Wu, Jiantian | Engineering Papers

NASA NTRS1992

New multilevel codes over GF(q)

Set partitioning to multi-dimensional signal spaces over GF(q), particularly GF sup q-1(q) and GF sup q (q), and show how to construct both multi-level block codes and multi-level trellis codes over GF(q). Two classes of multi-level (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d sub min greater than or = d, are presented. These two classes of codes use Reed-Solomon codes as component codes. They can be easily decoded as block length q-1 Reed-Solomon codes or block length q or q + 1 extended Reed-Solomon codes using multi-stage decoding. Many of these codes have larger distances than comparable q-ary block codes, as component codes. Low rate q-ary convolutional codes, work error correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multi-level trellis codes over GF(q) or binary-to-q-ary trellis codes, some of which have better performance than the above block codes. All of the new codes have simple decoding algorithms based on hard decision multi-stage decoding.

Wu, Jiantian↗

NASA NTRS1991

Multi-dimensional modulation codes for fading channel

Some new codes are presented which have good performance on Rician fading channel with small decoding complexities. A new M-way partition chain is proposed for the L x MPSK (L less than or equal to M) signal set which maximizes the intra-set distance of each subset at each partition level. Based on this partition chain, a class of asymptotical optimum codes was found. For M = 4, these codes have both large symbol distances and product distances. Multi-level coding scheme allows to construct a code by hand such that the code meets some desired parameters, e.g., symbol distance, product distance, etc. In design of a multi-level code, all factors were considered which affect the performance and complexity of the code, such as, the decoding scheme, decoding complexity, and performance under the decoding scheme, e.g., if the multi-stage decoding scheme is used, the performance degradation due to the suboptimum decoding is taken into consideration. The performance for most of the presented codes was simulated on Rayleigh fading channel, and the results show that these codes have good performance with small decoding complexities.

Lin, Shu↗

NASA NTRS1990

New multi-level codes over GF(q)

Set partitioning to multi-dimensional signal spaces over GF(q), particularly GF sup q-1(q) and GF sup q (q), and show how to construct both multi-level block codes and multi-level trellis codes over GF(q). Two classes of multi-level (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d sub min greater than or = d, are presented. These two classes of codes use Reed-Solomon codes as component codes. They can be easily decoded as block length q-1 Reed-Solomon codes or block length q or q + 1 extended Reed-Solomon codes using multi-stage decoding. Many of these codes have larger distances than comparable q-ary block codes, as component codes. Low rate q-ary convolutional codes, work error correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multi-level trellis codes over GF(q) or binary-to-q-ary trellis codes, some of which have better performance than the above block codes. All of the new codes have simple decoding algorithms based on hard decision multi-stage decoding.

Wu, Jiantian↗

NASA NTRS1990

Multi-level trellis coded modulation and multi-stage decoding

Several constructions for multi-level trellis codes are presented and many codes with better performance than previously known codes are found. These codes provide a flexible trade-off between coding gain, decoding complexity, and decoding delay. New multi-level trellis coded modulation schemes using generalized set partitioning methods are developed for Quadrature Amplitude Modulation (QAM) and Phase Shift Keying (PSK) signal sets. New rotationally invariant multi-level trellis codes which can be combined with differential encoding to resolve phase ambiguity are presented.

Costello, Daniel J., Jr.↗