406 research outputs found
Source Polarization
The notion of source polarization is introduced and investigated. This
complements the earlier work on channel polarization. An application to
Slepian-Wolf coding is also considered. The paper is restricted to the case of
binary alphabets. Extension of results to non-binary alphabets is discussed
briefly.Comment: To be presented at the IEEE 2010 International Symposium on
Information Theory
Polar codes for the two-user multiple-access channel
Arikan's polar coding method is extended to two-user multiple-access
channels. It is shown that if the two users of the channel use the Arikan
construction, the resulting channels will polarize to one of five possible
extremals, on each of which uncoded transmission is optimal. The sum rate
achieved by this coding technique is the one that correponds to uniform input
distributions. The encoding and decoding complexities and the error performance
of these codes are as in the single-user case: for encoding and
decoding, and for block error probability, where
is the block length.Comment: 12 pages. Submitted to the IEEE Transactions on Information Theor
How to Achieve the Capacity of Asymmetric Channels
We survey coding techniques that enable reliable transmission at rates that
approach the capacity of an arbitrary discrete memoryless channel. In
particular, we take the point of view of modern coding theory and discuss how
recent advances in coding for symmetric channels help provide more efficient
solutions for the asymmetric case. We consider, in more detail, three basic
coding paradigms.
The first one is Gallager's scheme that consists of concatenating a linear
code with a non-linear mapping so that the input distribution can be
appropriately shaped. We explicitly show that both polar codes and spatially
coupled codes can be employed in this scenario. Furthermore, we derive a
scaling law between the gap to capacity, the cardinality of the input and
output alphabets, and the required size of the mapper.
The second one is an integrated scheme in which the code is used both for
source coding, in order to create codewords distributed according to the
capacity-achieving input distribution, and for channel coding, in order to
provide error protection. Such a technique has been recently introduced by
Honda and Yamamoto in the context of polar codes, and we show how to apply it
also to the design of sparse graph codes.
The third paradigm is based on an idea of B\"ocherer and Mathar, and
separates the two tasks of source coding and channel coding by a chaining
construction that binds together several codewords. We present conditions for
the source code and the channel code, and we describe how to combine any source
code with any channel code that fulfill those conditions, in order to provide
capacity-achieving schemes for asymmetric channels. In particular, we show that
polar codes, spatially coupled codes, and homophonic codes are suitable as
basic building blocks of the proposed coding strategy.Comment: 32 pages, 4 figures, presented in part at Allerton'14 and published
in IEEE Trans. Inform. Theor
- …