Takuya Koumoto

A low-weight trellis-based iterative soft-decision decoding algorithm for binary linear block codes

This paper presents a new low-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The algorithm is devised based on a set of optimality conditions and the generation of a sequence of candidate codewords for an optimality test. The initial candidate codeword is generated by a simple decoding method. The subsequent candidate codewords, if needed, are generated by a chain of low-weight trellis searches, one at a time. Each search is conducted through a low-weight trellis diagram centered around the latest candidate codeword and results in an improvement over the previous candidate codewords that have been already tested. This improvement is then used as the next candidate codeword for a test of optimality. The decoding iteration stops whenever a candidate codeword is found to satisfy a sufficient condition on optimality or the latest low-weight trellis search results in a repetition of a previously generated candidate codeword. A divide-and-conquer technique is also presented for codes that are not spanned by their minimum-weight codewords. The proposed decoding algorithm has been applied to some well-known codes of lengths 48, 64, and 128. Simulation results show that the proposed algorithm achieves either practically optimal error performance for the example codes of length 48 and 64 or near optimal error performance for the (128, 29, 32) RM code with a significant reduction in computational decoding complexity.

The least stringent sufficient condition on the optimality of a suboptimally decoded codeword using the most reliable basis

Suppose a binary linear block code C with weight profile W is used for error control over the AWGN channel. A codeword c is mapped into the BPSK sequence x. Let r denote the received noisy vector and z=(z/sub 1/,...,z/sub N/) denote the corresponding bit-by-bit hard decoded sequence. Let V/sup N/ represent the set all binary N-tuples. For u=(u/sub 1/,...,u/sub N/) in V/sup N/, we define D/sub 1/(u)={i:u/sub i//spl ne/z/sub i/,i/spl les/N}, n(u)=|D/sub l/(u)| and D/sub 0/(u)={1,...,N}-D/sub l/(u). Then the maximum likelihood decoding (MLD) solution is the codeword c/sub opt/ which minimize the correlation discrepancy L(c)=/spl Sigma//sub i/spl isin/D1(c)/|Ti|. Consequently if for c*/spl isin/C and /spl alpha/(c*)=min/sub c/spl epsiv/C,c/spl ne/c*/{L(c)}, L(c*)/spl les//spl alpha/(c*), then c*=c/sub opt/. Therefore any lower bound on /spl alpha/(c*) will provide a sufficient condition on the optimality of a candidate codeword.

The least stringent sufficient condition on the optimality of suboptimally decoded codewords

The number of iterations of an iterative optimal or suboptimal decoding scheme for binary linear block codes without any effect on its error performance can be reduced by testing a sufficient condition on the optimality of a candidate codeword. The least stringent sufficient condition on the optimality of a decoded codeword is investigated under the assumption that the available information on the code is restricted to (1) the minimum weight or the distance profile and (2) for a given positive integer h, h or fewer already generated candidate codewords. The least stringent sufficient conditions of optimality for 1/spl les/h/spl les/3 are presented. Cond/sub 1/ is the same as the one given by Taipale and Pursley (1991), Cond/sub 2/ is less stringent than the one given by Kaneko, Nishijima, Inazumi and Hirasawa (see IEEE Trans. Inform. Theory, vol.IT-40, no.3, p.320, 1994), and Cond/sub 1/ and Cond/sub 2/ are derived from Cond/sub 3/ as special cases. These conditions can be used effectively to save computer simulation time for evaluating the error probability for maximum likelihood decoding.

Soft-input soft-output decoding algorithm of linear block codes based on minimum distance search

A new soft-input soft-output (SISO) decoding algorithm based on minimum distance search (MDS), called SISO-IMDS, is presented. The bit error rate of the proposed SISO decoding algorithm is almost the same as those of Max-Log-MAP and Log-MAP algorithms. Moreover, the average decoding complexity of the MDS based SISO decoding algorithm is much smaller than those of trellis-based SISO decoding algorithms. Consequently, the proposed SISO-IMDS can be applied in practical iterative decoding algorithms for a product code and a block turbo code

An improvement to GMD-like decoding algorithms

For binary linear block codes, we introduce a multiple generalized minimum distance (GMD) decoding algorithm, where GMD-like decoding is iterated around a few appropriately selected search centers. Compared with the original GMD decoding by Forney (1966), this decoding algorithm provides better error performance by increasing the number of iterations of erasure and error correction moderately. To reduce the number of iterations, we derive new effective sufficient conditions on the optimality of decoded codewords.

The structure and complexity of subtrellis diagrams for low weight codewords of binary linear block codes

This paper investigates the structure and complexity of low-weight subtrellises for binary linear block codes. The state and branch complexities of low-weight subtrellises for Reed-Muller (RM) codes and some extended permuted BCH (EBCH) codes are given.