Algebraic decoding of block codes over a q-ary input, Q-ary output channel, Q > q

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.

LDPC Codes over the q-ary Multi-Bit Channel

In this paper, we introduce a new channel model we term the q-ary multi-bit channel (QMBC). This channel models a memory device, where q-ary symbols (q = 2) are stored in the form of current/voltage levels. The symbols are read in a measurement process, which provides a symbol bit in each measurement step, starting from the most significant bit. An error event occurs when not all the symbol bit...

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.

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...