Decoding concatenated codes 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 data that was encoded with an outer code then encoded with an inner code, the method comprising:
receiving a collection of m pluralities of data symbols from a data sender using a noisy data channel, the number m being determined by the outer code;
for each received plurality of data symbols, until a termination condition is obtained, repeatedly:
selecting, by a noise guesser according to a noise guessing order, a sequence of noise symbols previously unselected for the given received plurality of data symbols;
forming, in a buffer, a block of formed symbols by inverting a noise effect, of the selected sequence of noise symbols, on the given received plurality of data symbols; and
obtaining the termination condition, by a codeword validator, if the formed symbols comprise a codeword for the inner code;
when the termination condition is obtained for each received plurality of data symbols, storing in a memory the formed symbols as a codeword for the inner code; and
when the memory stores at least a number k of codewords for the inner code wherein the number k≤m is determined by the outer code, collectively decoding the at least k stored codewords according to the outer code and outputting the decoded data.
2. A method according to claim 1 , performed simultaneously by a plurality of distributed decoders, each distributed decoder decoding, with respect to the inner code, one or more of the m pluralities of data symbols received from the data sender.
3. A method according to claim 1 , wherein decoding according to the outer code comprises decoding one or more of:
a maximum distance separable (MDS) block code capable of correcting m−k codeword erasures;
an MDS block code capable of correcting m−k errors made by the codeword validator;
a rateless code, wherein the data sender is capable to dynamically change the number m and to communicate the change to the decoder; and
a code whose codewords comprise data symbols randomly chosen from an alphabet of symbols.
4. A method according to claim 1 , wherein either the outer code or the inner code comprises a network code.
5. A method according to claim 4 , wherein the network code is a concatenation of encodings.
6. A method according to claim 4 , wherein the network code is a random code, a random linear network code, a Hamming code, or a Low Density Parity Check code.
7. A method according to claim 1 , wherein obtaining the termination condition further comprises validating, by the codeword validator, the formed symbols using one or more of: validation information received from the data sender, a codebook memory, and a function taking the formed symbols as input and having a binary output.
8. A method according to claim 1 , wherein obtaining the termination condition further comprises validating, by the codeword validator, the formed symbols using a codebook oracle that verifies the decoding of the inner code according to one or more dependencies induced by the outer code.
9. A method according to claim 1 , wherein outputting, by the sent codeword outputter, comprises outputting either or both of an error signal and information pertaining to an error.
10. A method according to claim 1 , further comprising:
incrementing a repetition count each time the codeword validator attempts to validate formed symbols for the given received sequence of data symbols; and
obtaining the termination condition, by the codeword validator, when the repetition count reaches a first threshold.
11. A method according to claim 10 , wherein obtaining the termination condition further 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.
12. A method according to claim 10 , wherein obtaining the termination condition further comprises determining that the codebook rate is greater than 1 due to a temporary decrease in channel capacity caused by transient noise.
13. A method according to claim 10 , wherein obtaining the termination condition further comprises the codeword validator declaring an erasure for the inner code.
14. A method according to claim 13 , wherein decoding the k stored codewords according to the outer code comprises declaring an erasure for the outer code when the codeword validator has declared m+1−k erasures for the inner code.
15. A method according to claim 1 , wherein a node, intermediate the data sender and the decoder, performs a method comprising:
receiving a collection of m′ pluralities of data symbols from the data sender or another such node using the noisy data channel, wherein the number m′≤m;
for each received plurality of data symbols, until a termination condition is obtained, repeatedly:
selecting, by a noise guesser according to a noise guessing order, a sequence of noise symbols previously unselected for the given received plurality of data symbols;
forming, in a buffer, a block of formed symbols by inverting a noise effect, of the selected sequence of noise symbols, on the given received plurality of data symbols; and
obtaining the termination condition, by a codeword validator, if the formed symbols comprise a codeword for the inner code;
when the termination condition is obtained for each received plurality of data symbols, storing in a memory the formed symbols as a codeword for the inner code; and
when the memory stores at least a number k′ of codewords for the inner code wherein the number k′≤m′, transmitting the k′ codewords to the decoder.
16. A method according to claim 15 , wherein the method of the intermediate node further comprises receiving soft information pertaining to at least one of the k′ codewords for the inner code.
17. A method according to claim 16 , wherein collectively decoding the at least k′ stored codewords comprises declaring an erasure.
18. A method according to claim 15 , wherein the method of the intermediate node further comprises recoding the outer code at a different rate, without decoding the outer code.
19. A method according to claim 18 , wherein either or both of the outer code and the recoded outer code comprises a random linear network code.
20. A decoder for decoding data that was encoded with an outer code then encoded with an inner code, the decoder comprising:
a receiver for receiving each sequence of data symbols in the plurality from a noisy data channel;
a noise guesser for selecting, according to a noise guessing order, a sequence of noise symbols previously unselected for each given received sequence of data symbols;
a buffer for storing symbols formed by inverting a noise effect, of the selected sequence of noise symbols, on the given received sequence of data symbols;
a codeword validator for obtaining a termination condition when the formed symbols comprise a codeword for the inner code;
a memory for storing, for the given received sequence of data symbols when the termination condition is obtained, the formed symbols as a codeword for the inner code;
an outer decoder for collectively decoding, when the memory stores a number k of codewords for the inner code wherein the number k≤m is determined by the outer code, the k stored codewords according to the outer code; and
an outputter for outputting the decoded data.