Hirosuke Yamamoto

Viterbi decoding algorithm for convolutional codes with repeat request

Using the Viterbi decoding algorithm with repeat request for convolutional codes is proposed, and the resulting performance is analyzed by random coding and generating function arguments and by simulation. It is shown that the reliability function of the proposed decoding algorithm is asymptotically twice that of the Viterbi decoding algorithm without repeat request, and that in certain practical situations the proposed algorithm can save about 50 percent in constraint length over the ordinary Viterbi algorithm for a given performance.

Rate-distortion theory for the Shannon cipher system

Considers Shannons cipher system with a memoryless broadcast channel. The source output sequence {S/sub l/}/sub t//sup /spl infin//=1 is independent drawings of a random variable S taking values in S, and the key W/sub k/ is a random variable which is independent of S. For simplicity, we assume that the main channel (X/spl rarr/Y) is less noisy than the wiretap channel (X/spl rarr/Z). The security of the system can be measured by the uncertainty or the attainable minimum distortion of the wiretapper who gets only Z/sup N/. For each case, we define the admissible region. >

Asymptotic performance of a modified Schalkwijk-Barron scheme for channels with noiseless feedback (Corresp.)

A modified Schalkwijk-Barron transmission scheme is presented for channels with noiseless feedback. The modified scheme employs blockwise decision and a fixed length transmission in place of Viterbis sequential decision feedback. The reliability functions of the modified scheme are derived for the additive white Gaussian noise (AWGN) channel and discrete memoryless channels (DMCs). For the AWGN channel the result obtained is asymptotically the same as in the case of the Schalkwijk-Barron scheme. On the other hand, the new result obtained for DMCs shows that the modified scheme also attains high reliability functions for DMCs.

Polar Coding Without Alphabet Extension for Asymmetric Models

This paper considers polar coding for asymmetric settings, that is, channel coding for asymmetric channels and lossy source coding for nonuniform sources and/or asymmetric distortion measures. The difficulty for asymmetric settings comes from the fact that the optimal symbol distributions of codewords are not always uniform. It is known that such nonuniform distributions can be realized by Gallagers scheme which maps multiple auxiliary symbols distributed uniformly to an actual symbol. However, the complexity of Gallagers scheme increases considerably for the case that the optimal distribution cannot be approximated by simple rational numbers. To overcome this problem for the asymmetric settings, a new polar coding scheme is proposed, which can attain the channel capacity without any alphabet extension by invoking results on polar coding for lossless compression. It is also shown that the proposed scheme achieves a better tradeoff between complexity and decoding error probability in many cases.

A coding theorem for lossy data compression by LDPC codes

Recently, low density parity check (LDPC) codes have been studied actively because of the high performance of error correction. Many previous researches showed that LDPC codes can attain near the Shannon limit by iterative decoding with belief propagation. On the other hand, it is well known that channel coding can be considered as the dual problem of lossy source coding in the rate-distortion theory, and a good error correcting code can be used for efficient lossy data compression. In this paper, we show that LDPC codes can also attain the rate-distortion function asymptotically for the same source.

A source coding problem for sources with additional outputs to keep secret from the receiver or wiretappers (Corresp.)

A new source coding problem is considered for a one-way communication system with correlated source outputs \{XY\} . One of the source outputs, i.e., \{X\} , must be transmitted to the receiver within a prescribed distortion tolerance as in ordinary source coding. On the other hand, the other source output, i.e., \{Y\} , has to be kept as secret as possible from the receiver or wiretappers. For this case the equivocation-distortion function \Gamma \ast(d) and the rate-distortion-equivocation function R\ast (d,e) are defined and evaluated. The former is the maximum achievable equivocation of \{Y\} under the distortion tolerance d for \{X\} , and the latter is the minimum rate necessary to attain both the equivocation tolerance e for \{Y\} and the distortion tolerance d for \{X\} . Some examples are included.

Wyner - Ziv theory for a general function of the correlated sources (Corresp.)

A source coding problem is considered for the Wyner-Ziv type system where the decoder is required to estimate the value of some function of the encoder input and the side information. The rate-distortion function is established for this system, and for some binary cases parametric expressions are obtained to enable numerical calculations.

Source coding theory for cascade and branching communication systems

A source coding problem is considered for cascade and branching communication systems. The achievable rate region is established for the cascade systems and bounds are obtained for the branching systems. Some examples are also included.

Private information retrieval for coded storage

Private information retrieval scheme for coded data storage is considered in this paper. We focus on the case where the size of each data record is large and hence only the download cost (but not the upload cost for transmitting retrieval queries) is of interest. We prove that the tradeoff between storage cost and retrieval/download cost depends on the number of data records in the system. We propose a class of linear storage codes and retrieval schemes, and derive conditions under which our schemes are error-free and private. Tradeoffs between the storage cost and retrieval costs are also obtained.

On secret sharing communication systems with two or three channels

The source coding problem is considered for secret sharing communication systems (SSCSs) with two or three channels. The SSCS, where the information X is shared and communicated through two or more channels, is an extension of Sbannons cipher communication system and the secret sharing system. The security level is measured with equivocation; that is, (1/N)H(X|W_{i}), (1/N)H(X|W_{i}W_{i}) , etc., where W_{i} and W_{j} are the wire-tapped codewords. The achievable rate region for the given security level is established for the SSCSs with two or three channels.