Development of two new mean codeword lengths

  • Authors:
  • Om Parkash;Priyanka Kakkar

  • Affiliations:
  • Department of Mathematics, Guru Nanak Dev University, Amritsar 143 005, India;Department of Mathematics, Guru Nanak Dev University, Amritsar 143 005, India

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2012

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Abstract

Two new mean codeword lengths L(@a,@b) and L(@b) are defined and it is shown that these lengths satisfy desirable properties as a measure of typical codeword lengths. Consequently two new noiseless coding theorems subject to Kraft's inequality have been proved. Further, we have shown that the mean codeword lengths L"1":"1(@a,@b) and L"1":"1(@b) for the best one-to-one code (not necessarily uniquely decodable) are shorter than the mean codeword length L"U"D(@a,@b) and L"U"D(@b) respectively for the best uniquely decodable code by no more than log"Dlog"Dn+3 for D=2. Moreover, we have studied tighter bounds of L(@a,@b).