107 lines
3.6 KiB
Python
107 lines
3.6 KiB
Python
import numpy as np
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from tqdm import tqdm
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class ProximalDecoder:
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"""Class implementing the Proximal Decoding algorithm. See "Proximal Decoding for LDPC Codes" by Tadashi
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Wadayama, and Satoshi Takabe.
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"""
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# TODO: How large should K be?
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# TODO: How large should eta be?
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# TODO: How large should step_size be?
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def __init__(self, H: np.array, K: int = 100, step_size: float = 0.5, gamma: float = 0.05, eta: float = 1.1):
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"""Construct a new ProximalDecoder Object.
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:param H: Parity Check Matrix
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:param K: Max number of iterations to perform when decoding
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:param step_size: Step size for the gradient descent process
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:param gamma: Positive constant. Arises in the approximation of the prior PDF
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:param eta: Positive constant slightly larger than one. See 3.2, p. 3
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"""
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self._H = H
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self._K = K
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self._step_size = step_size
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self._gamma = gamma
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self._eta = eta
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@staticmethod
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def _L_awgn(s: np.array, y: np.array) -> np.array:
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"""Variation of the negative log-likelihood for the special case of AWGN noise. See 4.1, p. 4."""
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return s - y
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# TODO: Is this correct?
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def _grad_h(self, x: np.array) -> np.array:
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"""Gradient of the code-constraint polynomial. See 2.3, p. 2."""
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# Calculate first term
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result = 4 * (x**2 - 1) * x
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# Calculate second term
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for k, x_k in enumerate(x):
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# TODO: Perform this operation for each row simultaneously
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B_k = np.argwhere(self._H[:, k] == 1)
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B_k = B_k[:, 0] # Get rid of one layer of arrays
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# TODO: Perform the summation with np.sum()
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sum_result = 0
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for i in B_k:
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# TODO: Perform this operation for each column simultaneously
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A_i = np.argwhere(self._H[i] == 1)
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A_i = A_i[:, 0] # Get rid of one layer of arrays
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prod = 1
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for j in A_i:
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prod *= x[j]
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sum_result += prod**2 - prod
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term_2 = 2 / x_k * sum_result
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result[k] += term_2
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return np.array(result)
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# TODO: Is this correct?
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def _projection(self, x):
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"""Project a vector onto [-eta, eta]^n in order to avoid numerical instability.
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Detailed in 3.2, p. 3 (Equation (15)).
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:param x:
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:return: x clipped to [-eta, eta]^n
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"""
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return np.clip(x, -self._eta, self._eta)
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def _check_parity(self, y_hat: np.array) -> bool:
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"""Perform a parity check for a given codeword.
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:param y_hat: codeword to be checked (element of [-1, 1]^n)
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:return: True if the parity check passes, i.e. the codeword is valid. False otherwise
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"""
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y_hat_binary = (y_hat == 1) * 1 # Map the codeword from [-1, 1]^n to [0, 1]^n
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syndrome = np.dot(self._H, y_hat) % 2
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return not np.any(syndrome)
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def decode(self, y: np.array) -> np.array:
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"""Decode a received signal. The algorithm is detailed in 3.2, p.3.
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This function assumes a BPSK-like modulated signal ([-1, 1]^n instead of [0, 1]^n) and an AWGN channel.
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:param y: Vector of received values. (y = x + n, where 'x' is element of [-1, 1]^m and 'n' is noise)
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:return: Most probably sent symbol
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"""
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s = 0
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x_hat = 0
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for k in range(self._K):
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r = s - self._step_size * self._L_awgn(s, y)
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s = r - self._gamma * self._grad_h(r)
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s = self._projection(s) # Equation (15)
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x_hat = (np.sign(s) == 1) * 1
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if self._check_parity(x_hat):
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break
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return x_hat
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