Locally repairable codes, which can repair erased symbols from other symbols, have attracted a good deal of attention in recent years because its local repair property is effective on distributed storage systems. (ru, δu)u∈[s]-locally repairable codes with multiple localities, which are an extension of ordinary locally repairable codes, can repair δu-1 erased symbols simultaneously from a set consisting of at most ru symbols. An upper bound on the minimum distance of these codes and a construction method of optimal codes, attaining this bound with equality, were given by Chen, Hao, and Xia. In this paper, we discuss the parameter restrictions of the existing construction, and we propose explicit constructions of optimal codes with multiple localities with relaxed restrictions based on the encoding polynomial introduced by Tamo and Barg. The proposed construction can design a code whose minimum distance is unrealizable by the existing construction.

Rapid process scaling and the introduction of the multilevel cell (MLC) concept have lowered costs of NAND Flash memories, but also degraded reliability. For this reason, the memories are depending on strong error correcting codes (ECCs), and this has enabled the memories to be used in wide range of storage applications, including solid-state drives (SSDs). Meanwhile, too strong error correcting capability requires excessive decoding complexity and check bits. In NAND Flash memories, cell errors to neighborhood voltage levels are more probable than those to distant levels. Several ECCs reflecting this characteristics, including limited-magnitude ECCs which correct only errors with a certain limited magnitude and low-density parity check (LDPC) codes, have been proposed. However, as most of these ECCs need the multiple bits in a cell for encoding, they cannot be used with multipage programing, a high speed programming method currently employed in the memories. Also, binary ECCs with Gray codes are no longer optimal when multilevel voltage shifts (MVSs) occur. In this paper, an error correction method reflecting the error characteristic is presented. This method detects errors by a binary ECC as a conventional manner, but a nonbinary value or whole the bits in a cell, are subjected to error correction, so as to be corrected into the most probable neighborhood value. The amount of bit error rate (BER) improvement is depending on the probability of the each error magnitude. In case of 2bit/cell, if only errors of magnitude 1 and 2 can occur and the latter occupies 5% of cell errors, acceptable BER is improved by 4%. This is corresponding to extending 2.4% of endurance. This method needs about 15% longer average latency, 19% longer maximum latency, and 15% lower throughput. However, with using the conventional method until the memories' lifetime number of program/erase cycling, and the proposed method after that, BER improvement can be utilized for extending endurance without latency and throughput degradation until the switch of the methods.

The technological development of wireless environment has made real-time multimedia communications possible in wireless networks. Many studies have been done on real-time communications in wireless networks in order to overcome a higher bit error rate in wireless channels. However, none of work deals with firm real-time communications which can be applied to multimedia communications. In this paper, we propose an adaptive error correcting scheme for firm real-time multimedia communications in wireless networks in order to maximize the expected net profit. The proposed scheme adaptively selects an error correcting code under the current air state and the message state of a message stream. Throughout simulation results, we show that the suggested scheme provides more profit than single error-correcting code schemes.

This paper presents a class of binary block codes capable of correcting single synchronization errors and single reversal errors with fewer check bits than the existing codes by 3 bits. This also shows a decoding circuit and analyzes its complexity.

Coding scheme is discussed for M-Choose-T communication in which at most T active users out of M potential users simultaneously transmit their messages over a common channel. The multiple-access channel considered in this paper is assumed to be a time-discrete noiseless adder channel without feedback with T binary inputs and one real-valued output, and is used on the assumption of perfect block and bit synchronization among users. In this paper a new class of uniquely decodable codes is proposed in order to realize error-free M-Choose-T communication over the adder channel described above. These codes are uniquely decodable in the sense that not only the set of active users can be specified but also their transmitted messages can be recovered uniquely as long as T or fewer users are active simultaneously. It is shown that these codes have a simple decoding algorithm and can achieve a very high sum rate arbitrarily close to unity if exactly T users are active.

Recently, a lot of research works have been carried out regarding intelligent communication. If the final information sink is assumed as a human being, a communication channel can be used more effectively when encoders/decoders work "intelligently" or take into account of the semantics of information to be sent. We have been studying error-controlling systems based on different importance of segmental information. The system divides the information input into segments to which individual importance can be assigned. The segments are individually encoded by appropriate error-correcting codes (ECCs) which correspond to their importance among codes with different error-correcting capabilities. For the information that difference of the importance is systematically aligned, conventional UEP (unequal error protection) codes can be applied, but we treat the case that alignment of the importance of the information source is not systematically aligned. Since the system uses multiple ECCs with different (n,k,d) parameters, information regarding what length of the next codeword is required for decoding. We propose error controlling schemes using mulriple ECCs; the first scheme and the second scheme use the obvious codelength identifying information. In the second scheme, information bits are sorted so that segments with the same importance can be encoded by an ECC with the same error-correcting capability. The third scheme is a main proposal in this paper and uses Variable Capability Coding scheme (VCC) which uses some ECCs having different error-correcting capabilities and codelengths. A sequence encoded by the VCC is separable into appropriate segments without obvious codelength identifying information when the channel error probability is low. Subsequently, we evaluate these schemes by coderate when (1) error correcting capability (2) codelength identifying capability are the same. One of the feature of VCC is the capability of resuming from propagative errors because errors beyond the codelength identifying capability occur and the proper beginning of the codeword is lost in the decoder. We also evaluate this capability as (3) resynchronizing capability.