低密度奇偶校验码英文翻译.docx

低密度奇偶校验码英文翻译 低密度奇偶校验码英文翻译 低密度奇偶校验码 4 .1 Introduction Chapter 3 analyzed the probability of decoding error for (n, j, k) codes on various binary-input channels using maximum-likelihood decoding. Maximum-likelihood decoding is a convenient concept since it minimizes the probability of decoding error and thus measure the effectiveness of a code apart from any particular decoding scheme. However, implementing a maximum-likelihood decoder that actually compares the received sequence with all possible code words is a most unattractive possibility; this is particularly true for long block lengths, since the size of the code set grows exponentially with block length. A decoder that is relatively simple in terms of equipment, storage, and computation is more desirable even if it moderately increases the probability of error. If the lower probability of error is required, one can simply increase the block length of the code. Two decoding schemes will be described here that appear to achieve a reasonable balance between complexity and probability of decoding error. The first is particularly simple but applicable only to the BSC at rates far below capacity. The second scheme, which decodes directly from the a posteriori probabilities at the channel output is more promising but can be understood more easily after the first scheme is described. In the first decoding scheme, the decoder computes all the parity-checks and then changes any digit that is contained in more than some fixed number of unsatisfied parity-check equations. Using these new values, the parity checks are recomputed, and the process is repeated until the parity checks are all satisfied. If the parity-check sets are small, this decoding procedure is reasonable, since most of the parity-check sets will contain either one transmission error or no transmission errors. Thus when most of the parity-check equations checking on a digit are unsatisfied, there is a strong indication that that