TL;DR: A number of on-chip coding techniques for the protection of Random Access Memories which use multi-level as opposed to binary storage cells are investigated, including row-column codes, burst codes, hexadecimal codes, Reed-Solomon codes, concatenated codes, and some new majority-logic decodable codes.
Abstract: In this talk we investigate a number of on-chip coding techniques for the protection of Random Access Memories which use multi-level as opposed to binary storage cells. The motivation for such RAM cells is of course the storage
of several bits per cell as opposed to one bit per cell [l].
Since the typical number of levels which a multi-level RAM can handle is 16 (the cell being based on a standard DRAM
cell which has varying amounts of voltage stored on
it) there are four bits recorded into each cell [2]. The disadvantage of multi-level RAMs is that they are much
more prone to errors, and so on-chip ECC is essential for reliable operation. There are essentially three reasons for error control coding in multi-level RAMs: To
correct soft errors, to correct hard errors, and to
correct read errors. The source of these errors is,
respectively, alpha particle radiation, hardware faults, and
data level ambiguities. On-chip error correction can be
used to increase the mean life before failure for all three types of errors. Coding schemes can be both bitwise and
cellwise. Bitwise schemes include simple parity checks and SEC-DED codes, either by themselves or as product codes
[3]. Data organization should allow for burst error correction, since alpha particles can wipe out all
four bits in a single cell, and for dense memory chips,
data in surrounding cells as well. This latter effect becomes more serious as feature sizes are scaled, and
a single alpha particle hit affects many adjacent cells. Burst codes such as those in [4] can be used to correct for
these errors. Bitwise coding schemes are more efficient
in correcting read errors, since they can correct single bit
errors and allow the remaining error correction power to be
used elsewhere. Read errors essentially affect one bit
only, since the use of Grey codes for encoding the bits
into the memory cells ensures that at most one bit is flipped with each successive change in level. Cellwise schemes include Reed-Solomon codes, hexadecimal
codes, and product codes. However, simple encoding and decoding algorithms are necessary, since excessive space taken by powerful but complex encoding/decoding circuits can
be offset by having more parity cells and using simpler
codes. These coding techniques are more useful for correcting hard and soft errors which affect the entire cell. They tend to be more complex, and they are not as
efficient in correcting read errors as the bitwise codes.
In the talk we will investigate the suitability and
performance of various multi-level RAM coding schemes,
such as row-column codes, burst codes, hexadecimal codes, Reed-Solomon codes, concatenated codes, and some new majority-logic decodable codes. In particular we investigate their tolerance to soft errors, and to feature size scaling.
TL;DR: An optimal scheme is given for interleaving using an n×m array when the maximum length burst of errors is greater than m and involves transmitting the rows of the array in a specified (nonsequential) order, but introduces no additional overheads.
Abstract: An optimal scheme is given for interleaving using an n×m array when the maximum length burst of errors is greater than m. It involves transmitting the rows of the array in a specified (nonsequential) order, but introduces no additional overheads. This scheme is particularly beneficial for convolutional coding.
TL;DR: Tables summarizing some results on the size of optimal unidirectional error-correcting codes which follow from upper bounds on thesize of a code of length n correcting t or fewer uniddirectional errors are given.
Abstract: A brief introduction is given on the theory of codes correcting unidirectional errors, in the context of symmetric and asymmetric error-correcting codes. Upper bounds on the size of a code of length n correcting t or fewer unidirectional errors are then derived. Methods in which codes correcting up to t unidirectional errors are constructed by expurgating t-fold asymmetric error-correcting codes or by expurgating and puncturing t-fold symmetric error-correcting codes are also presented. Finally, tables summarizing some results on the size of optimal unidirectional error-correcting codes which follow from these bounds and constructions are given. >
TL;DR: A Reed- Solomon generator matrix which possesses a certain inherent structure in GF(2) is derived and a structure representation of the code as a union of cosets, each coset being an interleaver of several binary BCH codes, is obtained.
Abstract: In this paper we present a Reed-Solomon decoder that makes use of bit soft decision information. A Reed- Solomon generator matrix which possesses a certain inherent structure in GF(2) is derived. Using this structure representation of the code as a union of cosets, each coset being an interleaver of several binary BCH codes, is obtained. Such partition into cosets provides a clue for efficient bit level soft decision decoding. The proposed decoding algorithms are in many cases orders of magnitude more efficient than conventional techniques.
TL;DR: In the letter a structure for a Reed-Solomon decoder is introduced which can decode a Reed -Solomon code generated by any generator polynomial.
Abstract: A Reed-Solomon code can be generated by n = 2m − 1 different generator polynomials, where 2m is the size of the field. In the letter a structure for a Reed-Solomon decoder is introduced which can decode a Reed-Solomon code generated by any generator polynomial.
TL;DR: A versatile codec for the Reed-Solomon (RS) code from this family is described, such that different RS codes can be programmed to correct errors and erasure, including shortening and singly extended codes.
Abstract: The nature of the mobile radio channel requires that the error control coding schemes chosen are effective for burst errors. Simple error correction methods such as interleaved block code are effective in the burst error mobile radio environment but do not utilize the memory characteristics of the error process. Reed-Solomon (RS) codes are ideally suitable, particularly for digitized voice. A versatile codec for the (31, k) code from this family is described. The structure of this decoder is such that different RS codes can be programmed to correct errors and erasure, including shortening and singly extended codes. >
TL;DR: A theoretical approach to ternary cyclic AN codes for burst error correction is presented, and the burst error correctability and a decoding method are provided.
Abstract: The arithmetic AN codes and the cyclic AN codes are useful for detecting and correcting errors that may arise in the arithmetic operations. When an arithmetic ANcode is closed under the cyclic shift, it is called a cyclic AN code. This paper provides a theoretical Approach to ternary cyclic AN codes for burst error correction. After describing the ternary cyclic AN codes and burst errors, we provide the burst error correctability and a decoding method of the codes generated b. A=(3% )pk.
TL;DR: Some necessary conditions are presented and the relation between the burst error correcting ability of the binary cyclic AN code and that of the 2/sup k/-ary cyclic An code is described.
Abstract: Cyclic AN codes are considered to be suitable for error detection and error correction in arithmetic operations. Cyclic AN codes using radix 2/sup k/ expressions are called 2/sup k/-ary cyclic AN codes. The paper is concerned with 2/sup k/-ary cyclic AN codes for burst error correction. After describing the structure of these codes and arithmetic burst errors, we present some necessary conditions for 2/sup k/-ary cyclic AN codes to have any burst error correcting ability and describe the relation between the burst error correcting ability of the binary cyclic AN code and that of the 2/sup k/-ary cyclic AN code.
TL;DR: It is reported that two optimal type-B1 burst correcting convolutional codes of rate 4/5 were found by computer search.
Abstract: It is reported that two optimal type-B1 burst correcting convolutional codes of rate 4/5 were found by computer search. The B/sub 0/ matrices of these codes are given. In octal, the columns are written as (53,357,756,1555,1000) and (53,357,1555,1203,1000), respectively. >