Introduction
A low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel by adding redundancy to the data bits. LDPC codes are capacity approaching codes, which means that practical constructions exist that allow for low error probability decoding at noise close to the theoretical maximum (the Shannon limit). LDPC codes are finding increasing use in data-corrupting noise is desired (10 Gbps Ethernet, DVBS-S, etc).
Gallager invented “regular” LDPC codes in 1960 in his Ph.D. thesis. The codes are often represented using a bipartite graph. An example is shown here. The codes are also called (c,d)-regular codes if the bit nodes have degree c and the check nodes have degree d. The goal of this project is to implement a simple LDPC decoder for a (3,4)-regular LDPC code using a message-passing decoding technique called the “Gallager A decoding algorithm”.
On the left is shown the bi-partite graph of an LDPC decoder. With no channel errors, all the parity-check equations (shown at the right) will all be satisfied. The information to be sent is represented by bits B1, B2, and the redundant bits (parity bits), P1, P2, …, P6. The rate of this code is therefore ¼.

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