Talk:Soft-in soft-out decoder

I'm considering adding the following:

As a simple, but unrealistic, example imagine a 100 dimensional multidimensional parity-check code with data bits arranged into a hypercube 2 bits to a side. Hence there are 2^100 data bits and, disregarding parity on parity, 100 * 2^99 parity bits. We then transimit a message consisting entirely of zeros over a noisy transmission line that results in 10% of the bits being flipped. when we analyze the resulting pattern we would naturally expect that if a data bit is zero then 90% of its parity bits will agree with its value and 10% will will disagree. For data bits that are ones we expect the exact opposite. Correcting this would be simple.

But if we now transmit a message over a transmission line that results in 30% of all bits being flipped then it is more difficult. we assume that data bits that are right will have more parity bits that agree with its value but we can no longer be sure about that. A first pass through the decoder will correct many mistakes but it will also introduce a small number of mistakes of its own. but the message as a whole will contain far fewer mistakes than it did before. multiple passes through the decoder get progressively closer to the original error free message.