D. MacKay's Gallager code resources

Papers on Gallager codes

All David MacKay's papers can be found here, and his textbook on information theory is here: Information Theory, Probability and Neural Networks | Canada mirror

Matrices for codes

Matrices `A', `Cn', and `G' are respectively the parity check matrix (in list format), the right hand square bit of A, and the generator matrix for the code.

Format for raw results

The following format is used in SOME of the raw results files, in particular, the Tanner Product code results.
```Column   Heading        Meaning
============================================================
1	 ebno		Literal value of Eb/No
2        (dB)           Eb/No expressed in decibels
3    distance           A crude measure of how far we are from the shannon limit
4          C            The capacity of the present channel
5          R            The Rate of the code (assumed value)
6          x            s.n.r. of Gaussian channel.
(The input to the channel is +/- x, and the added noise
has standard deviation 1.)
7	  errors	Total number of blocks decoded erroneously
8         trials        Number of blocks simulated
9          undet        Number of UNDETECTED errors
10          blep        Point estimate of block error probability
11          point       Alternate point estimate of block error probability
12          upper       Error bar
13           lower      Error bar
14           bitsw      Number of bits received in error ("bits wrong")
15           undet      Number of bit errors in the "undetected" community.
16      bitep:point	Bit error rate
17           upper      Error bar
18        lower         Error bar
19         maxloops     Number of loops of sum-product at which algorithm halts
and declares detected error
20    mean_lps		Mean number of loops needed to get valid decoding
21	   K		K
22	    N		N
23-27 loop05:25:50:75:95  The 5th, 25th, 50th, 75th, 95th percentiles of the number of
loops needed to get valid decoding.

```

Acknowledgements

The work of the inference group is supported by an award from IBM Zurich research laboratory, and by the Gatsby charitable foundation.
David MacKay <mackay@mrao.cam.ac.uk>