Gallager codes for CDMA applications - Part I: Generalizations, constructions, and performance bounds

We focus on applications of low-rate Gallager (low-density parity-check) co des in code-division multiple-access schemes. The codes that we present her e achieve good performance with relatively short frame-lengths in additive white Gaussian noise channels and, perhaps more importantly, in fading chan nels. These codes can be decoded with low complexity by using iterative dec oding procedures. We present a construction that yields good short frame-le ngth Gallager codes. Bounds on the frame-error probability for a maximum-li kelihood decoder are obtained.