Gallager codes for CDMA applications: generalizations, constructions and performance

We focus on applications of low rate (low-density parity-check) Gallager (1963) codes in code-division multiple access (CDMA) schemes. These codes can be decoded with low complexity by using iterative decoding procedures. We present a construction that yields good, short frame length, low rate Gallager codes. We estimate that by using Gallager codes, a factor of five improvement in CDMA cell capacity relative to an uncoded system can be achieved, equivalent to a factor of two improvement relative to state-of-the art orthogonal convolutional codes. Simulation results show that, compared with short frame length turbo codes, Gallager codes achieve a 0.5 dB improvement in AWGN channels and over 2 dB improvement in fading channels in the signal-to-noise ratio required to achieve frame error rates of 10/sup -3/.