A decoder including first and second decoding stages for selecting a codeword near to a given N-tuple r which is a sequence of N real values r.sub.i representing signals. The first stage includes substages associated respectively with sections r.sub.j of N-tuple r, each substage for evaluating distances between multiple sets of possible partial codewords and the section r.sub.j and for selecting a survivor from each of the multiple sets based on the distances. The second stage includes n-1 substages, each of which operates with respect to a supersection made up of a combination of two parts, each part being a section or a supersection combined in an earlier substage of the second stage and it includes a final substage which operates with respect to a final supersection whose parts make up the complete N-tuple r. Eachof the n-1 substages is for evaluating distances between multiple sets of possible partial codewords and the received values in the corresponding supersection based on the survivor distances for the survivors corresponding to each of the two parts and for selecting a survivor from each of the multiple sets based on the distances. The final substage is for evaluating distances between the codewords and the N-tuple r based on the survivor distances for the survivors corresponding to each of two parts, for selecting a finally decoded codeword based on the distances between the codewords and N-tuple r, and for providing information about the finally decoded codeword as decoder output.
A method for bounded distance decoding of symbols received in transmission when the original symbols belonged to a Block code featuring series of symbols forming legitimate codewords whose metric distance from the received transmission is measured in Square Euclidean Distance (SED), when the maximum number of errors per word is upward bound by d-1; in which the Block code can be divided into subsets which will each define the entire codeword; and in which the maximum number of errors in at least one subset is one. The method includes dividing the received symbols into a number of blocks per codeword and decoding each block separately and simultaneously with regard to a maximum of one error present in each block. The solution of the decoder is the legitimate codeword with the lowest overall metric distance (SED) from the received transmission.
Some embodiments of the present invention include a decoding system in which the decoding system uses iterative decoding techniques to decode signals encoded with lattice codes and/or multilevel coset codes. The decoding techniciucs according to some embodiments of the invention may be less complex than some decoding techniciues such as maximum likelihood decoding techniciues. Other embodiments of the prevent invention are described and claims.
Apparatus, and an associated method, for encoding and decoding data in a communication system. A hybrid dimensional Spherical Space-Time Code (SSTC) scheme is provided. Data to be transmitted upon a communication channel is encoded, and when received at a receiving station, the encoded sequence is decoded.
A method for constructing a simplified trellis diagram for BCH-encoded information is disclosed. BCH-encoded information is received, having a corresponding parity check matrix H. The parity check matrix H is expressed as an ordered sequence of columns of matrices. A sequence of sub-code words is provided, corresponding to one or more code words, each satisfying a given condition. A matrix H.sup.cp, having columns that are generated as a selected permutation of the columns of the matrix H through a column-permutation-for-binary-matching process, is provided, and a sequence of sub-matrices and a corresponding sequence of permuted sub-code words is provided. A trellis diagram, representing an ordered sequence of code word transitions in the received information and symmetric about a central location, is provided for each code word c, connecting n+1 stages, numbered i=0, 1, . . . , n, in an ordered sequence.
A trellis decoding system is provided having a memory for storing a sequence of received signals. The signals have been encoded prior to transmission by a trellis encoder such that each of a predetermined plurality of symbols represents an allowed transition from an originating state to a predetermined limited number of terminating states. The system includes a trellis decoder for decoding the sequence of received signals into a corresponding sequence of the symbols. A soft decision generator is provided. The soft decision generator is responsive to the signals stored in the memory and to the output of the trellis decoder and determines a soft decision parameter representative of confidence level of the trellis decoder in properly decoding the received signal into each one of the symbols. The determined soft decision parameter is tagged to each one of such symbols subsequent to the trellis decoder decoding the sequence of received signals into the corresponding sequence of symbols.
