Source code for sionna.fec.turbo.utils

# SPDX-FileCopyrightText: Copyright (c) 2021-2023 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
# SPDX-License-Identifier: Apache-2.0
"""Layer for utility functions needed for Turbo Codes."""

import math
import numpy as np
import tensorflow as tf

[docs]def polynomial_selector(constraint_length): r"""Returns the generator polynomials for rate-1/2 convolutional codes for a given ``constraint_length``. Input ----- constraint_length: int An integer defining the desired constraint length of the encoder. The memory of the encoder is ``constraint_length`` - 1. Output ------ gen_poly: tuple Tuple of strings with each string being a 0,1 sequence where each polynomial is represented in binary form. Note ---- Please note that the polynomials are optimized for rsc codes and are not necessarily the same as used in the polynomial selector :class:`~sionna.fec.conv.utils.polynomial_selector` of the convolutional codes. """ assert(isinstance(constraint_length, int)),\ "constraint_length must be int." assert(2 < constraint_length < 7),\ "Unsupported constraint_length." gen_poly_dict = { 3: ('111', '101'), # (7, 5) 4: ('1011', '1101'), # (13, 15) 5: ('10011','11011'), # (23, 33) 6: ('111101', '101011'), # (75, 53) } gen_poly = gen_poly_dict[constraint_length] return gen_poly
[docs]def puncture_pattern(turbo_coderate, conv_coderate): r"""This method returns puncturing pattern such that the Turbo code has rate ``turbo_coderate`` given the underlying convolutional encoder is of rate ``conv_coderate``. Input ----- turbo_coderate: float Desired coderate of the Turbo code conv_coderate: float Coderate of the underlying convolutional encoder Output ------ : tf.bool 2D tensor indicating the positions to be punctured. """ tf.debugging.assert_equal(conv_coderate, 1/2) if turbo_coderate == 1/2: pattern = [[1, 1, 0], [1, 0, 1]] elif turbo_coderate == 1/3: pattern = [[1, 1, 1]] turbo_punct_pattern = tf.convert_to_tensor( np.asarray(pattern), dtype=bool) return turbo_punct_pattern
[docs]class TurboTermination(object): # pylint: disable=line-too-long r"""TurboTermination(constraint_length, conv_n=2, num_conv_encs=2, num_bit_streams=3) Termination object, handles the transformation of termination bits from the convolutional encoders to a Turbo codeword. Similarly, it handles the transformation of channel symbols corresponding to the termination of a Turbo codeword to the underlying convolutional codewords. Parameters ---------- constraint_length: int Constraint length of the convolutional encoder used in the Turbo code. Note that the memory of the encoder is ``constraint_length`` - 1. conv_n: int Number of output bits for one state transition in the underlying convolutional encoder num_conv_encs: int Number of parallel convolutional encoders used in the Turbo code num_bit_streams: int Number of output bit streams from Turbo code """ def __init__(self, constraint_length, conv_n=2, num_conv_encs=2, num_bitstreams=3): tf.debugging.assert_type(constraint_length, tf.int32) tf.debugging.assert_type(conv_n, tf.int32) tf.debugging.assert_type(num_conv_encs, tf.int32) tf.debugging.assert_type(num_bitstreams, tf.int32) self.mu_ = constraint_length - 1 self.conv_n = conv_n tf.debugging.assert_equal(num_conv_encs, 2) self.num_conv_encs = num_conv_encs self.num_bitstreams = num_bitstreams
[docs] def get_num_term_syms(self): r""" Computes the number of termination symbols for the Turbo code based on the underlying convolutional code parameters, primarily the memory :math:`\mu`. Note that it is assumed that one Turbo symbol implies ``num_bitstreams`` bits. Input ----- None Output ------ turbo_term_syms: int Total number of termination symbols for the Turbo Code. One symbol equals ``num_bitstreams`` bits. """ total_term_bits = self.conv_n * self. num_conv_encs * self.mu_ turbo_term_syms = math.ceil(total_term_bits/self.num_bitstreams) return turbo_term_syms
[docs] def termbits_conv2turbo(self, term_bits1, term_bits2): # pylint: disable=line-too-long r""" This method merges ``term_bits1`` and ``term_bits2``, termination bit streams from the two convolutional encoders, to a bit stream corresponding to the Turbo codeword. Let ``term_bits1`` and ``term_bits2`` be: :math:`[x_1(K), z_1(K), x_1(K+1), z_1(K+1),..., x_1(K+\mu-1),z_1(K+\mu-1)]` :math:`[x_2(K), z_2(K), x_2(K+1), z_2(K+1),..., x_2(K+\mu-1), z_2(K+\mu-1)]` where :math:`x_i, z_i` are the systematic and parity bit streams respectively for a rate-1/2 convolutional encoder i, for i = 1, 2. In the example output below, we assume :math:`\mu=4` to demonstrate zero padding at the end. Zero padding is done such that the total length is divisible by ``num_bitstreams`` (defaults to 3) which is the number of Turbo bit streams. Assume ``num_bitstreams`` = 3. Then number of termination symbols for the TurboEncoder is :math:`\lceil \frac{2*conv\_n*\mu}{3} \rceil`: :math:`[x_1(K), z_1(K), x_1(K+1)]` :math:`[z_1(K+1), x_1(K+2, z_1(K+2)]` :math:`[x_1(K+3), z_1(K+3), x_2(K)]` :math:`[z_2(K), x_2(K+1), z_2(K+1)]` :math:`[x_2(K+2), z_2(K+2), x_2(K+3)]` :math:`[z_2(K+3), 0, 0]` Therefore, the output from this method is a single dimension vector where all Turbo symbols are concatenated together. :math:`[x_1(K), z_1(K), x_1(K+1), z_1(K+1), x_1(K+2, z_1(K+2), x_1(K+3),` :math:`z_1(K+3), x_2(K),z_2(K), x_2(K+1), z_2(K+1), x_2(K+2), z_2(K+2),` :math:`x_2(K+3), z_2(K+3), 0, 0]` Input ----- term_bits1: tf.int32 2+D Tensor containing termination bits from convolutional encoder 1 term_bits2: tf.int32 2+D Tensor containing termination bits from convolutional encoder 2 Output ------ : tf.int32 1+D tensor of termination bits. The output is obtained by concatenating the inputs and then adding right zero-padding if needed. """ term_bits = tf.concat([term_bits1, term_bits2],axis=-1) num_term_bits = term_bits.get_shape()[-1] num_term_syms = math.ceil(num_term_bits/self.num_bitstreams) extra_bits = self.num_bitstreams*num_term_syms - num_term_bits if extra_bits > 0: zer_shape = tf.stack([tf.shape(term_bits)[0], tf.constant(extra_bits)], axis=0) term_bits = tf.concat( [term_bits, tf.zeros(zer_shape, tf.float32)], axis=-1) return term_bits
[docs] def term_bits_turbo2conv(self, term_bits): # pylint: disable=line-too-long r""" This method splits the termination symbols from a Turbo codeword to the termination symbols corresponding to the two convolutional encoders, respectively. Let's assume :math:`\mu=4` and the underlying convolutional encoders are systematic and rate-1/2, for demonstration purposes. Let ``term_bits`` tensor, corresponding to the termination symbols of the Turbo codeword be as following: :math:`y = [x_1(K), z_1(K), x_1(K+1), z_1(K+1), x_1(K+2), z_1(K+2)`, :math:`x_1(K+3), z_1(K+3), x_2(K), z_2(K), x_2(K+1), z_2(K+1),` :math:`x_2(K+2), z_2(K+2), x_2(K+3), z_2(K+3), 0, 0]` The two termination tensors corresponding to the convolutional encoders are: :math:`y[0,..., 2\mu]`, :math:`y[2\mu,..., 4\mu]`. The output from this method is a tuple of two tensors, each of size :math:`2\mu` and shape :math:`[\mu,2]`. :math:`[[x_1(K), z_1(K)]`, :math:`[x_1(K+1), z_1(K+1)]`, :math:`[x_1(K+2, z_1(K+2)]`, :math:`[x_1(K+3), z_1(K+3)]]` and :math:`[[x_2(K), z_2(K)],` :math:`[x_2(K+1), z_2(K+1)]`, :math:`[x_2(K+2), z_2(K+2)]`, :math:`[x_2(K+3), z_2(K+3)]]` Input ----- term_bits: tf.float32 Channel output of the Turbo codeword, corresponding to the termination part Output ------ : tf.float32 Two tensors of channel outputs, corresponding to encoders 1 and 2, respectively """ input_len = tf.shape(term_bits)[-1] divisible = tf.math.floormod(input_len, self.num_bitstreams) tf.assert_equal(divisible, 0, 'Programming Error.') enc1_term_idx = tf.range(0, self.conv_n*self.mu_) enc2_term_idx = tf.range(self.conv_n*self.mu_, 2*self.conv_n*self.mu_) term_bits1 = tf.gather(term_bits, enc1_term_idx, axis=-1) term_bits2 = tf.gather(term_bits, enc2_term_idx, axis=-1) return term_bits1, term_bits2