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On iterative soft-decision decoding of linear binary block codes and product codes
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DOI：10.1109/49.661116.png)
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Abstract
En 中文
Iterative decoding methods have gained interest, initiated bg the results of the so-called turbo codes. The theoretical description of this decoding, however, seems to be difficult, Therefore, we study the iterative decoding of block codes. First, Re discuss the iterative decoding algorithms developed bg; Gallager, Battail et al, and Hagenauer et al, Based on their results, we propose a decoding algorithm which only uses parity check vectors of minimum weight. We give the relation of this iterative decoding to one-step majority-logic decoding, and interpret it as gradient optimization, It is shown that the used parity check set defines the region, where the iterative decoding decides on a particular codeword. We make plausible that, in almost all cases, the iterative decoding converges to a codeword after some iterations, We derive a computationally efficient implementation using the minimal ellis representing the used parity check set. Simulations will illustrate that our algorithm gives results close to soft decision maximum likelihood (SDML) decoding for many-code classes like BCH codes, Reed-Muller codes, quadratic residue codes, double circulant codes, and cyclic finite geometry codes, Ne also present simulation results far product codes and parallel concatenated codes based on black codes.
Keywords:
iterative decoding
linear binary block codes
majority-logic decoding
minimal trellis
product codes
separable (rectangular) codes
soft-decision decoding
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