theroleofspecializationinldpccodes(編輯修改稿)
2024-11-29 17:02 本頁(yè)面
【文章內(nèi)容簡(jiǎn)介】 |1()|0( evPevP ???Decision Rule ? After sufficiently many iterations, return the likelihood ratio: ????? ????o t h e r w i s e ,10)( if ,0?)1(|,ivcvcyx mBxvv?Theorem about MP Algorithm ? If the algorithm stops after r iterations, then the algorithm returns the maximum a posteriori probability estimate of xv given y within radius r of v. ? However, the variables within a radius r of v must be dependent only by the equations within radius r of v, v r ... ... ... Analysis of Message Passing Decoding (Density Evolution) ? in Density Evolution we keep track of message densities, rather than the densities themselves. ? At each iteration, we average over all of the edges which are connected by a permutation. ? We assume that the allzeros codeword was transmitted (which requires that the channel be symmetric). . Update Rule ? The update rule for Density Evolution is defined in the additive domain of each type of node. ? Whereas in , we add (log) messages: ? In , we convolve message densities: ???vcvicvivc mBm39。|)(,39。)(, )(39。???vcvicvivc mDBmD39。|)(,39。)(, ))((39。*)(Familiar Example: ? If one die has density function given by: ? The density function for the sum of two dice is given by the convolution: 1 3 6 5 4 2 2 4 7 6 5 3 8 10 12 11 9 . Threshold ? Fixing the channel message densities, the message densities will either converge to minus infinity, or they won39。t. ? For the gaussian chan
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