Fast Min-Sum Algorithms for Decoding of LDPC over GF(q)

In this paper, we present a fast min-sum algorithm for decoding LDPC codes over GF(q). Our algorithm is different from the one presented by David Declercq and Marc Fossorier in ISIT 05 only at the way of speeding up the horizontal scan in the min-sum algorithm. The Declercq and Fossorier's algorithm speeds up the computation by reducing the number of configurations, while our algorithm uses the dynamic programming instead. Compared with the configuration reduction algorithm, the dynamic programming one is simpler at the design stage because it has less parameters to tune. Furthermore, it does not have the performance degradation problem caused by the configuration reduction because it searches the whole configuration space efficiently through dynamic programming. Both algorithms have the same level of complexity and use simple operations which are suitable for hardware implementations.Comment: Accepted by IEEE Information Theory Workshop, Chengdu, China, 200

Single-Scan Min-Sum Algorithms for Fast Decoding of LDPC Codes

Many implementations for decoding LDPC codes are based on the (normalized/offset) min-sum algorithm due to its satisfactory performance and simplicity in operations. Usually, each iteration of the min-sum algorithm contains two scans, the horizontal scan and the vertical scan. This paper presents a single-scan version of the min-sum algorithm to speed up the decoding process. It can also reduce memory usage or wiring because it only needs the addressing from check nodes to variable nodes while the original min-sum algorithm requires that addressing plus the addressing from variable nodes to check nodes. To cut down memory usage or wiring further, another version of the single-scan min-sum algorithm is presented where the messages of the algorithm are represented by single bit values instead of using fixed point ones. The software implementation has shown that the single-scan min-sum algorithm is more than twice as fast as the original min-sum algorithm.Comment: Accepted by IEEE Information Theory Workshop, Chengdu, China, 200

Deriving the Normalized Min-Sum Algorithm from Cooperative Optimization

The normalized min-sum algorithm can achieve near-optimal performance at decoding LDPC codes. However, it is a critical question to understand the mathematical principle underlying the algorithm. Traditionally, people thought that the normalized min-sum algorithm is a good approximation to the sum-product algorithm, the best known algorithm for decoding LDPC codes and Turbo codes. This paper offers an alternative approach to understand the normalized min-sum algorithm. The algorithm is derived directly from cooperative optimization, a newly discovered general method for global/combinatorial optimization. This approach provides us another theoretical basis for the algorithm and offers new insights on its power and limitation. It also gives us a general framework for designing new decoding algorithms.Comment: Accepted by IEEE Information Theory Workshop, Chengdu, China, 200