Sung-Chul Han (PhD. thesis, Electrical and Computer Engineering, Carnegie Mellon University, 2007)
A Flexible Decoder and Performance Evaluation of Array-Structured LDPC Codes
Preprint (1.4 MB)

The low density parity check (LDPC) codes designed by a pseudorandom construction, as proposed in Gallagerís original work, have been shown to perform very close to the Shannon limit (when constructed as very long codes); however, the lack of structure in such codes makes them unsuitable for practical applications due to high encoding complexity and costly decoder implementations. These difficulties have lead to numerous works on the structured LDPC codes, especially array-structured codes with quasi-cyclic property. Among the array-structured codes, those with an array of cyclic permutation matrices have been of particular interest due to the balanced edge partitioning inherent in the structure that simplifies the implementation of highly parallel decoders. While many construction methods have been proposed for this circulant permutation array (CPA) structure, the performance of the codes has been reported to a very limited extent. Especially, the effect on the performance by the explicit control of graph parameters has not been provided despite the fact their importance is emphasized in the construction process. In the decoder design for quasi-cyclic LDPC codes, the primary concern is to exploit the array structure for efficient implementation. Fast hardware-based decoders on a medium-capacity FPGA are often faster than the software implementation by at least one or two orders of magnitude, and thus important for both actual deployment in practical systems and evaluation of error performance. As a large number of high-throughput decoders in the literature are designed for specific array dimensions and the bus and memory connections are simplified using the array structure of the code, the degree of parallelism in the decoders is dependent on the code parameters, making it difficult to parameterize the hardware to use a desired amount of hardware resource. Furthermore, such architectures cannot support a large class of array-structured codes with very different array dimensions. In this thesis, we present a generalized hardware decoder that supports any kind of quasi-cyclic LDPC codes including CPA-structured codes. The decoder has been designed with a priority on high flexibility. In the synthesis step, the degree of parallelism can be chosen independently from the code parameters. Thus, for FPGA implementation, the decoder can be parameterized to fully utilize a given amount of hardware resource. Also, it supports run-time reconfiguration of code parameters, i.e., different codes can be supported by changing register contents without a new synthesis. In wireless applications, such flexibility makes it possible to choose a channel code based on the varying channel condition. When used for performance evaluation purposes for a large set of codes, it saves a considerable amount of time by eliminating the need for re-synthesis for each code. Using the FPGA implementation of the proposed decoder, we characterize the performance of array-structured LDPC codes, with a primary focus on pseudorandomly constructed CPA-structured codes. Based on the obtained simulation results, we show the effect of combinatorial parameters (girth, diameter and column weight) on the error performance. The pseudorandom construction is also compared with algebraic construction, and with the codes specified in the IEEE 802.16e standards.

LDPC codes, IP cores for FPGA/ASIC

More information:

LDPC website