Complex M-spotty byte error control codes

Spotty byte error control codes are very effective for correcting/detecting errors in semiconductor memory systems using recent high-density RAM chips with wide I/O data, e.g. 8, 16, or 32 bits. A spotty byte error is defined as t-bit errors within a byte of length b-bit, where 1 ≤ t ≤ b, and denoted as t/b-error. This paper proposes a new error model of two spotty byte errors occurred simultaneously, i.e., t/b-error and t´/b-error, where t ≠ t´, called complex spotty byte errors. This paper presents two complex m-spotty byte error control codes, i.e., (S_tb/EC-(S_tb/+S_t´b/)ED) codes which correct all single t/b-errors and detect both t/b-errors and t´/b-errors simultaneously, and ((S_tb/+S_t´b/)EC) codes which correct both single t/b-errors and single t´/b-errors simultaneously. This paper also presents practical examples of the codes with parameter t´ = 1, that is, S_tb/EC-(S_tb/+S)ED codes and (S_tb/+S) EC codes which require smaller check-bit length than the existing S_tb/EC-D_tb/ED codes and the D_tb/EC codes, respectively.