 29, 47 ],
[ 2, 8, 81 ],
[ 56, 67, 73 ],
[ 5, 38, 50 ],
[ 12, 38, 64 ],
[ 59, 72, 80 ],
[ 3, 26, 79 ],
[ 45, 76, 81 ],
[ 1, 65, 74 ],
[ 7, 18, 77 ],
[ 11, 56, 59 ],
[ 14, 39, 54 ],
[ 16, 37, 66 ],
[ 10, 28, 55 ],
[ 15, 60, 70 ],
[ 17, 25, 82 ],
[ 20, 30, 31 ],
[ 12, 67, 68 ],
[ 23, 75, 80 ],
[ 27, 32, 62 ],
[ 24, 69, 75 ],
[ 19, 21, 71 ],
[ 34, 53, 61 ],
[ 35, 46, 47 ],
[ 33, 59, 76 ],
[ 40, 43, 83 ],
[ 41, 42, 63 ],
[ 49, 75, 83 ],
[ 20, 44, 48 ],
[ 42, 49, 57 ],
]
#
# LDPC generator matrix from WSJT-X's ldpc_174_91_c_generator.f90.
# 83 rows, since LDPC(174,91) needs 83 parity bits.
# each row has 23 hex digits, to be turned into 91 bits,
# to be xor'd with the 91 data bits.
#
rawg = [
"8329ce11bf31eaf509f27fc",
"761c264e25c259335493132",
"dc265902fb277c6410a1bdc",
"1b3f417858cd2dd33ec7f62",
"09fda4fee04195fd034783a",
"077cccc11b8873ed5c3d48a",
"29b62afe3ca036f4fe1a9da",
"6054faf5f35d96d3b0c8c3e",
"e20798e4310eed27884ae90",
"775c9c08e80e26ddae56318",
"b0b811028c2bf997213487c",
"18a0c9231fc60adf5c5ea32",
"76471e8302a0721e01b12b8",
"ffbccb80ca8341fafb47b2e",
"66a72a158f9325a2bf67170",
"c4243689fe85b1c51363a18",
"0dff739414d1a1b34b1c270",
"15b48830636c8b99894972e",
"29a89c0d3de81d665489b0e",
"4f126f37fa51cbe61bd6b94",
"99c47239d0d97d3c84e0940",
"1919b75119765621bb4f1e8",
"09db12d731faee0b86df6b8",
"488fc33df43fbdeea4eafb4",
"827423ee40b675f756eb5fe",
"abe197c484cb74757144a9a",
"2b500e4bc0ec5a6d2bdbdd0",
"c474aa53d70218761669360",
"8eba1a13db3390bd6718cec",
"753844673a27782cc42012e",
"06ff83a145c37035a5c1268",
"3b37417858cc2dd33ec3f62",
"9a4a5a28ee17ca9c324842c",
"bc29f465309c977e89610a4",
"2663ae6ddf8b5ce2bb29488",
"46f231efe457034c1814418",
"3fb2ce85abe9b0c72e06fbe",
"de87481f282c153971a0a2e",
"fcd7ccf23c69fa99bba1412",
"f0261447e9490ca8e474cec",
"4410115818196f95cdd7012",
"088fc31df4bfbde2a4eafb4",
"b8fef1b6307729fb0a078c0",
"5afea7acccb77bbc9d99a90",
"49a7016ac653f65ecdc9076",
"1944d085be4e7da8d6cc7d0",
"251f62adc4032f0ee714002",
"56471f8702a0721e00b12b8",
"2b8e4923f2dd51e2d537fa0",
"6b550a40a66f4755de95c26",
"a18ad28d4e27fe92a4f6c84",
"10c2e586388cb82a3d80758",
"ef34a41817ee02133db2eb0",
"7e9c0c54325a9c15836e000",
"3693e572d1fde4cdf079e86",
"bfb2cec5abe1b0c72e07fbe",
"7ee18230c583cccc57d4b08",
"a066cb2fedafc9f52664126",
"bb23725abc47cc5f4cc4cd2",
"ded9dba3bee40c59b5609b4",
"d9a7016ac653e6decdc9036",
"9ad46aed5f707f280ab5fc4",
"e5921c77822587316d7d3c2",
"4f14da8242a8b86dca73352",
"8b8b507ad467d4441df770e",
"22831c9cf1169467ad04b68",
"213b838fe2ae54c38ee7180",
"5d926b6dd71f085181a4e12",
"66ab79d4b29ee6e69509e56",
"958148682d748a38dd68baa",
"b8ce020cf069c32a723ab14",
"f4331d6d461607e95752746",
"6da23ba424b9596133cf9c8",
"a636bcbc7b30c5fbeae67fe",
"5cb0d86a07df654a9089a20",
"f11f106848780fc9ecdd80a",
"1fbb5364fb8d2c9d730d5ba",
"fcb86bc70a50c9d02a5d034",
"a534433029eac15f322e34c",
"c989d9c7c3d3b8c55d75130",
"7bb38b2f0186d46643ae962",
"2644ebadeb44b9467d1f42c",
"608cc857594bfbb55d69600"
]
# gen[row][col], derived from rawg, has one row per
# parity bit, to be xor'd with the 91 data bits.
# thus gen[83][91].
# as in encode174_91.f90
gen = [ ]
# turn rawg into gen.
def make_gen():
global gen
# hex digit to number
hex2 = { }
for i in range(0, 16):
hex2[hex(i)[2]] = i
assert len(rawg) == 83
for e in rawg:
row = numpy.zeros(91, dtype=numpy.int32)
for i,c in enumerate(e):
x = hex2[c]
for j in range(0, 4):
ind = i*4 + (3-j)
if ind >= 0 and ind < 91:
if (x & (1 << j)) != 0:
row[ind] = 1
else:
row[ind] = 0
gen.append(row)
make_gen()
# turn gen[] into a systematic array by prepending
# a 91x91 identity matrix.
gen_sys = numpy.zeros((174, 91), dtype=numpy.int32)
gen_sys[91:,:] = gen
gen_sys[0:91,:] = numpy.eye(91, dtype=numpy.int32)
# plain is 91 bits of plain-text.
# returns a 174-bit codeword.
# mimics wsjt-x's encode174_91.f90.
def ldpc_encode(plain):
assert len(plain) == 91
ncw = numpy.zeros(174, dtype=numpy.int32)
numpy.dot(gen_sys[91:,:], plain, out=ncw[91:])
numpy.mod(ncw[91:], 2, out=ncw[91:])
ncw[0:91] = plain
return ncw
# given a 174-bit codeword as an array of log-likelihood of zero,
# return a 91-bit plain text, or zero-length array.
# this is an implementation of the sum-product algorithm
# from Sarah Johnson's Iterative Error Correction book.
# codeword[i] = log ( P(x=0) / P(x=1) )
# returns [ nok, plain ], where nok is the number of parity
# checks that worked out, should be 83=174-91.
def ldpc_decode_python(codeword, ldpc_iters):
# 174 codeword bits:
# 91 systematic data bits
# 83 parity checks
mnx = numpy.array(Mn, dtype=numpy.int32)
nmx = numpy.array(Nm, dtype=numpy.int32)
# Mji
# each codeword bit i tells each parity check j
# what the bit's log-likelihood of being 0 is
# based on information *other* than from that
# parity check.
m = numpy.zeros((83, 174))
for i in range(0, 174):
for j in range(0, 83):
m[j][i] = codeword[i]
for iter in range(0, ldpc_iters):
# Eji
# each check j tells each codeword bit i the
# log likelihood of the bit being zero based
# on the *other* bits in that check.
e = numpy.zeros((83, 174))
# messages from checks to bits.
# for each parity check
#for j in range(0, 83):
# # for each bit mentioned in this parity check
# for i in Nm[j]:
# if i <= 0:
# continue
# a = 1
# # for each other bit mentioned in this parity check
# for ii in Nm[j]:
# if ii != i:
# a *= math.tanh(m[j][ii-1] / 2.0)
# e[j][i-1] = math.log((1 + a) / (1 - a))
for i in range(0, 7):
a = numpy.ones(83)
for ii in range(0, 7):
if ii != i:
x1 = numpy.tanh(m[range(0, 83), nmx[:,ii]-1] / 2.0)
x2 = numpy.where(numpy.greater(nmx[:,ii], 0.0), x1, 1.0)
a = a * x2
# avoid divide by zero, i.e. a[i]==1.0
# XXX why is a[i] sometimes 1.0?
b = numpy.where(numpy.less(a, 0.99999), a, 0.99)
c = numpy.log((b + 1.0) / (1.0 - b))
# have assign be no-op when nmx[a,b] == 0
d = numpy.where(numpy.equal(nmx[:,i], 0),
e[range(0,83), nmx[:,i]-1],
c)
e[range(0,83), nmx[:,i]-1] = d
# decide if we are done -- compute the corrected codeword,
# see if the parity check succeeds.
# sum the three log likelihoods contributing to each codeword bit.
e0 = e[mnx[:,0]-1, range(0,174)]
e1 = e[mnx[:,1]-1, range(0,174)]
e2 = e[mnx[:,2]-1, range(0,174)]
ll = codeword + e0 + e1 + e2
# log likelihood > 0 => bit=0.
cw = numpy.select( [ ll < 0 ], [ numpy.ones(174, dtype=numpy.int32) ])
if ldpc_check(cw):
# success!
# it's a systematic code, though the plain-text bits are scattered.
# collect them.
decoded = cw[0:91]
return [ 91, decoded ]
# messages from bits to checks.
for j in range(0, 3):
# for each column in Mn.
ll = codeword
if j != 0:
e0 = e[mnx[:,0]-1, range(0,174)]
ll = ll + e0
if j != 1:
e1 = e[mnx[:,1]-1, range(0,174)]
ll = ll + e1
if j != 2:
e2 = e[mnx[:,2]-1, range(0,174)]
ll = ll + e2
m[mnx[:,j]-1, range(0,174)] = ll
# could not decode.
return [ 0, numpy.array([]) ]
# turn log-likelihood bits into hard bits.
# codeword[i] = log ( P(x=0) / P(x=1) )
# so > 0 means bit=0, < 0 means bit=1.
def soft2hard(codeword):
hard = numpy.less(codeword, 0.0)
hard = numpy.array(hard, dtype=numpy.int32) # T/F -> 1/0
two = numpy.array([0, 1], dtype=numpy.int32)
hardword = two[hard]
return hardword
# given a 174-bit codeword as an array of log-likelihood of zero,
# return a 91-bit plain text, or zero-length array.
# this is an implementation of the bit-flipping algorithm
# from Sarah Johnson's Iterative Error Correction book.
# codeword[i] = log ( P(x=0) / P(x=1) )
# returns [ nok, plain ], where nok is the number of parity
# checks that worked out, should be 83=174-91.
def ldpc_decode_flipping(codeword):
cw = soft2hard(codeword)
for iter in range(0,100):
# for each codeword bit,
# count of votes for 0 and 1.
votes = numpy.zeros((len(codeword), 2))
# for each parity check equation.
for e in Nm:
# for each codeword bit mentioned in e.
for bi in e:
if bi == 0:
continue
# value for bi implied by remaining bits.
x = 0
for i in e:
if i != bi:
x ^= cw[i-1]
# the other bits in the equation suggest that
# bi must have value x.
votes[(bi-1),x] += 1
for i in range(0, len(cw)):
if cw[i] == 0 and votes[i][1] > votes[i][0]:
cw[i] = 1
elif cw[i] == 1 and votes[i][0] > votes[i][1]:
cw[i] = 0
if ldpc_check(cw):
# success!
# it's a systematic code; data is first 91 bits.
return [ 91, cw[0:91] ]
return [ 0, numpy.array([]) ]
# does a 174-bit codeword pass the LDPC parity checks?
def ldpc_check(codeword):
for e in Nm:
x = 0
for i in e:
if i != 0:
x ^= codeword[i-1]
if x != 0:
return False
return True
libldpc = None
try:
libldpc = ctypes.cdll.LoadLibrary("libldpc/libldpc.so")
except:
libldpc = None
sys.stderr.write("ft8: using the Python LDPC decoder, not the C decoder.\n")
if False:
# test CRC
# nov 30 2018: crc12 works
# dec 3 2018: crc14 works
msg = numpy.zeros(82, dtype=numpy.int32)
msg[3] = 1
msg[7] = 1
msg[44] = 1
msg[45] = 1
msg[46] = 1
msg[51] = 1
msg[61] = 1
msg[71] = 1
expected = [ 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, ]
cksum = crc_python(msg, crc14poly)
eq = numpy.equal(cksum, numpy.array(expected, dtype=numpy.int32))
assert numpy.all(eq)
cksum = crc_c(msg)
eq = numpy.equal(cksum, numpy.array(expected, dtype=numpy.int32))
assert numpy.all(eq)
sys.exit(1)
def ldpc_test(ldpci):
tt = 0.0
niters = 5000
ok = 0
for iter in range(0, niters):
# ldpc_encode() takes 91 bits.
a91 = numpy.random.randint(0, 2, 91, dtype=numpy.int32)
a174 = ldpc_encode(a91)
if True:
# check that ldpc_encode() generated the right parity bits.
assert ldpc_check(a174)
# turn hard bits into 0.99 vs 0.01 log-likelihood,
# log( P(0) / P(1) )
# log base e.
two = numpy.array([ 4.6, -4.6 ])
ll174 = two[a174]
if True:
# check decode is perfect before wrecking bits.
[ nn, d91 ] = ldpc_decode(ll174, ldpci)
assert numpy.array_equal(a91, d91)
assert nn == 83
# wreck some bits
#for junk in range(0, 70):
# ll174[random.randint(0, len(ll174)-1)] = (random.random() - 0.5) * 4
perm = numpy.random.permutation(len(ll174))
perm = perm[0:70]
for i in perm:
p = random.random()
bit = a174[i]
if random.random() > p:
# flip the bit
bit = 1 - bit
if bit == 0:
p = 0.5 + (p / 2)
else:
p = 0.5 - (p / 2)
ll = math.log(p / (1.0 - p))
ll174[i] = ll
t0 = time.time()
# decode LDPC(174,91)
[ _, d91 ] = ldpc_decode(ll174, ldpci)
t1 = time.time()
tt += t1 - t0
if numpy.array_equal(a91, d91):
ok += 1
print("ldpc_iters %d, success %.2f, %.6f sec/call" % (ldpci,
ok / float(niters),
tt / niters))
# success 0.88
# 0.019423 per call
# but Dec 28 2017
# ldpc_iters 20, success 0.64, 0.000592 sec/call
# ldpc_iters 33, success 0.68, 0.000749 sec/call
# ldpc_iters 37, success 0.68, 0.000806 sec/call
# ldpc_iters 50, success 0.69, 0.000943 sec/call
# ldpc_iters 100, success 0.71, 0.001515 sec/call
# fast_tanh is a bit faster, but has same success as tanh()
# ldpc_decode_python() has about the same success rate
# nov 30 2018, old FT8
# ldpc_iters 15, success 0.60, 0.000383 sec/call
# dec 3 2018, new FT8
# ldpc_iters 15, success 0.43, 0.000341 sec/call
# ldpc_iters 15, success 0.41, 0.014654 sec/call
# codeword is 174 log-likelihoods.
# return is [ ok, 83 bits ].
# ok is 83 if all ldpc parity checks worked, < 83 otherwise.
# result is usually garbage if ok < 83.
def ldpc_decode_c(codeword, ldpc_iters):
double174 = ctypes.c_double * 174
int174 = ctypes.c_int * 174
c174 = double174()
for i in range(0, 174):
c174[i] = codeword[i]
out174 = int174()
for i in range(0, 174):
out174[i] = -1;
ok = ctypes.c_int()
ok.value = -1
libldpc.ldpc_decode(c174, ldpc_iters, out174, ctypes.byref(ok))
plain174 = numpy.zeros(174, dtype=numpy.int32);
for i in range(0, 174):
plain174[i] = out174[i];
plain91 = plain174[0:91]
return [ ok.value, plain91 ]
# returns [ nok, plain ], where nok is the number of parity
# checks that worked out, should be 83=174-91.
def ldpc_decode(codeword, ldpc_iters):
if libldpc != None:
return ldpc_decode_c(codeword, ldpc_iters)
else:
return ldpc_decode_python(codeword, ldpc_iters)
if False:
ldpc_test(1*17)
ldpc_test(2*17)
ldpc_test(4*17)
ldpc_test(8*17)
sys.exit(1)
# nov 30 2018:
# C: ldpc_iters 15, success 0.59, 0.000383 sec/call
# python: ldpc_iters 15, success 0.58, 0.013829 sec/call
# dec 3 2018:
# ldpc_iters 15, success 0.45, 0.000339 sec/call
# XXX why worse now?
# apr 26 2019:
# ldpc_iters 17, success 0.46, 0.000139 sec/call
# ldpc_iters 34, success 0.51, 0.000183 sec/call
# ldpc_iters 68, success 0.51, 0.000272 sec/call
# ldpc_iters 136, success 0.52, 0.000436 sec/call
# gauss-jordan elimination of rows.
# m[row][col]
# inverts the square top of the matrix, swapping
# with lower rows as needed.
# returns the inverse of the top of the matrix.
# cooks up the identity matrix (the right-hand half)
# as needed.
# mod 2, so elements should be 0 or 1.
# keeps track of swaps in which[] -- every time it swaps two
# rows, it swaps the same two rows in which[].
# which[] could start out as range(0, n_rows).
def python_gauss_jordan(m, which):
rows = m.shape[1] # rows to invert = columns
# assert numpy.all(numpy.greater_equal(m, 0))
# assert numpy.all(numpy.less_equal(m, 1))
b = numpy.zeros((m.shape[0], rows * 2), dtype=m.dtype)
b[:,0:rows] = m
for row in range(0, rows):
if b[row,row] != 1:
# oops, find a row that has a 1 in row,row,
# and swap.
for row1 in range(row+1,m.shape[0]):
if b[row1,row] == 1:
tmp = numpy.copy(b[row])
b[row] = b[row1]
b[row1] = tmp
tmp = which[row]
which[row] = which[row1]
which[row1] = tmp
break
if b[row,row] != 1:
sys.stderr.write("not reducible\n")
print(b)
return numpy.array([])
# lazy creation of identity matrix in right half
b[row,rows+row] = (b[row,rows+row] + 1) % 2
# now eliminate
for row1 in range(0, m.shape[0]):
if row1 == row:
continue
if b[row1,row] != 0:
b[row1] = numpy.mod(b[row]+b[row1], 2)
# assert numpy.array_equal(b[0:rows,0:rows],
# numpy.eye(rows, dtype=numpy.int32))