Performance comparison of imperfect symbol- and bit-interleaving of block codes over GF(2/sup m/) on a Markovian channel

• Published in: IEEE transactions on wireless communications Vol. 3; no. 1; pp. 269 - 277
• Main Authors: Sakakibara, K., Yamakita, J.
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.01.2004; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Block codes; Channels; Codes; Coding, codes; Decoding; Detection, estimation, filtering, equalization, prediction; Diversity reception; Error analysis; Error correction; Error correction codes; Error probability; Errors; Exact sciences and technology; Fading; Information, signal and communications theory; Interleaved codes; Mathematical analysis; Mobile communication; Optimization; Performance analysis; Signal and communications theory; Signal, noise; Strategy; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Performance evaluation; Block code; Error probability; Wireless telecommunication; Analytical method; Transmission channel; Decoding; Markov model
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2003.821157

We analytically compare the performance of imperfectly symbol- and bit-interleaved block codes over GF(2/sup m/) on a first-order Markovian channel in terms of the error probability of a received word. The analytical method developed in Sakakibara (2000) is extended, so that binary transmission of block codes over GF(2/sup m/) can be incorporated with the assumption of negligible probabilities of decoding error. Expressions are derived for two decoding strategies; independent bounded-distance (IBD) decoding and error-forecasting (EF) decoding. In the IBD decoding, channel errors up to half of the minimum distance can be decoded in each received word. On the other hand, combining an erasures-and-errors decoding algorithm, more errors may be corrected in the EF decoding. The derived expressions are examined on two typical classes of two-state Markovian channels. Numerical results indicate that a combination of symbol-interleaving and the EF decoding offers the best performance even for imperfect interleaving. This can compensate for the superiority of perfect symbol-interleaving to perfect bit-interleaving addressed by Wicker (1992). It is also found that the optimum depths of symbol- and bit-interleaver is approximately given by 2b and 4b, respectively, where b is the average length of burst errors in bits.