  In a digital communication system, information is sent from one place to
another over a noisy communication channel. It may be possible to detect and
correct errors that occur during the transmission if one encodes the original
information by adding redundant bits. Low-density parity-check (LDPC)
convolutional codes, a member of the LDPC code family, encode the original
information to improve error correction capability. In practice these codes are
used to decode very long information sequences, where the information arrives
in subsequent packets over time, such as video streams. We consider the problem
of decoding the received information with minimum error from an optimization
point of view and investigate integer programming-based exact and heuristic
decoding algorithms for its solution. In particular, we consider relax-and-fix
heuristics that decode information in small windows. Computational results
indicate that our approaches identify near-optimal solutions significantly
faster than a commercial solver in high channel error rates. Our proposed
algorithms can find higher quality solutions compared with commonly used
iterative decoding heuristics.
