Performance of Sphere Decoding of Block Codes

• Published in: IEEE transactions on communications Vol. 57; no. 10; pp. 2940 - 2950
• Main Authors: El-Khamy, M., Vikalo, H., Hassibi, B., McEliece, R.J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; AWGN channels; Block codes; Channels; Coding, codes; Complexity; Decoders; Decoding; Exact sciences and technology; High definition video; Information theory; Information, signal and communications theory; Lattices; Linear code; Maximum likelihood decoding; Modulation; Modulation, demodulation; Performance analysis; performance bounds; radius; Reed-Solomon codes; Searching; Signal and communications theory; sphere decoding; symmetric channels; Telecommunications and information theory; Upper bound; Reed Solomon code; Performance evaluation; Block code; symmetric channels; Maximum likelihood decoding; AWGN channels; Reed-Solomon codes; sphere decoding; Linear code; Upper bound; decoding radius; Modulation; block codes; Soft decision; performance bounds
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2009.10.080402

A sphere decoder searches for the closest lattice point within a certain search radius. The search radius provides a tradeoff between performance and complexity. We focus on analyzing the performance of sphere decoding of linear block codes. We analyze the performance of soft-decision sphere decoding on AWGN channels and a variety of modulation schemes. A hard-decision sphere decoder is a bounded distance decoder with the corresponding decoding radius. We analyze the performance of hard-decision sphere decoding on binary and q -ary symmetric channels. An upper bound on the performance of maximum-likelihood decoding of linear codes defined over F q (e.g. Reed- Solomon codes) and transmitted over q -ary symmetric channels is derived and used in the analysis. We then discuss sphere decoding of general block codes or lattices with arbitrary modulation schemes. The tradeoff between the performance and complexity of a sphere decoder is then discussed.