Name
Abstract | ||
|---|---|---|
Use of Extrinsic Information Transfer (EXIT) func- tions, characterizing the amplification of mutual information between the input and output of the Maximum A-Posteriori (MAP) decoder, significantly facilitates analysis of iterative coding schemes. Previously EXIT functions derived for Binary Era- sure Channel (BEC) were used as an approximation for other channels. Here we improve on this approach by introducing more accurate methods to construct EXIT functions for Binary input, Memoryless, Symmetric (BMS) channels. By defining an alternative pseudo-MAP decoder coinciding with the MAP decoder over BEC, we provide an expression for the EXIT functions of block codes over BEC. Furthermore, we draw a connection between the EXIT function over BEC and the EXIT function over BMS channel under certain conditions. This is used for deriving accurate or approximated expressions for EXIT functions over BMS channels in certain scenarios. coding schemes by matching the EXIT functions of the constituent codes. Much less is known on EXIT functions for other Binary input, Memoryless, Symmetric (BMS) channels. In (11),(7) upper and lower bounds on the EXIT functions of the repetition and single parity-check codes were obtained by defining the least and most informative channels for these constraints . The problem can also be approached, especially for more complex codes, using Monte-Carlo simulations (3), or using the EXIT function over BEC as an approximation. In this paper we take another approach and show that in certain scenarios the EXIT function of a code over BMS channels can be expressed (or approximated) as a series having the EXIT function over BEC as its terms. The paper is organized as follows. In Section III, we derive a general expression for computing the extrinsic information at the output of the MAP decoder over BMS channel. In Section IV, we define a pseudo-MAP decoder that coincides with the MAP decoder of a linear code in BEC. Using the pseudo-MAP decoder we derive an expression for the EXIT function of a linear block code over BEC as a function of combinatorial parameters of the code. Furthermore, we draw a connection between the EXIT function of a code over a BMS channel and its EXIT function over the BEC when the pseudo-MAP and MAP decoders coincide. This is used for computing the EXIT functions of single-parity check codes over any BMS channel. In Section V we derive approximations for the EXIT functions and bit error probability curves of some block code over the binary input Additive White Gaussian Noise (biAWGN) channel. The approximations have the form of a series expansion of the EXIT function of the code in BEC. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1109/TCOMM.2006.877956 | IEEE Transactions on Communications |
Keywords | Field | DocType |
block codes,channel coding,maximum likelihood decoding,pseudonoise codes,EXIT functions,binary input memoryless symmetric channels,block codes,extrinsic information transfer,maximum a posteriori decoder,pseudo-MAP decoder,Extrinsic information transfer (EXIT) functions,iterative decoding,maximum a posteriori (MAP) decoding,mutual information | Topology,Combinatorics,Expression (mathematics),Computer science,Control theory,Iterative method,Block code,Turbo code,Communication channel,Input/output,Transfer function,Maximum a posteriori estimation | Journal |
Volume | Issue | ISSN |
54 | 7 | 0090-6778 |
Citations | PageRank | References |
21 | 1.19 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| E. Sharon | 1 | 86 | 4.99 |
| Alexei Ashikhmin | 2 | 2546 | 179.44 |
| Simon N. Litsyn | 3 | 843 | 106.44 |