Abstract: A system of determining unknown symbols of an error correcting code using the Discrete Fourier Transform (DFT) with arithmetic corresponding to the number field of the error correcting code, including complex numbers. Encoder and decoder configurations are described. Parallel generation of independent parity check equations, simultaneous solution of unknown symbols generating, or regenerating a codeword of the error correcting code.

Abstract: This invention provides an error correction system whereby codes, including codes known to be optimum, may be concatenated together so that a longer code is produced which may be decoded by decoding the individual codes using any type of error correcting decoder including list decoders, Dorsch decoders in particular, and iterative decoders. The concatenated code consists of one or more codes having replicated codewords to which are added codewords from one or more other codes. The code construction is utilised in the receiver with a decoder that firstly decodes one or more individual codewords from a received vector. The detected codewords from this first decoding are used to undo the code concatenation within the received vector to allow the replicated codewords to be decoded. Examples of the performance benefits of the invention in comparison to the well known state of the art coding arrangement of LDPC codes, and turbo codes using iterative decoders are given for (256,128) and (512,256) codes.

Abstract: In packet digital communications using a two way communications medium such as wireless each received packet is subject to noise and/or interference which causes errors in some of the received symbols. A common method known as Incremental Redundancy (IR), Hybrid Automatic Repeat Request (HARQ) for corrects these transmission errors by using error detection in conjunction with transmission of additional redundant symbols forming a sequence of forward error correcting codes. Any residual errors are detected by means of a Cyclic Redundancy Check (CRC). The CRC symbols represent transmission overhead and degrade the throughput regardless of the quality of the transmission channel. This invention is concerned with providing error detection without the need for a CRC thereby improving the throughput. In a further embodiment of the invention for those systems that employ a CRC increased reliability of detection is provided which also leads to an improvement in throughput.