Generalized minimum-distance decoding

<p>In <a href="/facts/Coding_theory/SBqStoGL">coding theory</a>, generalized minimum-distance (GMD) decoding provides an efficient <a href="/facts/Algorithm/fnl5NmRt">algorithm</a> for decoding <a href="/facts/Concatenated_code/kMtLmN80">concatenated codes</a>, which is based on using an <a href="/facts/Error/20QgR4EI">errors</a>-and-<a href="/facts/Erasure_code/ea1C1z2X">erasures</a> decoder for the <a href="/facts/Outer_code/kMtLmN80">outer code</a>.
</p><p>A <a href="/facts/Concatenated_error_correction_code/kMtLmN80">naive decoding algorithm</a> for concatenated codes can not be an optimal way of decoding because it does not take into account the information that <a href="/facts/Maximum_likelihood_decoding/A0x9Dpgq">maximum likelihood decoding</a> (MLD) gives. In other words, in the naive algorithm, inner received <a href="/facts/Code_word_(communication)/sASREopJ">codewords</a> are treated the same regardless of the difference between their <a href="/facts/Hamming_distance/MgdtbYPo">hamming distances</a>. Intuitively, the outer decoder should place higher confidence in symbols whose inner <a href="/facts/Code/CSntvnEo">encodings</a> are close to the received word. <a href="/facts/David_Forney/dKvnKPT2">David Forney</a> in 1966 devised a better algorithm called generalized minimum distance (GMD) decoding which makes use of those information better. This method is achieved by measuring confidence of each received codeword, and erasing symbols whose confidence is below a desired value. And GMD decoding algorithm was one of the first examples of <a href="/facts/Soft-decision_decoder/MXyhx2cC">soft-decision decoders</a>. We will present three versions of the GMD decoding algorithm. The first two will be <a href="/facts/Randomized_algorithm/Fngl1zgk">randomized algorithms</a> while the last one will be a <a href="/facts/Deterministic_algorithm/v8x4wz35">deterministic algorithm</a>.
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Generalized minimum-distance decoding open-in-new

Generalized minimum-distance decoding