Abstract: The compact disk read-only memory (CD-ROM) is a mature storage medium with complex error control. It comprises four levels of Reed Solomon codes allied to a sequence of sophisticated interleaving strategies and 8:14 modulation coding. New storage media are being developed and introduced that place still further demands on signal processing for error correction. It is therefore appropriate to explore thoroughly the limit of existing strategies to assess future requirements. We describe a simulation of all stages of the CD-ROM coding, modulation, and decoding. The results of decoding the burst error of a prescribed number of modulation bits are discussed in detail. Measures of residual uncorrected error within a sector are displayed by C1, C2, P, and Q error counts and by the status of the final cyclic redundancy check (CRC). Where each data sector is encoded separately, it is shown that error-correction performance against burst errors depends critically on the position of the burst within a sector. The C1 error measures the burst length, whereas C2 errors reflect the burst position. The performance of Reed Solomon product codes is shown by the P and Q statistics. It is shown that synchronization loss is critical near the limits of error correction. An example is given of miscorrection that is identified by the CRC check.

Abstract: Reed-Solomon (RS) error-correcting codes are often proposed for communication systems requiring burst-error-correction capabilities. The performance of RS codes is examined for the case when symbol errors are dependent and therefore not random. This situation arises when interleaving is not possible due to delay constraints, such as in most voice-communication systems. The performance is compared with that obtained using a random-error assumption.

Abstract: This paper presents various lower and upper bounds on the number of parity check digits required for linear codes having sub-block structure that detect and correct random or/and burst errors.

Abstract: Arithmetic an codes are useful for detecting and correcting errors in arithmetic operations and digital data transmission. Especially, cyclic an codes are considered to be useful. First, outlines of binary cyclic an codes and burst errors are described. Second, a method to construct the binary cyclic an codes consisting of 2m - 1 codewords is presented and the burst error correcting ability of these codes is discussed. the number of codewords generally is one of the most important parameters for selecting a suitable code for a given system. From these codes, a binary cyclic an code satisfying requirements of both the number of codewords and the correcting ability in the system can easily be chosen. A relation between the code rate and the correcting ability also is discussed. Finally, another relation between the burst error correcting ability and the random error correcting ability is discussed. As a result, using the constructing method proposed here, binary cyclic an codes can be constructed which will be useful not only for the burst error correction but also for the random error correction.

Abstract: Cyclic codes are often used for the purpose of correcting burst errors in digital transmission and recording systems. Since the implementations of the encoding and syndrome calculations of these codes are simple, these codes have superior properties from a practical perspective. In this paper, an effective decoding method is given for certain burst errors (multiple solid-burst errors) that are contained within the detected errors resulting from a binary cyclic “predecoding” proces, where the precoding process for burst error correction is terminated at the detection stage. Such burst errors can be expressed as random errors by superimposing a copy of itself that has been cyclically shifted by one bit. So, by performing random error decoding on a version of the received sequence that has been superimposed with a one-bit cyclically shifted copy of itself, burst errors can be accurately corrected. This decoding method completely preserves the correction capacity of the precode and is applicable to any binary cyclic code with a minimum distance of at least 5. the correctable multiple solid-burst errors depend on the minimum distance of the code. Furthermore, by applying this technique to interleaved random error-correction codes for the purpose of correcting burst errors, it is shown that it is possible to extend the length of correctable burst errors.

Abstract: Cyclic an codes are considered to be suitable for error detection and error correction in arithmetic operations. Cyclic an codes using radix 2k representation are called 2k-ary cyclic an codes. This paper is concerned with 2k-ary cyclic an codes for burst error correction. After describing the structure of these codes and arithmetic burst errors, the smallest code generator A1 that provides a 2k-ary cyclic an code with the burst error correcting ability b is presented. We also suggest burst error correcting 2k-ary cyclic an codes generated by A1.p. Furthermore, error-trapping decoding for 2k-ary cyclic an codes is shown.