Capacity achieving code constructions for two classes of (d,k) constraints

• Published in: IEEE transactions on information theory Vol. 52; no. 7; pp. 3333 - 3343
• Main Authors: Sankarasubramaniam, Y., McLaughlin, S.W.
• Format: Journal Article
• Language: English
• Published: IEEE 01-07-2006
• Subjects: Algorithms; Bending machines; Binary sequences; Bit flipping; bit stuffing; Construction; Disk recording; Encoders; Encoding; History; Information theory; Interference constraints; Interleaved codes; Intersymbol interference; Magnetic separation; Optical recording; Optical sensors; Shannon capacity; Streams; Symbols; Timing
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2006.876224

This correspondence presents two variable-rate encoding algorithms that achieve capacity for the (d,k) constraint when k=2d+1, or when k-d+1 is not prime. The first algorithm, symbol sliding, is a generalized version of the bit flipping algorithm introduced by Aviran In addition to achieving capacity for (d,2d+1) constraints, it comes close to capacity in other cases. The second algorithm is based on interleaving and is a generalized version of the bit stuffing algorithm introduced by Bender and Wolf. This method uses fewer than k-d biased bit streams to achieve capacity for (d,k) constraints with k-d+1 not prime. In particular, the encoder for (d,d+2/sup m/-1) constraints 2 /spl les/ m < /spl infin/ requires only m biased bit streams.