Rate-Diversity Optimal Multiblock Space-Time Codes via Sum-Rank Codes

Abstract

Just as rank-metric or Gabidulin codes may be used to construct rate-diversity tradeoff optimal space-time codes, a recently introduced generalization for the sum-rank metric, linearized Reed-Solomon codes, accomplishes the same in the case of multiple fading blocks. We provide the first explicit construction of minimal-delay rate-diversity optimal multiblock space-time codes as an application of linearized Reed-Solomon codes. We then demonstrate in simulation an example of a 2-block 2-by-2 code which, with a small performance penalty—less than 1 dB at a codeword error rate of 1e-4—matches the bit rate of a full diversity alternative while using a much smaller transmitted constellation. A stack decoder for this code is then suggested.