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Unable to decode specific combination of symbols #6

@c-fjord

Description

@c-fjord

I have attempted to encode a message using a Cauchy Reed Solomon using 4 symbols and 2 parities. It has been done using the encoding_fragments and decoding_fragments functions below:

import math

import pyerasure
import pyerasure.finite_field
import pyerasure.generator


def encoding_fragments(data_in: bytes, symbols: int, parity: int):
    # padding input to ensure correct size
    symbol_bytes = math.ceil(len(data_in) / symbols)
    padded_data = data_in.ljust(symbol_bytes * symbols, b'\0')

    field = pyerasure.finite_field.Binary8()
    encoder = pyerasure.Encoder(field, symbols, symbol_bytes)
    encoder.set_symbols(padded_data)

    generator = pyerasure.generator.RSCauchy(field, symbols)

    fragments = []
    for idx in range(symbols + parity):
        if encoder.rank > idx:
            symbol = encoder.symbol_data(idx)
            fragments.append((1, idx, symbol))
        else:
            coefficients, index = generator.generate()
            symbol = encoder.encode_symbol(coefficients)
            fragments.append((0, index, bytes(symbol)))
    return fragments

# Decoding fragments
def decoding_fragments(fragments, symbols):
    field = pyerasure.finite_field.Binary8()

    symbol_bytes = math.ceil(len(fragments[0][2]) / symbols)
    decoder = pyerasure.Decoder(field, symbols, symbol_bytes)
    generator = pyerasure.generator.RSCauchy(field, symbols)

    for systematic, index, symbol in fragments:
        if systematic:
            decoder.decode_systematic_symbol(bytearray(symbol), index)
        else:
            coefficients = generator.generate_specific(index)
            decoder.decode_symbol(bytearray(symbol), bytearray(coefficients))

        if decoder.is_complete():
            return decoder.block_data().rstrip(b'\0')
    return 'Cannot decode'

The encoding_fragments function output a list of tuples consisting of 3 elements:

  1. Systematic/parity symbol
  2. Index
  3. Symbol bytes

I can decode the message for all combinations of 4 symbols except when using systematic symbols 0, 2, 3 and parity symbol 1. Below is an example of the combination of symbols that cannot be decoding. The example contains the message b"This messages will never be lost".

[(1, 0, b'This mes'), (1, 2, b'll never'), (1, 3, b' be lost'), (0, -1, b'`}>\xb25\r\xf1g')]

I have been unable to figure out why this occurs and if there is a problem with my code. I hope someone can help me figure out how to overcome this problem.

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