TY - GEN

T1 - On-The-Fly Stochastic Codebook Re-generation for Sources with Memory

AU - Elshafiy, Ahmed

AU - Namazi, Mahmoud

AU - Zamir, Ram

AU - Rose, Kenneth

N1 - Publisher Copyright:
©2021 IEEE

PY - 2021/4/11

Y1 - 2021/4/11

N2 - This paper proposes a generalized stochastic mechanism for codebook generation in lossy coding settings for sources with memory. Earlier work has shown that the rate-distortion bound can be asymptotically achieved for discrete memoryless sources by a “natural type selection” (NTS) algorithm. In iteration n, the distribution that is most likely to produce the types of a sequence of K codewords of finite length ` that “dmatch” a respective sequence of K source words of length `, (i.e., which satisfy the distortion constraint), is used to regenerate the codebook for iteration n + 1. The resulting sequence of codebook generating distributions converges to the optimal distribution Q∗ that achieves the rate-distortion bound for the memoryless source, asymptotically in `, K, and n. This work generalizes the NTS algorithm to account for sources with memory. The algorithm encodes m`-length source words consisting of ` vectors (or super-symbols) of length m. We show that for finite m and `, the sequence of codebook reproduction distributions Q0,m,`, Q1,m,`, . . . (each computed after observing a sequence of K d-match events) converges to the optimal achievable distribution Q∗m,` (within a set of achievable distributions determined by m and `), asymptotically in K and n. It is further shown that Q∗m,` converges to the optimal reproduction distribution Q∗ that achieves the rate-distortion bound for sources with memory, asymptotically in m and `.

AB - This paper proposes a generalized stochastic mechanism for codebook generation in lossy coding settings for sources with memory. Earlier work has shown that the rate-distortion bound can be asymptotically achieved for discrete memoryless sources by a “natural type selection” (NTS) algorithm. In iteration n, the distribution that is most likely to produce the types of a sequence of K codewords of finite length ` that “dmatch” a respective sequence of K source words of length `, (i.e., which satisfy the distortion constraint), is used to regenerate the codebook for iteration n + 1. The resulting sequence of codebook generating distributions converges to the optimal distribution Q∗ that achieves the rate-distortion bound for the memoryless source, asymptotically in `, K, and n. This work generalizes the NTS algorithm to account for sources with memory. The algorithm encodes m`-length source words consisting of ` vectors (or super-symbols) of length m. We show that for finite m and `, the sequence of codebook reproduction distributions Q0,m,`, Q1,m,`, . . . (each computed after observing a sequence of K d-match events) converges to the optimal achievable distribution Q∗m,` (within a set of achievable distributions determined by m and `), asymptotically in K and n. It is further shown that Q∗m,` converges to the optimal reproduction distribution Q∗ that achieves the rate-distortion bound for sources with memory, asymptotically in m and `.

KW - Natural Type Selection

KW - Random Codebook

KW - Rate-Distortion function

KW - String Matching

UR - http://www.scopus.com/inward/record.url?scp=85113323018&partnerID=8YFLogxK

U2 - 10.1109/ITW46852.2021.9457666

DO - 10.1109/ITW46852.2021.9457666

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AN - SCOPUS:85113323018

T3 - 2020 IEEE Information Theory Workshop, ITW 2020

BT - 2020 IEEE Information Theory Workshop, ITW 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2020 IEEE Information Theory Workshop, ITW 2020

Y2 - 11 April 2021 through 15 April 2021

ER -