TABLE OF CONTENTS Error correcting codes (ECC) are a powerful method for increasing the performance of a communications system in AWGN. The basic idea is to add redundancy to a block of bits in such a way that errors that occur in transmission can be corrected giving an overall system performance. In this appendix, we will detail the two most common code types: block codes and convolutional codes. Additional FEC code structures are trellis codes, and low-density parity check codes.
This appendix is designed as a brief introduction to FEC, to familiarize the reader with some its basic concepts. More in depth presentations can be found in the references at the end.
As the name implies, block codes deal with a finite group of input bits at a time. There are three basic numbers associated with such codes:
The number of input bits in the block: k;
The number of output bits in the block: n;
The number of errors that can be corrected: t.
The general notation is simply a [n, k, t] code. For example, the Golay code has the notation [23, 12, 3]. The rate of the code, r, is given by r=k/n.
The algebra of coding theory is Boolean logic. The multiplication operator 
is the common AND gate and has the algebra given in Table C.1.
| Input 1 | Input 2 | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 |
