Decoding signals by guessing noise
Devices and methods described herein decode a sequence of coded symbols by guessing noise. In various embodiments, noise sequences are ordered, either during system initialization or on a periodic basis. Then, determining a codeword includes iteratively guessing a new noise sequence, removing its effect from received data symbols (e.g. by subtracting or using some other method of operational inversion), and checking whether the resulting data are a codeword using a codebook membership function. This process is deterministic, has bounded complexity, asymptotically achieves channel capacity as in convolutional codes, but has the decoding speed of a block code. In some embodiments, the decoder tests a bounded number of noise sequences, abandoning the search and declaring an erasure after these sequences are exhausted. Abandonment decoding nevertheless approximates maximum likelihood decoding within a tolerable bound and achieves channel capacity when the abandonment threshold is chosen appropriately.
1. A method, in a decoder, of decoding as a codeword a plurality of symbols received from a data sender using a noisy data channel, the method comprising:
selecting, by a noise guesser according to a noise guessing order, a sequence of noise symbols previously unselected for the received plurality of symbols;
forming, in a buffer, a block of symbols by inverting a noise effect, of the selected sequence of noise symbols, on the received plurality of symbols; and
determining whether the formed block of symbols is a codeword.
2. A method according to claim 1 , wherein selecting according to the noise guessing order comprises selecting according to a maximum likelihood order.
3. A method according to claim 2 , further comprising determining the maximum likelihood order according to a probabilistic model.
4. A method according to claim 3 , wherein the probabilistic model prioritizes noise effects toward the latest received symbols in the plurality of received symbols.
5. A method according to claim 1 , further comprising determining the noise guessing order according to machine learning.
6. A method according to claim 1 , wherein determining the noise guessing order comprises measuring one or more characteristics of the noisy data channel that include: a signal-to-noise ratio, an interference ratio, a change in a codeword error rate, and a multiple-user conflict interference.
7. A method according to claim 1 , wherein selecting according to the noise guessing order comprises selecting according to information, provided by the data sender, regarding a pattern of noise mixed with the codeword by the data sender.
8. A method according to claim 1 , wherein inverting the noise effect comprises subtracting or dividing the selected sequence of noise symbols from the received plurality of symbols.
9. A method according to claim 1 , wherein the codeword is contained in a random codebook, a random linear codebook, a Hamming codebook, or a Low Density Parity Check codebook.
10. A method according to claim 1 , wherein determining whether the formed block of symbols is a codeword comprises validating, by a codeword validator, the formed block of symbols using one or more of: validation information received from the data sender, a codebook memory, a function taking the formed block of symbols as input and having a binary output, and a codebook oracle.
11. A method according to claim 1 , further comprising, in response to determining whether the formed block of symbols is a codeword, outputting, by a noise outputter, the selected sequence of noise symbols.
12. A method according to claim 1 , further comprising storing, by a codeword validator in a storage as a list, each formed block of symbols that is a codeword, then when the list has reached a given number of elements, outputting the list.
13. A method according to claim 1 , performed simultaneously by each of a plurality of distributed decoders on the plurality of symbols received from the data sender.
14. A method according to claim 1 , further comprising:
incrementing a repetition count each time a codeword validator attempts to validate a formed block of symbols; and
determining whether the formed block of symbols is a codeword, by the codeword validator, when the repetition count reaches a first threshold.
15. A method according to claim 14 , further comprising outputting either or both of an error signal and diagnostic information pertaining to an error.
16. A method according to claim 14 , further comprising:
storing, as a list in a codeword memory, each formed block of symbols that is a codeword; and
when the list has reached a given number of elements, outputting the list.
17. A method according to claim 14 , wherein determining whether the formed block of symbols is a codeword comprises determining that the repetition count has reached at least a second threshold that is a function of a codebook rate, an estimated noise property, or both.
18. A method according to claim 17 , wherein determining whether the formed block of symbols is a codeword further comprises determining that the codebook rate is greater than 1 due to a temporary decrease in channel capacity caused by transient noise.
19. A method according to claim 14 , wherein determining whether the formed block of symbols is a codeword further comprises the codeword validator declaring an erasure.
20. A decoder for decoding a plurality of symbols as a codeword, the decoder comprising:
a receiver for receiving the plurality of symbols from a data sender using a noisy data channel;
a noise guesser for selecting, according to a noise guessing order, a sequence of noise symbols previously unselected for the received plurality of symbols;
a buffer for storing a block of symbols formed by inverting a noise effect, of the selected sequence of noise symbols, on the received plurality of symbols; and
a codeword validator for determining whether the formed block of symbols is a codeword.