Standard array: Difference between revisions

Revision as of 07:49, 7 October 2015

Revision as of 14:03, 18 February 2016

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To decode a vector using a standard array, subtract the error vector - or coset leader - from the vector received. The result will be one of the codewords in <math>C</math>. For example, say we are using the code C = {0000, 1011, 0101, 1110}, and have constructed the corresponding standard array, as shown from the example above. If we receive the vector 0110 as a message, we find that vector in the standard array. We then subtract the vector's coset leader, namely 1000, to get the result 1110. We have received the codeword 1110.

Decoding via a standard array is a form of [[nearest neighbour decoding]]. In practisepractice, decoding via a standard array requires large amounts of storage - a code with 32 codewords requires a standard array with <math>2^{32}</math> entries. Other forms of decoding, such as [[syndrome decoding]], are more efficient.

Note that decoding via standard array does not guarantee that all vectors are decoded correctly. If we receive the vector 1010, using the standard array above would decode the message as 1110, a codeword distance 1 away. However, 1010 is also distance 1 away from the codeword 1011. In such a case some implementations might ask for the message to be resent. This ambiguity is another reason that different decoding methods are sometimes used.