List decoding

About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.

Error Exponents for Broadcast Channels With Degraded Message Sets

Abstract: We consider a broadcast channel with a degraded message set, in which a single transmitter sends a common message to two receivers and a private message to one of the receivers only. The main goal of this work is to find new lower bounds to the error exponents of the strong user, the one that should decode both messages, and of the weak user, that should decode only the common message. Unlike previous works, where suboptimal decoders were used, the exponents we derive in this work pertain to optimal decoding and depend on both rates. We take two different approaches. The first approach is based, in part, on variations of Gallager-type bounding techniques that were presented in a much earlier work on error exponents for erasure/list decoding. The resulting lower bounds are quite simple to understand and to compute. The second approach is based on a technique that is rooted in statistical physics, and it is exponentially tight from the initial step and onward. This technique is based on analyzing the statistics of certain enumerators. Numerical results show that the bounds obtained by this technique are tighter than those obtained by the first approach and previous results. The derivation, however, is more complex than the first approach and the retrieved exponents are harder to compute.

Early detection and trellis splicing: reduced-complexity iterative decoding

Abstract: The bit-error rate (BER) performance of new iterative decoding algorithms (e,g,, turbodecoding) is achieved at the expense of a computationally burdensome decoding procedure. We present a method called early detection that can be used to reduce the computational complexity of a variety of iterative decoders. Using a confidence criterion, some information symbols, state variables, and codeword symbols are detected early on during decoding. In this way, the computational complexity of further processing is reduced with a controllable increase in the BER. We present an easily implemented instance of this algorithm, called trellis splicing, that can be used with turbodecoding. For a simulated system of this type, we obtain a reduction in the computational complexity of up to a factor of four, relative to a turbodecoder that obtains the same increase in the BER by performing fewer iterations.

Distance distribution of binary codes and the error probability of decoding

Abstract: We address the problem of bounding below the probability of error under maximum-likelihood decoding of a binary code with a known distance distribution used on a binary-symmetric channel (BSC). An improved upper bound is given for the maximum attainable exponent of this probability (the reliability function of the channel). In particular, we prove that the "random coding exponent" is the true value of the channel reliability for codes rate R in some interval immediately below the critical rate of the channel. An analogous result is obtained for the Gaussian channel.

Multiple-Bases Belief-Propagation for Decoding of Short Block Codes

Abstract: A novel soft-decoding method for algebraic block codes is presented. The algorithm is designed for soft-decision decoding and is based on belief-propagation (BP) decoding using multiple bases of the dual code. Compared to other approaches for high-performance BP decoding, this method is conceptually simple and does not change at each stage of the decoding process. With its multiple BP decoders the proposed scheme achieves the performance of a standard BP algorithm with a significantly lower number of iterations per decoder realization. By this means the data delay introduced by decoding is reduced. Moreover, a significant improvement in decoding performance is achieved while keeping the data delay small. It is shown that for selected codes the proposed scheme approaches near maximum likelihood (ML) performance for very small data processing delays.

Construction of uniquely decodable codes for the two-user binary adder channel

Abstract: A construction of uniquely decodable codes for the two-user binary adder channel is presented. The rates of the codes obtained by this construction are greater than the rates guaranteed by the Coebergh van den Braak and van Tilborg construction and these codes can be used with simple encoding and decoding procedures.