Generalized minimum-distance (GMD) decoding is well-known as a soft decision decoding technique for such linear block codes as BCH and RS codes. The GMD decoding algorithm generates a set of candidate codewords and selects as a decoded codeword that candidate with the smallest reliable distance. In this paper, for a GMD decoder of RS and BCH codes, we present a new sufficient condition for the decoded codeword to be optimal, and we show that this sufficient condition is less stringent than the one presented by Taipale and Pursely.

We study Lempel-Ziv-Yokoo algorithm [1, Algorithm 4] for universal data compression. In this paper, we give a simpler implementation of Lempel-Ziv-Yokoo algorithm than the original one [1, Algorithm 4] and show its asymptotic optimality for a stationary ergodic source.