Patent ID: 8473826

Claim:
A method comprising: (a) inputting received code symbols into a hard decision (HD) Reed Solomon (RS) decoding method; (b) decoding the received code symbols with the HD RS decoding method; (c) determining whether a decoding failure occurs; (d) wherein when a decoding failure does not occur, outputting decoded data; (e) wherein when a decoding failure occurs, computing soft decision (SD) reliability information for each code symbol to determine most likely code symbol errors, wherein computing SD reliability information for each code symbol further comprises: computing a single matrix for all possible code symbols at each code symbol location where each matrix element is given by P r ⁡ ( T = t α ❘ R = r β ) = f ⁡ ( r β ❘ t α ) ∑ t ∈ T ⁢ f ⁡ ( r β ❘ t ) where T is an M-ary signal that represents a transmitted symbol, R is a random variable that models the received code signal, f(r β |t α ), is a conditional probability density function, α varies from 1 to M, M being a number of symbols in a constellation, and β varies from 1 to n, n being a block length of a code; (f) selecting the most likely code symbol errors for each code symbol from the single matrix; (g) inputting the most likely code symbol errors for each code symbol into the HD RS decoding method to generate a revised HD RS decoding method; (h) decoding the received code symbols with the revised HD RS decoding method; (i) determining whether a decoding failure occurs; (j) wherein when a decoding failure does not occur, outputting the decoded data; (k) wherein when a decoding failure occurs, selecting next most likely code symbol errors for each code symbol; (l) inputting the next most likely code symbol errors for each code symbol into the HD RS decoding method to generate a revised HD RS decoding method; and (m) returning to operation (h).