A bounded-distance decoding algorithm for binary linear block codes achieving the minimum effective error coefficient

A new bounded-distance (BD) decoding algorithm is presented for binary linear (n, k, d) block codes on additive white Gaussian noise channels. The algorithm is based on the generalized minimum distance (GMD) decoding algorithm of Forney (1989) using the acceptance criterion of Taipale and Pursley (GMD/TP) proposed in 1991. It is shown that the GMD/TP decoding algorithm is a BD decoding algorithm with effective error coefficient (ⁿ_d). It is also shown that the decision regions of GMD/TP are good inner approximations of those of full GMD decoding, and therefore full GMD decoding is BD and has an effective error coefficient that is well approximated by (ⁿ _d). Moreover, by adding a d-erasure-correction step to GMD decoding, the effective error coefficient can be reduced to A_d, the number of minimum-weight codewords, which is the same as the effective error coefficient of maximum-likelihood decoding. The decoding algorithm is mainly based on algebraic errors-and-erasures decoding and therefore has polynomial rather than exponential complexity