Optimization–based decoding algorithms for LDPC convolutional codes in communication systems

Abstract

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.LDPC Convolutional (LDPC-C) codes, introduced by J. Feltström and Zigangirov in 1999, are preferred to LDPC block codes in decoding for the cases where information is obtained continuously. They can be decoded by sliding window decoders which implement iterative decoding algorithms (such as belief propagation and density evaluation) at each window [19].Although LDPC-C codes provide short-delay and low-complexity in decoding, they are not in communication standards such as WiMax and DVB-S2 yet [20].In this study, we consider LDPC-C codes and propose optimization based sliding window decoders that can give a near optimal decoded codeword for a received vector of practical length (approximately n = 4000) in an acceptable amount of time. The mathematical formulation and proposed decoding algorithms are explained in Section 3. Our proposed decoders can be used in a real-time reliable communication system since they have low decoding latency.Besides, they are applicable in settings such as deep-space communication system due to their 3 high error correction capability.The rest paper is organized as follows: we define the problem in more detail in the next section. Section 3 explains the proposed decoding techniques. We give the corresponding computational results in Section 4. Some concluding remarks and comments on future work appear in Section 5. Problem DefinitionDigital communication systems transmit information from a sender to a receiver over a communication channel. Communication channels are unreliable environments, such as air, that many sender-receiver pairs share. Hence, during transmission some of the transmitted symbols can be lost or their values can change. In coding theory, information is encoded in order to overcome the occurance of such errors during the transmission. Let the information to be sent be represented by a k-bits long sequence u = u 1 u 2 ...u ...

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