Lower bounds on achievable rates for limited bitshift correctingcodes

Limited codes (runlength-limited, charge constrained, and so on) capable of correcting shifts of their symbols are considered. The error-correction ability is characterized by the minimal bitshift distance d_BS of a code. For a given δ=d_BS/n, where n is the code length, the achievable code rate R_α is lower bounded. We prove the existence of codes of rate R⩾R_α     

Bounds on the zero-error capacity of the input-constrainedbit-shift channel

New lower and upper bounds on a maximal achievable rate fur runlength-limited codes, capable of correcting any combination of bit-shift errors (i.e. a zero-error capacity of the bit-shift channel), are presented. The lower bound is a generalization of the bound obtained by Shamai and Zehavi (1991). It is shown that in certain cases, the upper and the lower bounds asymptotically coincide     

Reed-Solomon codes for correcting phased error bursts

A code structure is introduced that represents a Reed-Solomon (RS) code in two-dimensional format. Based on this structure, a novel approach to multiple error burst correction using RS codes is proposed. For a model of phased error bursts, where each burst can affect one of the columns in a two-dimensional transmitted word, it is shown that the bursts can be corrected using a known multisequence shift-register synthesis algorithm. It is further shown that the resulting codes posses nearly optimal burst correction capability, under certain probability of decoding failure. Finally, low-complexity systematic encoding and syndrome computation algorithms for these codes are discussed. The proposed scheme may also find use in decoding of different coding schemes based on RS codes, such as product or concatenated codes.