60 research outputs found
Polar codes with a stepped boundary
We consider explicit polar constructions of blocklength
for the two extreme cases of code rates and
For code rates we design codes with complexity order of in code construction, encoding, and decoding. These codes achieve the
vanishing output bit error rates on the binary symmetric channels with any
transition error probability and perform this task with a
substantially smaller redundancy than do other known high-rate codes,
such as BCH codes or Reed-Muller (RM). We then extend our design to the
low-rate codes that achieve the vanishing output error rates with the same
complexity order of and an asymptotically optimal code rate
for the case of Comment: This article has been submitted to ISIT 201
Long Nonbinary Codes Exceeding the Gilbert - Varshamov Bound for any Fixed Distance
Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance
d. We study the minimum asymptotic redundancy \rho(q,n,d)=n-log_q A(q,n,d) as n
grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are
designed that improve on the BCH codes and have the lowest asymptotic
redundancy \rho(q,n,d) <= ((d-3)+1/(d-2)) log_q n known to date. Prior to this
work, codes of fixed distance that asymptotically surpass BCH codes and the
Gilbert-Varshamov bound were designed only for distances 4,5 and 6.Comment: Submitted to IEEE Trans. on Info. Theor
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