Another theoretically interesting thread within this topic is: "How will the rules change, when two or more independent users transmit simultaneously?" A beginning graduate student in our group has come up with some number theoretic constructions. As a new tool he needed some facts from Diophantine approximation. The information theory in that thread is, I'm sad to say, over my head. I am willing to also bet that this question on MO derives its motivation from this problem area :-)

Another theoretically interesting thread within this topic is: "How will the rules change, when two or more independent users transmit simultaneously?" A beginning graduate student in our group has come up with some number theoretic constructions. As a new tool he needed some facts from Diophantine approximation. The information theory in that thread is, I'm sad to say, over my head. I am willing to also bet that this question on MO derives its motivation from this problem area :-)

Many a standard (IIRC in addition to DVB also, MediaFlo, a US standard for something similar) uses families of LDPC-codes designed around a specific decoding circuitry. This is more or less necessary, because otherwise the problem of routing the messages generated by the belief propagation algorithm becomes prohibitive. An exception to this rule is the Chinese video broadcast standard. At least the parts of that standard that I have seen describe the LDPC-codes in such a way that no structure is apparent. They may be protecting their intellectual property :-)

By using basic facts of global class field theory my graduate students managed to "improve" upon the Golden code. I put the "improve" in quotes, because the improvement is somewhat theoretical. A more precise way of stating their result is that if you carve a given number of multiantenna signals from their lattice (representing a maximal order of a division algebra), you are less likely to make an error at the receiving end than what would happen, if you carve your signal set from one of the codes proposed by Oggier et al. However, that's not the end of the story. If you combine that multiantenna constellation with, for example, an LDPC code, our construction loses its theoretical advantage, because an LDPC-decoder wants to have reliability information about individual bits. When you pack several bits worth of information into a selection of a single multiantenna signal, our method creates more dependencies among those reliability figures, and that makes things worse in the end. Anyway, the math in the construction of my students is fun, and they all graduated, so...

This question hit too close. It is not entirely clear that I managed to be objective.

Many a standard (IIRC in addition to European DVB also MediaFlo, a US standard for something similar) uses families of LDPC-codes designed around a specific decoding circuitry. This is more or less necessary, because otherwise the problem of routing the messages generated by the belief propagation algorithm becomes prohibitive. An exception to this rule is the Chinese video broadcast standard. At least the parts of that standard that I have seen describe the LDPC-codes in such a way that no structure is apparent. They may be protecting their intellectual property :-)

By using basic facts of global class field theory my graduate students managed to "improve" upon the Golden code (by Oggier et al). I put the "improve" in quotes, because the improvement is somewhat theoretical. A more precise way of stating their result is that if you carve a given number of multiantenna signals from their lattice (representing a maximal order of a division algebra), you are less likely to make an error at the receiving end than what would happen, if you carve your signal set from one of the codes proposed by Oggier et al. However, that's not the end of the story. If you combine that multiantenna constellation with, for example, an LDPC code, our construction loses its theoretical advantage, because an LDPC-decoder wants to have reliability information about individual bits. When you pack several bits worth of information into a selection of a single multiantenna signal, our method creates more dependencies among those reliability figures, and that makes things worse in the end. Anyway, the math in the construction of my students is fun, and they all graduated, so...

This question hit too close. It is not entirely clear that I managed to be objective.

The Golden Code (Oggier et al) is in a hyperWLAN standard. Don't know how widely that part of the standard is used. Multiantenna coding in cellular applications goes largely by different rules. This is because there is a feedback channel there, so the transmitter also has an idea of the channel state, and can take advantage. The math becomes easier then (so I've been told). This is not possible in a broadcast application, because there may be millions of receivers, and knowing their channel states is A) impossible, B) useless because you can't optimize the transmission for all of them simultaneously.