Hitoshi Tokushige

On soft-decision iterative decoding algorithms by using algebraic decoding for RS codes

We consider an iterative decoding algorithm by using algebraic decoding for non-binary codes. In the decoding algorithm, algebraic decoding are carried out with respect to successively chosen input words, called the search centers. We present a new method for selecting sequences of search centers of algebraic decoding. Over the AWGN channel using BPSK signaling, we show simulation results on the error performances of the iterative decoding algorithms whose search centers are given by the proposed method, abbreviated IAD, for Reed-Solomon codes. From the simulation results, IAD provides considerably better error performance than GMD and CGA decoding with the same number of iterations.

An improved search algorithm for the adaptive and recursive MLD algorithm

An efficient algorithm for the soft-decision maximum likelihood decoding of linear block codes is presented. The algorithm makes use of the structural properties of linear block codes, and a call-by-need computing strategy to reduce the time and space complexity.

On the binary images of (8, 5) shortened cyclic codes over GF(2/sup 8/)

We consider the binary images of (8, 5) shortened cyclic codes. The (8, 5) shortened cyclic codes have a variety of choices. We have generated about 30000 sample codes with different weight distributions. Let S/sub w/ denote the set of generated sample codes with minimum weight w. The largest minimum weight of sample codes is 8. Let A/sub w/ denote the number of codewords of weight w of a sample code. In S/sub 7/, the smallest of A/sub 7/ is 10 for 10 sample codes and the second smallest of A/sub 7/ is 11 for six sample codes. In S/sub 7/, the smallest of A/sub 8/ is 728 for a sample code and the second smallest of A/sub 8/ is 729 for a sample code. We have chosen two sample codes from each of S/sub 7/ and S/sub 8/ which have the smallest and the second smallest sums of A/sub w/ for 7/spl les/w/spl les/9 in S/sub 7/ and S/sub 8/, respectively. For the AWGN channel using BPSK signaling, we have made simulation to evaluate the decoding error probabilities by a soft-decision decoding based on ordered statistics for the chosen four sample codes at SNR 2.0 to 5.0. These error probabilities are considerably smaller than the optimum error probabilities for (64, 40) subcodes of (64, 42) Reed-Muller code.

Sufficient Conditions on Most Likely Local Sub-codewords in Recursive Maximum Likelihood Decoding Algorithms

First, top-down RMLD (recursive maximum likelihood decoding) algorithms are reviewed. Then, in connection with adjacent sub-codewords, a concept of conditional syndrome is introduced. Based on this, sufficient conditions of most likely local sub-codewords in top-down RMLD algorithms are presented. These conditions lead to efficient implementations of top-down RMLD algorithms.

Selection Method of Test Patterns in Soft-Input and Output Iterative Bounded Distance Decoding Algorithm

In this paper, we consider a soft-input and soft-output iterative bounded-distance decoding (SISO-IBDD) algorithm in which the bounded-distance decodings are performed sequentially. And we study a computation method of a soft-output value to approximate Max-Log-MAP. In the decoding algorithm, search centers are generated by the sums of the hard-decision sequence obtained from a received sequence and test patterns which are selected beforehand, and the bounded-distance decodings with respect to the search centers are performed. We have proposed a selection method of test patterns for an iterative bounded-distance decoding (IBDD) algorithm in [5]. Simulation results have shown that the IBDD algorithm whose test patterns are selected by the proposed method with considerably small number of iterations provides better error performance than the Chase II decoding algorithm for several BCH codes over an AWGN channel using BPSK signaling. We adopt the selection method of test patterns for the SISO-IBDD algorithm and a computation method of a soft-output value which is modified based on the proposed method in [2] with respect to reliability factors. Over the AWGN channel using the BPSK signaling, we show bit error rates and average soft-output values given by the SISO-IBDD algorithm for the extended BCH (64, 36, 12) and (64, 45, 8) codes by computer simulation. For the extended BCH codes, the simulation results show that bit error rates of the SISO-IBDD algorithm are relatively smaller than those of a Chase-like decoding algorithm with the same number of iterations of the bounded-distance decodings and for each component bit, average soft-output values provided by the SISO-IBDD algorithm are close to those by the Max-Log-MAP decoding algorithm by computer simulation.

On binary images of shortened cyclic (8, 5) codes over GF(2/sup 8/)

We have generated binary images of a large number of shortened cyclic (8, 5) codes over GF(2/sup 8/) and have computed weight distributions of the binary images of the codes. Based on the weight distributions, we have chosen four codes with the largest minimum weight 8 and the second largest minimum weight 7 among the generated codes. Over an additive white Gaussian noise channel with binary phase-shift keying modulation, simulation results have shown that block error rates of the chosen codes by a soft-decision decoding based on order-2 reprocessing are smaller than those of (64, 40) subcodes of Reed-Muller (64, 42) code by maximum likelihood decoding.