Power/subcarrier allocation and decoding schedule for LDPC coded OFDM systems
The low density parity check (LDPC) codes are powerful error-correcting codes that, thanks in part to the belief propagation (BP) decoding algorithms, offers near-Shannon Limit performance when the code length is sufficiently (but finite) long. The BP algorithms refer to a class of iterative algorithms that passes probabilistic (reliability) messages on a graph that describes the probabilistic (Markovian) relations amongst the associated random variables. With proper message-updating rules and message-passing schedule, a BP algorithm can efficiently compute the a posterior probability (APP) or likelihood function needed in maximum likelihood (ML) or APP decoding. Two parallel-serial decoding algorithms, namely, the horizontal shuffled BP (HSBP) and the vertical shuffled BP (VSBP) algorithms, have been proposed in the literature. They partition either the check or variable nodes into several groups where a group consists of (almost) the same number of consecutive nodes according to the natural order of the parity-check matrix and carry out the BP process in group-by-group manner. Three design issues for the resulting parallel-serial decoder arise: the degree of parallelism (the cardinality of a group), the partition rule (which nodes should be in the same group) and the associated message-passing schedule. All of these three design concerns affect the decoder complexity, convergence speed and the error rate performance. The basic per-sub-iteration message-passing behavior of a shuffled BP algorithm is determined by the corresponding submatrices of the parity check matrix H. That of a shuffled BP using a partition which is not based on the natural order can be described by a permuted version of the original H. An all-zero column (row) in a sub-matrix implies that the corresponding nodes will undergo no information update. It is thus desired that there be as few all-zero columns (rows) in a sub-matrix as possible. We present two partition criteria; the first criterion is based on the innovation rate (new uncorrelated information collected per sub-iteration) while the second one is based on the bit nodes' normalized correlation spreads (NCS) which are used to measure the degree of local flooding uniformity of a bit node in each iteration. As the NCS also reveals the unequal error protection (UEP) nature of a irregular LDPC code, the second partition actually divides the bit nodes into groups with different error rate performance. In a muticarrier transmission system, such an UEP property can be exploited to improve the overall performance by using a proper power and subcarrier allocation in carrying out BP decoding. Numerical simulation indicate that both approaches yield improved error rate and convergence performance.
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