Codes for high-noise memoryless channels

We consider code design for high-noise memoryless channels, which emerge in various low-power applications, such as IoT or sensor networks. To address this case, we design simple LDPC-type codes that have growing dimension m and length m(m + 1)/2. These codes can be regarded as a "weakly-coded" modulation: they outperform uncoded modulation for the signal-to-noise ratios (SNR) above -3 dB per information bit and achieve a 3 dB gain as SNR grows. Similar to uncoded modulation, these codes also exhibit a floor on the output bit error rate (BER) for any m. To improve code performance, information bits are further protected with some polar code of length m. The overall design has low complexity of order m
²
log m and a vanishing BER of order exp{-m
^1/2
}. It substantially outperforms biorthogonal codes for any SNR > 0 dB given the same code rate or blocklength.