Polar Codes for $q$-Ary Channels, $q=2^{r}$

Polar codes for q-ary channels, q=2r

We study polarization for nonbinary channels with input alphabet of size q = 2 , r = 2, 3, . . . . Using Arıkan’s polarizing kernel H2, we prove that the virtual channels that arise in the process of polarization converge to q-ary channels with capacity 1, 2, . . . , r bits, and that the total transmission rate approaches the symmetric capacity of the channel. This leads to an explicit transmis...

Nonequivalent q-ary Perfect Codes

Prefixless q-ary Balanced Codes

We will present a Knuth-like method for balancing q-ary codewords, which is characterized by the absence of a prefix that carries the information on the balancing index. Lookup tables for coding and decoding the prefix are avoided. Index Terms Constrained code, balanced code, running digital sum, Knuth code, error correction.

New Constructions for q-ary Covering Codes

Upper bounds on Kq (n; R), the minimum number of codewords in a q-ary code of length n and covering radius R, are improved. Such bounds are obtained by constructing corresponding covering codes. In particular, codes of length q + 1 are discussed. Good such codes can be obtained from maximum distance separable (MDS) codes. Furthermore, they can often be combined eeectively with other covering co...

Construction of new completely regular q-ary codes from perfect q-ary codes

In this paper from q-ary perfect codes a new completely regular q-ary codes are constructed. In particular two new ternary completely regular codes are obtained from the ternary Golay [11,6,5] code and new families of q-ary completely regular codes are obtained from q-ary 1-perfect codes.