期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 57, 期 2, 页码 803-834出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2010.2095072
关键词
Belief-propagation (BP) decoder; capacity-achieving codes; convolutional low-density parity-check (LDPC) codes; density evolution (DE); EXIT curves; maximum a posteriori (MAP) decoder; protographs
资金
- Swiss National Science Foundation [200020-113412]
Convolutional low-density parity-check (LDPC) ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed to date, all of which share the good performance characteristics of convolutional LDPC ensembles. We describe the fundamental mechanism that explains why convolutional-like or spatially coupled codes perform so well. In essence, the spatial coupling of individual codes increases the belief-propagation (BP) threshold of the new ensemble to its maximum possible value, namely the maximum a posteriori (MAP) threshold of the underlying ensemble. For this reason, we call this phenomenon threshold saturation. This gives an entirely new way of approaching capacity. One significant advantage of this construction is that one can create capacity-approaching ensembles with an error correcting radius that is increasing in the blocklength. Although we prove the threshold saturation only for a specific ensemble and for the binary erasure channel (BEC), empirically the phenomenon occurs for a wide class of ensembles and channels. More generally, we conjecture that for a large range of graphical systems a similar saturation of the dynamical threshold occurs once individual components are coupled sufficiently strongly. This might give rise to improved algorithms and new techniques for analysis.
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