Distributed Reed-Solomon codes for simple multiple access networks
A computer-based distributed error correction scheme with an efficient decoding algorithm is disclosed. The efficiency of the corresponding decoding algorithm, based on standard single source Reed-Solomon error correcting codes, makes the practical employment of the DECC feasible. Various implementation examples are also provided.
1. A single computer-based receiver node comprising a processor configured to:
i) communicate over a computer-based network with distributed error correction code (DECC),
ii) receive source files from multiple computer-based source nodes of the computer-based network via a plurality of computer-based relay nodes of the computer-based network, the source files being encoded by the computer-based relay nodes for transmission to the computer-based receiver, node into encoded source files, and
iii) decode the encoded source files according to a single-source error correcting code having a parity check matrix and a generator matrix whose dimensions are selected based on a number of the plurality of computer-based relay nodes, decoding being operatively implemented in one of: a) hardware, b) software, and c) a combination of a) and b),
wherein one or more of the plurality of encoded source files received by the computer-based receiver node are erroneous due to an erroneous relay transmission link and/or an erroneous computer-based relay node, and
wherein the source files are encoded by the plurality of computer-based relay nodes based on the single source error correcting code.
2. The single computer-based receiver node of claim 1 , wherein the single-source error correcting code is a single-source Reed-Solomon code.
3. The single computer-based receiver node of claim 1 , wherein the processor is further configured to perform the following steps:
1) after receiving the encoded source files from the computer-based relay nodes, organizes the encoded source files as a received single vector;
2) uses the received single vector in combination with the parity check matrix and the generator matrix of the single-source error correcting code to find locations and values of errors in the received single vector; and
3) knowing the errors from step 2), either subtracts the errors from the received encoded source files to decode corrected source files, or obtains a corrected vector, which is a concatenation of the corrected source files, and extracts the corrected source files therefrom.
4. The single computer-based receiver node of claim 3 , wherein the single-source error correcting code is a single-source error correcting code with low encoding and decoding complexity used in the encoding of the encoded source files.
5. The single computer-based receiver node of claim 3 , wherein the single-source error correcting code is a single-source Reed-Solomon code.